Scipedia: Documents published in 2020

Point-to-point connectivity, an abstract concept or a key issue for risk assessment studies?

María Jesús Samper — Wed, 18 Mar 2020 13:47:11 +0100

Connectivity of high/low-permeability areas has been recognized to significantly impact groundwater flow and solute transport. The task of defining a rigorous quantitative measure of connectivity for continuous variables has failed so far, and thus there exist a suite of connectivity indicators which are dependent on the specific hydrodynamic processes and the interpretation method. Amongst the many existing indicators, we concentrate on those characterizing connectivity between the points involved in a hydraulic or tracer test. The flow connectivity indicator used here is based on the time elapsed for hydraulic response in a pumping test (e.g., the storage coefficient estimated by the Cooper–Jacob method, Sest). Regarding transport, we select the estimated porosity from the breakthrough curve (ϕest). According to Knudby and Carrera [Knudby C, Carrera J. On the relationship between indicators of geostatistical, flow and transport connectivity. Adv Water Resour 2005;28(4):405–21] these two indicators measure connectivity differently, and are poorly correlated. Here, we use perturbation theory to analytically investigate the intrinsic relationship between Sest and ϕest. We find that ϕest can be expressed as a weighted line integral along the particle trajectory involving two parameters: the transmissivity point values, T, and the estimated values of Sest along the particle path. The weighting function is linear with the distance from the pumping well, thus the influence of the weighting function is maximum at the injection area, whereas the hydraulic information close to the pumping well becomes redundant (null weight). The relative importance of these two factors is explored using numerical simulations in a given synthetic aquifer and tested against intermediate-scale laboratory tracer experiments. We conclude that the degree of connectivity between two points of an aquifer (point-to-point connectivity) is a key issue for risk assessment studies aimed at predicting the travel time of a potential contaminant.

Influence of heterogeneity on the interpretation of pumping test data in leaky aquifers

María Jesús Samper — Wed, 18 Mar 2020 13:35:50 +0100

Pumping tests are routinely interpreted from the analysis of drawdown data and their derivatives. These interpretations result in a small number of apparent parameter values which lump the underlying heterogeneous structure of the aquifer. Key questions in such interpretations are (1) what is the physical meaning of those lumped parameters and (2) whether it is possible to infer some information about the spatial variability of the hydraulic parameters. The system analyzed in this paper consists of an aquifer separated from a second recharging aquifer by means of an aquitard. The natural log transforms of the transmissivity, ln T, and the vertical conductance of the aquitard, ln C, are modeled as two independent second‐order stationary spatial random functions (SRFs). The Monte Carlo approach is used to simulate the time‐dependent drawdown at a suite of observation points for different values of the statistical parameters defining the SRFs. Drawdown data at each observation point are independently used to estimate hydraulic parameters using three existing methods: (1) the inflection‐point method, (2) curve‐fitting, and (3) the double inflection‐point method. The resulting estimated parameters are shown to be space dependent and vary with the interpretation method since each method gives different emphasis to different parts of the time‐drawdown data. Moreover, the heterogeneity in the pumped aquifer or the aquitard influences the estimates in distinct manners. Finally, we show that, by combining the parameter estimates obtained from the different analysis procedures, information about the heterogeneity of the leaky aquifer system may be inferred

Relative importance of geostatistical and transport models in describing heavily tailed breakthrough curves at the Lauswiesen site

María Jesús Samper — Wed, 18 Mar 2020 13:14:07 +0100

We analyze the relative importance of the selection of (1) the geostatistical model depicting the structural heterogeneity of an aquifer, and (2) the basic processes to be included in the conceptual model, to describe the main aspects of solute transport at an experimental site. We focus on the results of a forced-gradient tracer test performed at the “Lauswiesen” experimental site, near Tübingen, Germany. In the experiment, NaBr is injected into a well located 52 m from a pumping well. Multilevel breakthrough curves (BTCs) are measured in the latter. We conceptualize the aquifer as a three-dimensional, doubly stochastic composite medium, where distributions of geomaterials and attributes, e.g., hydraulic conductivity (K) and porosity (ϕ), can be uncertain. Several alternative transport processes are considered: advection, advection–dispersion and/or mass-transfer between mobile and immobile regions. Flow and transport are tackled within a stochastic Monte Carlo framework to describe key features of the experimental BTCs, such as temporal moments, peak time, and pronounced tailing. We find that, regardless the complexity of the conceptual transport model adopted, an adequate description of heterogeneity is crucial for generating alternative equally likely realizations of the system that are consistent with (a) the statistical description of the heterogeneous system, as inferred from the data, and (b) salient features of the depth-averaged breakthrough curve, including preferential paths, slow release of mass particles, and anomalous spreading. While the available geostatistical characterization of heterogeneity can explain most of the integrated behavior of transport (depth-averaged breakthrough curve), not all multilevel BTCs are described with equal success. This suggests that transport models simply based on integrated measurements may not ensure an accurate representation of many of the important features required in three-dimensional transport models.

Reaction rates and effective parameters in stratified aquifers

María Jesús Samper — Wed, 18 Mar 2020 12:56:05 +0100

Chemical species are advected by water and undergo mixing processes due to effects of local diffusion and/or dispersion. In turn, mixing causes reactions to take place so that the system can locally equilibrate. In general, a multicomponent reactive transport problem is described through a system of coupled non-linear partial differential equations. Under instantaneous chemical equilibrium, a complex geochemical problem can be highly simplified by fully defining the system in terms of conservative quantities, termed master species or components, and the space–time distribution of reaction rates. We investigate the parameters controlling reaction rates in a heterogeneous aquifer at short distances from the source. Hydraulic conductivity at this scale is modeled as a random process with highly anisotropic correlation structure. In the limit for very large horizontal integral scales, the medium can be considered as stratified. Upon modeling transport by means of an ADE (Advection Dispersion Equation), we derive closed-form analytical solutions for statistical moments of reaction rates for the particular case of negligible transverse dispersion. This allows obtaining an expression for an effective hydraulic conductivity, , as a representative parameter describing the mean behavior of the reactive system. The resulting is significantly smaller than the effective conductivity representative of the flow problem. Finally, we analyze numerically the effect of accounting for transverse local dispersion. We show that transverse dispersion causes no variation in the distribution of (ensemble) moments of local reaction rates at very short travel times, while it becomes the dominant effect for intermediate to large travel times.

Conditional probability density functions of concentrations for mixing-controlled reactive transport in heterogeneous aquifers

María Jesús Samper — Wed, 18 Mar 2020 12:44:49 +0100

This paper presents an approach conducive to an evaluation of the probability density function (pdf) of spatio-temporal distributions of concentrations of reactive solutes (and associated reaction rates) evolving in a randomly heterogeneous aquifer. Most existing approaches to solute transport in heterogeneous media focus on providing expressions for space–time moments of concentrations. In general, only low order moments (unconditional or conditional mean and covariance) are computed. In some cases, this allows for obtaining a confidence interval associated with predictions of local concentrations. Common applications, such as risk assessment and vulnerability practices, require the assessment of extreme (low or high) concentration values. We start from the well-known approach of deconstructing the reactive transport problem into the analysis of a conservative transport process followed by speciation to (a) provide a partial differential equation (PDE) for the (conditional) pdf of conservative aqueous species, and (b) derive expressions for the pdf of reactive species and the associated reaction rate. When transport at the local scale is described by an Advection Dispersion Equation (ADE), the equation satisfied by the pdf of conservative species is non-local in space and time. It is similar to an ADE and includes an additional source term. The latter involves the contribution of dilution effects that counteract dispersive fluxes. In general, the PDE we provide must be solved numerically, in a Monte Carlo framework. In some cases, an approximation can be obtained through suitable localization of the governing equation. We illustrate the methodology to depict key features of transport in randomly stratified media in the absence of transverse dispersion effects. In this case, all the pdfs can be explicitly obtained, and their evolution with space and time is discussed.

A New Method for the Interpretation of Pumping Tests in Leaky Aquifers

María Jesús Samper — Wed, 18 Mar 2020 12:07:25 +0100

A novel methodology for the interpretation of pumping tests in leaky aquifer systems, referred to as the double inflection point (DIP) method, is presented. The method is based on the analysis of the first and second derivatives of the drawdown with respect to log time for the estimation of the flow parameters. Like commonly used analysis procedures, such as the type‐curve approach developed by Walton (1962) and the inflection point method developed by Hantush (1956), the mathematical development of the DIP method is based on the assumption of homogeneity of the leaky aquifer layers. However, contrary to the two methods developed by Hantush and Walton, the new method does not need any fitting process. In homogeneous media, the two classic methods and the one proposed here provide exact results for transmissivity, storativity, and leakage factor when aquifer storage is neglected and the recharging aquifer is unperturbed. The real advantage of the DIP method comes when applying all methods independently to a test in a heterogeneous aquifer, where each method yields parameter values that are weighted differently, and thus each method provides different information about the heterogeneity distribution. Therefore, the methods are complementary and not competitive. In particular, the combination of the DIP method and Hantush method is shown to lead to the identification of contrasts between the local transmissivity in the vicinity of the well and the equivalent transmissivity of the perturbed aquifer volume.

Gestión de los recursos hídricos: los modelos hidrogeológicos como herramienta auxiliar

María Jesús Samper — Wed, 18 Mar 2020 11:34:51 +0100

Water is scarce, and thus must be managed adequately in order to satisfy the global demand within a water resources integral planning. Management can act either on offer or demand. Proper management implies an accountability system capable both of reproducing the existing situation and quantifying the effect of management scenarios upon resources quantity and quality. The need for quantification makes indispensable numerical models in general, and hydrogeological models in particular. We present some of the elements that are included in a hydrogeological model, including the need for managing huge amounts of data and some technical aspects on discretization and calibration of numerical models. Hydrogeological models must be included into management models that account for conjunctive use of all available resources.

On the meaning of the transmissivity values obtained from recovery tests

María Jesús Samper — Wed, 18 Mar 2020 11:27:38 +0100

Recovery tests are based on estimating transmissivity, T, from the heads that rebound after pumping has stopped. Recovery tests can be performed in wells where conventional constant-rate pumping tests would not be possible. Test interpretation is based on the simple Theis recovery method, related to late time drawdown in an infinite homogeneous aquifer. Yet, field data often cannot be explained by the homogeneous theory. Because T is heterogeneous over an evolving range of scales, it is important to evaluate the support scale of hydraulic tests. Numerical simulations are performed to show that heterogeneity in T can explain these field observations. It is also shown that the local T value around the well can be inferred from early time-recovery data, assuming ideal conditions, whereas late time data yield a large-scale (regional) representative value. Even when recovery is observed for a short time, indirect information about the regional value can also be obtained. A method for the interpretation of recovery tests is proposed based on the Theis recovery method that takes into account the heterogeneity of aquifers. Finally, some guidelines are provided for best test performance depending on the scale of the problem.

A mixing ratios‐based formulation for multicomponent reactive transport

María Jesús Samper — Wed, 18 Mar 2020 11:14:30 +0100

Chemical reactions are driven by disequilibrium, which is often caused by mixing. Therefore quantification of the mixing rate is essential for evaluating the fate of solutes in natural systems, such as rivers, lakes, and aquifers. We propose a novel mixing ratios‐based formulation to evaluate solute concentrations and reaction rates when equilibrium aqueous reactions and precipitation/dissolution of minerals are driven by mixing of different end‐members. Each end‐member corresponds to a water from a given source with a specific chemical signature. The approach decouples the solute transport and chemical speciation problems, so that mixing ratios can be first obtained from the solution of conservative transport and then be used in general speciation codes to obtain the concentration of reacting species. One key finding is a general expression for reaction rates which demonstrates that the amount of reactants evolving into products depends on the rate at which solutions mix. Our formulation constitutes a general framework according to which one can design and interpret experimental analyses devoted to study mixing‐driven reactive processes and obtain transverse dispersion coefficients. The formulation is also proposed as a useful tool to derive analytical solutions of reactive transport problems and may result computationally advantageous when compared to previous approaches to reactive transport modeling. We apply the developed formulation to provide an analytical solution of the reactive transport process resulting from mixing different CaCO3‐saturated waters in a two‐dimensional setup

Quasi-horizontal circulation cells in 3D seawater intrusion

María Jesús Samper — Wed, 18 Mar 2020 10:59:39 +0100

The seawater intrusion process is characterized by the difference in freshwater and seawater density that causes freshwater to float on seawater. Many confined aquifers have a large horizontal extension with respect to thickness. In these cases, while buoyancy acts in the vertical direction, flow is confined between the upper and bottom boundaries and the effect of gravity is controlled by variations of aquifer elevation. Therefore, the effective gravity is controlled by the slope and the shape of the aquifer boundaries. Variability in the topography of the aquifer boundaries is one case where 3D analysis is necessary. In this work, density-dependent flow processes caused by 3D aquifer geometry are studied numerically and specifically, considering a lateral slope of the aquifer boundaries. Sub-horizontal circulation cells are formed in the saltwater entering the aquifer. The penetration of the saltwater can be quantified by a dimensionless buoyancy number that measures the lateral slope of the aquifer relative to freshwater flux. The penetration of the seawater intrusion wedge is controlled more by this slope than by the aquifer thickness and dispersivity. Thus, the slope must be taken into account in order to accurately evaluate seawater intrusion.

Transport‐controlled reaction rates under local non‐equilibrium conditions

María Jesús Samper — Wed, 18 Mar 2020 10:17:38 +0100

Chemical reactions are driven by non‐equilibrium and can be fully described by the spatio‐temporal distribution of the reaction rate. We present an analytical approach for the computation of reaction rates under local non‐equilibrium conditions for a precipitation/dissolution problem. We derive an original non‐linear partial differential equation for the reaction rate r and present a series expansion of r for large Damköhler numbers, i.e., fast local scale reactions. The impact of local scale non‐equilibrium conditions on the transport‐controlled reaction rate is studied for reactive transport in a column.

Anisotropic dispersive Henry problem

María Jesús Samper — Wed, 18 Mar 2020 10:09:32 +0100

The Henry problem has played a key role in our understanding of seawater intrusion into coastal aquifers and in benchmarking density dependent flow codes. This paper seeks to modify Henry’s problem to ensure sensitivity to density variations and vertical salinity profiles that resemble field observations. In the proposed problem, the “dispersive Henry problem”, mixing is represented by means of the traditional Scheidegger dispersion tensor (dispersivity times water flux). Anisotropy in the hydraulic conductivity is acknowledged and Henry’s seaside boundary condition of prescribed salt concentration is replaced by a flux dependent boundary condition, which represents more realistically salt transport across the seaside boundary. This problem turns out to be very sensitive to density variations and its solution gets closer to reality. However, an improvement in the traditional Henry problem (gain in sensitivity and realism) can be also achieved if the value of the Peclet number is significantly reduced.

Although the dispersive problem lacks an analytical solution, it can shed light on flow in coastal aquifers. It provides significant information about the factors controlling seawater penetration, width of the mixing zone and influx of seawater. The width of the mixing zone depends basically on dispersion with longitudinal and transverse dispersion controlling different parts of the mixing zone but displaying similar overall effects. Toe penetration is mainly controlled by the horizontal permeability and by the geometric mean of the dispersivities. Finally, transverse dispersivity and the geometric mean of the hydraulic conductivity are the leading parameters controlling the amount of saltwater that enters the aquifer

Ergodicity of pumping tests

María Jesús Samper — Wed, 18 Mar 2020 09:55:01 +0100

Standard interpretations of pumping tests in heterogeneous formations rely on effective representations of porous media, which replace spatially varying hydraulic properties with their constant counterparts averaged over the support volume of a test. Rigorous approaches for deriving representative (effective, apparent, upscaled, etc.) parameters employ either ensemble or spatial averaging. We derive a set of conditions under which these two paradigms yield identical results. We refer to them as conditions for the ergodicity of pumping tests. This allows one to use stochastic approaches to estimate the statistics of the spatial variability of hydraulic parameters on scales smaller than the support volume of a pumping test.

Ensemble based optimization for electric demand forecast: Genetic programming and heuristic algorithms

Sergio Rivera — Wed, 18 Mar 2020 01:20:09 +0100

Power generation using renewable energy such as wind and solar energy depend on weather behavior. An accurate weather forecast improves the operation management of a Smart Grid. However, the environmental conditions vary with both time and space and, depending on the location have different classifications. The environmental conditions vary with time and depending on the country, also the changes between standard, local and summer time can result in days of 23 h, to obtain days of 24 h; the two adjacent hours are used to calculate the missing hour. In this paper is addressed a nonlinear symbolic regression (RS by its acronym in Spanish) model is used to make annual demand forecasts. This algorithm is assessment with real measurements creating models that conform to the load forecasting of 28 weather stations. The learning variables are loads of demand and temperatures; that are grouped by hours for a two-year time interval. The RS-DEEPSO algorithm is proposed to improve the forecast. This is used due to its evolutionary, self-adaptive qualities and the possibility of exploring new scenarios in search of optimum. The forecast obtained using the new hybrid RS-DEEPSO has an average error per day less than 3.9% and per hour is less than 5.62% during a period of 1 year.

Effective dispersion in a chemically heterogeneous medium under temporally fluctuating flow conditions

María Jesús Samper — Tue, 17 Mar 2020 17:50:39 +0100

We investigate effective solute transport in a chemically heterogeneous medium subject to temporal fluctuations of the flow conditions. Focusing on spatial variations in the equilibrium adsorption properties, the corresponding fluctuating retardation factor is modeled as a stationary random space function. The temporal variability of the flow is represented by a stationary temporal random process. Solute spreading is quantified by effective dispersion coefficients, which are derived from the ensemble average of the second centered moments of the normalized solute distribution in a single disorder realization. Using first-order expansions in the variances of the respective random fields, we derive explicit compact expressions for the time behavior of the disorder induced contributions to the effective dispersion coefficients. Focusing on the contributions due to chemical heterogeneity and temporal fluctuations, we find enhanced transverse spreading characterized by a transverse effective dispersion coefficient that, in contrast to transport in steady flow fields, evolves to a disorder-induced macroscopic value (i.e., independent of local dispersion). At the same time, the asymptotic longitudinal dispersion coefficient can decrease. Under certain conditions the contribution to the longitudinal effective dispersion coefficient shows superdiffusive behavior, similar to that observed for transport in s stratified porous medium, before it decreases to its asymptotic value. The presented compact and easy to use expressions for the longitudinal and transverse effective dispersion coefficients can be used for the quantification of effective spreading and mixing in the context of the groundwater remediation based on hydraulic manipulation and for the effective modeling of reactive transport in heterogeneous media in general.

Variable density flow in porous media

María Jesús Samper — Tue, 17 Mar 2020 16:56:55 +0100

We review the state of the art in modeling of variable-density flow and transport in porous media, including conceptual models for convection systems, governing balance equations, phenomenological laws, constitutive relations for fluid density and viscosity, and numerical methods for solving the resulting nonlinear multifield problems. The discussion of numerical methods addresses strategies for solving the coupled spatio-temporal convection process, consistent velocity approximation, and error-based mesh adaptation techniques. As numerical models for those nonlinear systems must be carefully verified in appropriate tests, we discuss weaknesses and inconsistencies of current model-verification methods as well as benchmark solutions. We give examples of field-related applications to illustrate specific challenges of further research, where heterogeneities and large scales are important.

Representative hydraulic conductivities in saturated groundwater flow

María Jesús Samper — Tue, 17 Mar 2020 16:41:08 +0100

Heterogeneity is the single most salient feature of hydrogeology. An enormous amount of work has been devoted during the last 30 years to addressing this issue. Our objective is to synthesize and to offer a critical appraisal of results related to the problem of finding representative hydraulic conductivities. By representative hydraulic conductivity we mean a parameter controlling the average behavior of groundwater flow within an aquifer at a given scale. Three related concepts are defined: effective hydraulic conductivity, which relates the ensemble averages of flux and head gradient; equivalent conductivity, which relates the spatial averages of flux and head gradient within a given volume of an aquifer; and interpreted conductivity, which is the one derived from interpretation of field data. Most theoretical results are related to effective conductivity, and their application to real world scenarios relies on ergodic assumptions. Fortunately, a number of results are available suggesting that conventional hydraulic test interpretations yield (interpreted) hydraulic conductivity values that can be closely linked to equivalent and/or effective hydraulic conductivities. Complex spatial distributions of geologic hydrofacies and flow conditions have a strong impact upon the existence and the actual values of representative parameters. Therefore it is not surprising that a large body of literature provides particular solutions for simplified boundary conditions and geological settings, which are, nevertheless, useful for many practical applications. Still, frequent observations of scale effects imply that efforts should be directed at characterizing well‐connected stochastic random fields and at evaluating the corresponding representative hydraulic conductivities

Travel time and trajectory moments of conservative solutes in two-dimensional convergent flows

María Jesús Samper — Tue, 17 Mar 2020 16:29:02 +0100

We address advective transport of a solute traveling toward a single pumping well in a two-dimensional randomly heterogeneous aquifer. The two random variables of interest are the trajectory followed by an individual particle from the injection point to the well location and the particle travel time under steady-state conditions. Our main objective is to derive the predictors of trajectory and travel time and the associated uncertainty, in terms of their first two statistical moments (mean and variance). We consider a solute that undergoes mass transfer between a mobile and an immobile zone. Based on Lawrence et al. [Lawrence, A.E., Sánchez-Vila, X., Rubin, Y., 2002. Conditional moments of the breakthrough curves of kinetically sorbing solute in heterogeneous porous media using multirate mass transfer models for sorption and desorption. Water Resour. Res. 38 (11), 1248, doi:10.1029/2001WR001006.], travel time moments can be written in terms of those of a conservative solute times a deterministic quantity. Moreover, the moments of solute particles trajectory do not depend on mass transfer processes. The resulting mean and variance of travel time and trajectory for a conservative species can be written as functions of the first, second moments and cross-moments of trajectory and velocity components. The equations are developed from a consistent second order expansion in σY (standard deviation of the natural logarithm of hydraulic conductivity). Our solution can be completely integrated with the moment equations of groundwater flow of Guadagnini and Neuman [Guadagnini, A., Neuman, S.P., 1999a. Nonlocal and localized analyses of conditional mean steady state flow in bounded, randomly non uniform domains 1. Theory and computational approach. Water Resour. Res. 35(10), 2999–3018.,Guadagnini, A., Neuman, S.P., 1999b. Nonlocal and localized analyses of conditional mean steady state flow in bounded, randomly non uniform domains 2. Computational examples. Water Resour. Res. 35(10), 3019–3039.], it is free of distributional assumptions regarding the log conductivity field, and formally includes conditioning. We present analytical expressions for the unconditional case by making use of the results of Riva et al. [Riva, M., Guadagnini, A., Neuman, S.P., Franzetti, S., 2001. Radial flow in a bounded randomly heterogeneous aquifer. Transport in Porous Media 45, 139–193.]. The quality of the solution is supported by numerical Monte Carlo simulations. Potential uses of this work include the determination of aquifer reclamation time by means of a single pumping well, and the demarcation of the region potentially affected by the presence of a contaminant in the proximity of a well, whenever the aquifer is very thin and Dupuit–Forchheimer assumption holds.

A procedure for the solution of multicomponent reactive transport problems

María Jesús Samper — Tue, 17 Mar 2020 16:04:51 +0100

Modeling transport of reactive solutes is a challenging problem, necessary for understanding the fate of pollutants and geochemical processes occurring in aquifers, rivers, estuaries, and oceans. Geochemical processes involving multiple reactive species are generally analyzed using advanced numerical codes. The resulting complexity has inhibited the development of analytical solutions for multicomponent heterogeneous reactions such as precipitation/dissolution. We present a procedure to solve groundwater reactive transport in the case of homogeneous and classical heterogeneous equilibrium reactions induced by mixing different waters. The methodology consists of four steps: (1) defining conservative components to decouple the solution of chemical equilibrium equations from species mass balances, (2) solving the transport equations for the conservative components, (3) performing speciation calculations to obtain concentrations of aqueous species, and (4) substituting the latter into the transport equations to evaluate reaction rates. We then obtain the space‐time distribution of concentrations and reaction rates. The key result is that when the equilibrium constant does not vary in space or time, the reaction rate is proportional to the rate of mixing, ∇TuD ∇u, where u is the vector of conservative components concentrations and D is the dispersion tensor. The methodology can be used to test numerical codes by setting benchmark problems but also to derive closed‐form analytical solutions whenever steps 2 and 3 are simple, as illustrated by the application to a binary system. This application clearly elucidates that in a three‐dimensional problem both chemical and transport parameters are equally important in controlling the process.

Travel time and trajectory moments of conservative solutes in three dimensional heterogeneous porous media under mean uniform flow

María Jesús Samper — Tue, 17 Mar 2020 15:45:35 +0100

We present expressions satisfied by the first statistical moments (mean and variance–covariance) of travel time and trajectory of conservative solute particles advected in a three-dimensional heterogeneous aquifer under uniform in the mean flow conditions. Closure of the model is obtained by means of a consistent second-order expansion in σY (standard deviation of the log hydraulic conductivity) of (statistical) moments of quantities of interest. As such, the results obtained are nominally limited to mildly non-uniform fields, with σY < 1. Resulting mean and variance of particles travel time and trajectory are functions of first and second moments and cross-moments of trajectory and velocity components. Our solution is applicable to infinite domains and is free of distributional assumptions. As an important application of the methodology we obtain closed-form expressions for the unconditional mean and variance of travel time and particle trajectory for isotropic log-conductivity domain characterized by an exponential variogram. This allows us to recover the non linear behavior of mean travel time versus distance, in agreement with numerical results published in the literature, as well as a non-linear effect in the mean trajectory. The analysis of trajectory variance allows recovering some known results regarding transverse macro-dispersion, evidencing some limitations typical of perturbation theory.

A methodolgy to compute mixing ratios with uncertain end-members

María Jesús Samper — Tue, 17 Mar 2020 15:31:59 +0100

Mixing calculations involve computing the ratios in which two or more end‐members are mixed in a sample. Mixing calculations are useful for a number of tasks in hydrology, such as hydrograph separation, water or solute mass balances, and identification of groundwater recharge sources. Most methods available for computing mixing ratios are based on assuming that end‐member concentrations are perfectly known, which is rarely the case. Often, end‐members cannot be sampled, and their concentrations vary in time and space. Still, much information about them is contained in the mixtures. To take advantage of this information, we present here a maximum likelihood method to estimate mixing ratios, while acknowledging uncertainty in end‐member concentrations. Maximizing the likelihood of concentration measurements with respect to both mixing ratios and end‐member concentrations leads to a general constrained optimization problem. An algorithm for solving this problem is presented and applied to two synthetic examples of water mixing problems. Results allow us to conclude that the method outperforms traditional approaches, such as least squares or linear mixing, in the computation of mixing ratios. The method also yields improved estimates of end‐member concentrations, thus enlarging the potential of mixing calculations. The method requires defining the reliability of measurements, but results are quite robust with respect to the assumed standard deviations. A nice feature of the method is that it allows for improving the quality of computations by increasing the number of samples and/or analyzed species.

Introductory review of specific factors influencing urban groundwater, an emerging branch of hydrogeology, with reference to Barcelona, Spain

María Jesús Samper — Tue, 17 Mar 2020 15:17:34 +0100

A number of specific factors must be considered when dealing with groundwater in urban areas. Urbanization significantly affects the natural water cycle, both in terms of quantity and quality. In particular, the main contributors to recharge and discharge clearly differ from those in natural systems. Moreover, water can affect underground structures and infrastructure characteristics of cities such as basements, public transport services (trains, underground railways, etc.), and utility conduits. As a result, urban groundwater is emerging as a distinct branch of hydrogeology. The objective of this paper is to review some of the topics that are specific to urban groundwater. These include (1) fluctuations in groundwater levels caused by changes in land and water uses; (2) pollution problems caused by point or non-point sources in urban areas; (3) characterization and quantification of the components contributing to groundwater recharge and discharge; (4) specific characteristics of groundwater flow and solute transport models in urban areas; and (5) integration of data for sustainable urban water management. Some of these issues are illustrated for the particular case of Barcelona, where a comprehensive hydrogeological study has been carried out during the last few years by both the public and the private sectors.

On the striking similarity between the moments of breakthrough curves for a heterogeneous medium and a homogeneous medium with a matrix diffusion term

María Jesús Samper — Tue, 17 Mar 2020 14:57:25 +0100

A usual method to obtain aquifer parameters is to analyze the moments of the breakthrough curves (BTCs) in tracer tests. The parameters to be estimated in this analysis would depend on the conceptual model adopted. Intuitively, if different processes were considered, the shape of the BTCs should be quite different, and one would tend to think that the time and space evolution of the temporal moments should also be quite different. Contrarily, in this paper, we show that two very different conceptual models of solute transport lead to virtually identical moments of the BTC. The two models selected for this study are the classical advection–dispersion equation with a Fickian macrodispersive term and a homogeneous medium advection model with mass-transfer between mobile and immobile matrix phases, for three different models of matrix shape. In both models, the first three moments are linear with travel distance, while the fourth moment is a second order polynomial. This agreement allows us to choose parameters yielding the same moments in the two models. As we consider two fitting parameters, we select them to match the second and third moment. Match in the first moment is obtained from physical arguments. It turns out that the resulting leading term of the fourth moment is identical for both models. As a direct consequence of this work, it follows that for large travel distances it would not be possible to discriminate between conceptual models using data from a single BTC.

A perturbation solution to the transient Henry problem for seawater intrusion

María Jesús Samper — Tue, 17 Mar 2020 14:48:55 +0100

Henry's formulation of seawater intrusion in coastal aquifers consists of a fully coupled system of flow and transport equations with variable density. While the Henry problem often serves as a benchmark for numerical codes, the accuracy of the existing analytical solutions is hard to gauge. We use a perturbation expansion in a small parameter, the ratio between the densities of seawater and freshwater, to derive an analytical solution for the transient Henry problem, which describes the saline intrusion caused by a sudden change in fresh groundwater discharge. This approach is effective for other variable density flow scenarios, since it allows one to decouple the flow and transport equations.

Sobre la no identificabilidad de los momentos estadísticos del tiempo de llegada de un soluto en un medio heterogéneo

María Jesús Samper — Tue, 17 Mar 2020 14:40:19 +0100

El análisis de las curvas de llegada procedentes de ensayos de trazadores es una de las metodologías habituales para la obtención de parámetros hidráulicos. En cualquier interpretación de un ensayo, loe parámetros estimados dependerán del modelo conceptual adoptado. Intuitivamente, la inclusión conceptual de diferentes modelos debería dar lugar a curvas con una apariencia muy distinta, lo que a su vez supondría unos momentos estadísticos de la curva de llegada muy distintos. Por el contrarío, en este articulo se muestra que la utilización de algunos modelos conceptuales habituales y en apariencia muy distintos dan lugar e momentos estadísticos virtualmente idénticos en cuanto e su variación con respecto e la distancia o el tiempo recorrido por el soluto. Loe modelos presentados corresponden a:

(1) la ecuación de advección dispersión clásica IADEI con un término macrodispersivo de tipo Fickiano: 121 un medio homogéneo con un término de transferencia de masa entre la fase móvil y la matriz rocosa (fase inmóvil) dentro de la cual el soluto presenta transporte difusivo; y 131 el transporte de un soluto que experimente reacciones de adsorción con cinética de equilibrio. En los tres modelos estudiados loe primeros tres momentos de la curva de llegada son lineales con la distancia, mientras que el término dominante del momento de cuarto orden es cuadrático. Este similar comportamiento permite encontrar pare cede modelo conceptual un conjunto de parámetros de modo que reproduzcan de manera similar une curva de llegada concrete. Esto supone un problema importante de identificabilidad de parámetros cuando se usen datos procedentes de une única curve de llegada, puesto que por le apariencia de le curve no seré posible deducir cuáles han sido los procesos dominantes o, por lo menos, descartar alguno de loe procesos posibles. En cualquier ejemplo real será necesario recurrir e información externa pera identificar loe procesos relevantes que han dedo forme e le curva de llegada

Mean travel time of conservative solutes in randomly heterogeneous unbounded domains under mean uniform flow

María Jesús Samper — Tue, 17 Mar 2020 13:58:06 +0100

We derive a closed‐form expression for mean travel time of a conservative solute migrating under uniform in the mean flow conditions within an infinite stationary field with simple exponential correlation of the natural logarithm of hydraulic conductivity. Our expression is developed from a consistent second‐order expansion in σY (standard deviation of the log hydraulic conductivity) of the equations for moments of travel time and trajectories of conservative solutes in two‐dimensional randomly nonuniform flows of Guadagnini et al. [2001]. As such, it is nominally valid for moderately heterogeneous fields, with σY2 < 1. Its validity for larger heterogeneity degrees is tested against numerical Monte Carlo simulations. Our results clarify the nonlinear effect in the mean travel time with respect to distance that has been observed numerically (and modeled empirically) in the literature.

Travel time moments for sorbing solutes in heterogeneous domains under nonuniform flow conditions

María Jesús Samper — Tue, 17 Mar 2020 13:43:10 +0100

A methodology for evaluating the unconditional and conditional moments of travel time for a sorbing solute is presented. The approach is applicable for any flow configuration and for a wide range of mass transfer rate‐limited linear processes. The methodology is applicable to the general case of spatially variable hydrological and chemical parameters. The sorption model used to derive the temporal moments is that of a continuous distribution of mass rate coefficients [Haggerty and Gorelick, 1998]. Models such as instantaneous equilibrium, first‐order and two‐site sorption kinetics, among others, can be considered as particular cases of this general model. Using a deterministic approach, the low‐order moments of the breakthrough curves for reactive solutes can be obtained as a function of those for conservative tracers. Using a stochastic approach, the unconditional low‐order statistics of the travel time moments can be obtained. These moments depend on the statistics of two Lagrangian functions, the travel time for a conservative solute, and an integral of the variations of the chemical parameters weighted by the inverse local velocity along the trajectory. Finally, conditional temporal moments are derived. Moments can be conditioned to any type of information, hard or soft, hydraulic or geochemical. Conditioning is found to reduce uncertainty, characterized by a reduction in the variance of the travel time. The general results are particularized for both uniform in the mean and convergent flow conditions and for simple sorption models such as linear instantaneous equilibrium and first‐order kinetics. In all such cases, close‐form results, based on small perturbations expansions, are presented for the travel time moments.

Conditional moments of the breakthrough curves of kinetically sorbing solute in heterogeneous porous media using multirate mass transfer models for sorption and desorption

María Jesús Samper — Tue, 17 Mar 2020 13:27:25 +0100

A methodology is presented for evaluating the temporal moments of solutes undergoing linear rate‐limited mass transfer processes based on a Lagrangian approach to solute transport in heterogeneous media. The temporal moments of sorbing solutes are written as a function of those of conservative tracers. The general continuous diffusion rate model that has recently appeared in the hydrologic literature is used to model the rate‐limited mass transfer processes. The methodology is also applied to desorption from an initially uniformly contaminated aquifer, and the concentration expected value and variance are found quasi‐analytically. The conditional temporal moments of sorbing solutes can be written as a function of the conditional moments of conservative tracers. Conditioning results in a reduction of the variance of travel time. The amount of reduction depends on the chemical model selected

Using Geostatistical Analysis to Evaluate the Presence of Rotylenchulus reniformis in Cotton Crops in Brazil: Economic Implications.

María Jesús Samper — Tue, 17 Mar 2020 13:18:32 +0100

In recent years, the productivity of cotton in Brazil has been progressively decreasing, often the result of the reniform nematode Rotylenchulus reniformis. This species can reduce crop productivity by up to 40%. Nematodes can be controlled by nematicides but, because of expense and toxicity, application of nematicides to large crop areas may be undesirable. In this work, a methodology using geostatistics for quantifying the risk of nematicide application to small crop areas is proposed. This risk, in economic terms, can be compared to nematicide cost to develop an optimal strategy for Precision Farming. Soil (300 cm(3)) was sampled in a regular network from a R. reniformis-infested area that was a cotton monoculture for 20 years. The number of nematodes in each sample was counted. The nematode number per volume of soil was characterized using geostatistics, and 100 conditional simulations were conducted. Based on the simulations, risk maps were plotted showing the areas where nematicide should be applied in a Precision Farming context. The methodology developed can be applied to farming in countries that are highly dependent on agriculture, with useful economic implications.

Convergent-flow tracer tests in heterogeneous media: combined experimental–numerical analysis for determination of equivalent transport parameters

María Jesús Samper — Tue, 17 Mar 2020 12:57:40 +0100

In modeling transport within naturally heterogeneous aquifers, it is usually assumed that the transport equations valid at local scales can also be applied at larger scales. At larger scales, the heterogeneous domain is represented by an equivalent homogeneous medium. Convergent-flow tracer tests constitute one of the most frequently used field tests to estimate effective input parameters of equivalent homogeneous aquifers. Traditionally, statistical approaches applied to groundwater flow and solute transport have provided tools to estimate these equivalent parameters. These approaches are based on a number of simplifications including the assumption that the point transmissivity values follow a multilog-normal random function. Several investigators have found that this assumption may not be valid in many field cases. In order to study the applicability of the equivalent homogeneous formulation in a nontraditional stochastic field, a number of experimental and numerical studies were conducted. The results are used to determine the apparent values of porosity and dispersivity that would be obtained if convergent-flow tracer tests were conducted in a deterministically generated heterogeneous transmissivity field displaying anisotropy in the correlation structure. It is shown that in this particular heterogeneous media, apparent porosity strongly depends on connectivity rather than on transmissivity. This dependence on connectivity questions the theoretical results obtained in continuum equivalent fields to estimate effective porosity.

Simulation of Gas Dipole Tests in Fractures at the Intermediate Scale Using a New Upscaling Method

María Jesús Samper — Tue, 17 Mar 2020 12:47:07 +0100

A high-level radioactive waste disposal site may lead to gas generation by different physical mechanisms. As these sites are to be located in areas with low water flow, any small amount of gas can lead to relative high gas pressures, so that multiphase flow analysis becomes relevant. The movement of gas and water through the system has two important implications. Firstly, water flow takes place in unsaturated conditions, and thus travel times of the radioactive particles transported are affected; and secondly, gas can also carry radioactive particles. Therefore, one of the key points in such studies is the time when gas would break through the biosphere under a number of different flow conditions. In fractured zones, gas would flow preferentially through the most conductive features. We consider a two-dimensional system representing an isolated fracture. In each point we assign a local porosity and permeability and a local pressure-saturation relationship. A dipole (injector-producer) gas flow system is generated and the variation in water saturation is studied. A simple method is proposed for obtaining upscaled values for several parameters involved in two-phase flow. It is based on numerical simulation on a block scale assuming steady-state conditions and absence of capillary pressure gradients. The proposed method of upscaling is applied to simulate a dipole test using a coarser grid than that of the reference field. The comparison between the results in both scales shows an encouraging agreement

Geostatistical analysis of the spatial distribution of Rotylenchulus reniformis on cotton cultivated under crop rotation

María Jesús Samper — Tue, 17 Mar 2020 11:59:33 +0100

The spatial distribution of Rotylenchulus reniformis on cotton cultivated in crop rotation with sorghum-peanut-velvetbean was studied using geostatistics. The experimental field, which had been continuously cropped with cotton during 20 years, comprised two 32 x 48 m-grids, each divided in sixty-four 4 x 6 m sampling plots. For all crops, 300 cm 3 of soil samples were taken at the center of each plot at crop germination (Pi) and again at harvest (Pf), from which the numbers of nematodes were determined. The results revealedthat the spatial distribution of R. reniformis was highly aggregated and with the aid of the geostatistical techniques the nematode intensities were mapped and the risk areas accurately identified. Consequently, geostatistics is here considered a useful tool for planning nematode control strategies, particularly in Precision Agriculture.

Solute transport in heterogeneous media: the impact of anisotropy and non-ergodicity in risk assessment

María Jesús Samper — Tue, 17 Mar 2020 11:38:09 +0100

Conceptual model selection is a key issue in risk assessment studies. We analyze the effect of a number of conceptual aspects related to solute transport in two-dimensional heterogeneous media. The main issues addressed are non-ergodicity, anisotropy in the correlation structure of the transmissivity field, and dispersion at the local scale. In particular, we study the development of a solute plume when mean flow is oriented at an angle with respect to the principal directions of anisotropy. The study is carried out in a Lagrangian framework using Monte Carlo analysis.

Of special interest is the evolution of individual plumes. A number of aspects are analyzed, namely the location of the center of mass for each plume and the different ways to compute the angles that the main axes of the plume develop with respect to the direction of the mean flow. Stochastic theories based upon ergodicity conclude that the plume gets oriented in the mean flow direction. In our non-ergodic simulations, the mean of the offset angles, for each individual plume in each particular realization, is offset from the mean flow direction towards the direction of maximum anisotropy. If, instead, the analysis is performed on the ensemble plume (superposition of all different simulations), it is then found oriented closer to the direction of the mean flow than the average offset angle for the different plumes considered separately. This last result adds an extra word of caution to the use of ensemble averaged values in solute transport studies.

Serious implications for risk assessment follow from the conceptual model adopted. First, in any single realization there will a large uncertainty in locating the plume at any given time; second, real dilution would be less than what would be expected if the macrodispersion values obtained for ergodic conditions were applied; third, the volume that is affected by a non-zero concentration is smaller than that predicted from macrodispersion concepts; fourth, the orientation of the plume does not correspond to that of the mean flow; and fifth, accounting for local dispersion helps reducing uncertainty.

Sobre la interpretación de ensayos hidráulicos en acuíferos no homogéneos

María Jesús Samper — Tue, 17 Mar 2020 11:10:45 +0100

La obtención de parámetros hidráulicos de un acuífero suele realizarse a partir de la interpretación de ensayos hidráulicos con condiciones de flujo radial convergente. El objetivo de este artículo es ver como las fórmulas habituales de la hidráulica de pozos se pueden extender para incluir explícitamente la heterogeneidad del medio, y más importante, que los valores que se obtienen de la interpretación de ensayos en medios heterogéneos son valores representativos del medio y con un claro significado e interés hidrogeológico. Para ello es preciso relacionar la transmisividad deducida de ensayos de bombeo con la heterogeneidad natural. Esto se ha realizado analítica y numéricamente. El resultado, que coincide con las observaciones de campo, es que cuando existen varios puntos de observación, la transmisividad (T) deducida por el método de Jacob tiende a ser la misma para todos los puntos de observación. Más importante, dicha transmisividad es, bajo condiciones muy generales, igual a la T efectiva, es decir, a la que controla el flujo natural bajo condiciones de gradiente uniforme. Esto apoya la metodología que han venido usando tradicionalmente los hidrogeólogos

Gestión de las aguas subterráneas en zonas urbanas. conceptualización y modelización: aplicación a barcelona (españa)

María Jesús Samper — Tue, 17 Mar 2020 10:58:17 +0100

Availability and quality of groundwater resources is seriously affected by urbanization in many large cities. This leads to significant social, environmental, economical, and political implications. Any urban hydrology study requires a detailed analysis of water fluxes flowing in and out of the system, including their magnitude and relative importance. Analyzing the quality of the resources is another key issue. In any real case study one has to face at least three aspects: (1) process identification, (2) aquifer characterization, and (3) water resources management. This methodology has been applied to the city of Barcelona. The outcome is a groundwater model that allows defining, characterizing, and quantifying the potential risk of aquifers, both on urban structures, and upon population. In this sense, it may become a management tool. This is an important step towards convincing city managers to consider groundwater as one of the topics to be taken into account in city planning.

A Numerical Study on the Relationship Between Transmissivity and Specific Capacity in Heterogeneous Aquifers

María Jesús Samper — Tue, 17 Mar 2020 10:16:32 +0100

Specific capacity (Q/s) data are usually much more abundant than transmissivity (T) data. Theories which assume uniform transmissivity predict a nearly linear relationship between T and Q/s. However, linear dependence is seldom observed in field studies. Since hydrogeologic studies usually require T data, many hydrogeologists use linear regression analysis of T versus Q/s data to estimate T values where only Q/s data are available. In this paper we use numerical models to investigate the effects of aquifer heterogeneity on the relationship between Q/s and T estimates. The simulations of hydraulic tests in heterogeneous media show that estimates of T derived using Jacob's method tend to their late‐time effective value much faster than Q/s values. The latter are found to be more dependent upon local transmissivities near the well. This explains why the regression parameters for T versus Q/s data depend on heterogeneity and the‘lateness’of the test period analyzed. Since this effect is more marked in high T zones than in low T zones, we conclude that natural aquifer heterogeneity can explain the convex deviation from linearity often observed in the field. A further result is that the geometric mean of T estimates, obtained from short and intermediate time pumping tests, seems to systematically underestimate effective T (Teff) of heterogeneous aquifers. In the studied simulation cases, the median of the T values or the arithmetic mean yield better estimates for Teff

Pumping tests in heterogeneous aquifers: An analytical study of what can be obtained from their interpretation using Jacob's Method

María Jesús Samper — Tue, 17 Mar 2020 09:57:47 +0100

Interpretation of pumping tests to estimate hydraulic parameter values is typically based on the assumption of aquifer homogeneity. The applicability of the traditional methods of interpretation in real aquifers can be questioned, since the evaluation of the drawdown curves observed at different locations in a single test may not result in one consistent set of hydraulic parameters. Thus most hydrogeologists tend to look at estimated transmissivities (T) as some average property of the medium, while estimated storativities (S) are disregarded in some cases, particularly when they are obtained from data measured at the pumping well. An analytical study of drawdown under radially convergent flow toward a single point in heterogeneous aquifers shows that large time drawdown values form a straight line on a drawdown versus log time plot. Jacob's method consists of obtaining estimates for T and S from the slope and intercept of this line. We find that even in a heterogeneous field, these estimates provide valuable information about the aquifer. Estimated T values for different observation points tend to converge to a single value, which corresponds to the effective T derived under parallel flow conditions. Estimated storativities, however, display higher variability, but the geometric mean of the Sest values can be used as an unbiased estimator of the actual S. Thus it appears that although Jacob's method was originally derived for homogeneous media, it can provide valuable information in real aquifers

Upscaling transmissivity under radially convergent flow in heterogeneous media

María Jesús Samper — Tue, 17 Mar 2020 09:42:32 +0100

Most field methods used to estimate transmissivity values rely on the analysis of drawdown under convergent flow conditions. For a single well in a homogeneous and isotropic aquifer and under steady state flow conditions, drawdown s is directly related to the pumping rate Q through transmissivity T. In real, nonhomogeneous aquifers, s and Q are still directly related, now through a value called equivalent transmissivity Teq. In this context, Teq is defined as the value that best fits Thiem's equation and would, for example, be the transmissivity assigned to the well location in the classical interpretation of a steady state pumping test. This equivalent or upscaled transmissivity is clearly not a local value but is some representative value of a certain area surrounding the well. In this paper we present an analytical solution for upscaling transmissivities under radially convergent steady state flow conditions produced by constant pumping from a well of radius rw in a heterogeneous aquifer based upon an extension of Thiem's equation. Using a perturbation expansion, we derive a second‐order expression for Teq given as a weighted average of the fluctuations in log T throughout the domain. This expression is compared to other averaging formulae from the literature, and differences are pointed out. Teq depends upon an infinite series which may be expressed in terms of coefficients of the finite Fourier transform of the log transmissivity function. Sufficient conditions for convergence of this series are examined. Finally, we show that our solution agrees with existing analytical ones to second order and test the solution with a numerical example

An evaluation of Jacob's Method for the interpretation of pumping tests in heterogeneous formations

María Jesús Samper — Tue, 17 Mar 2020 09:32:33 +0100

Most pumping tests are interpreted using the classical Theis assumption of large‐scale homogeneity with various corrections to account for early time behavior of drawdown curves. When drawdowns are plotted versus log time, late time data often delineate a straight line, which is consistent with Jacob's approximation of Theis' solution but may seem surprising in view of the heterogeneity of natural media. The aim of our work is to show that Jacob's method leads to a good approximation of the effective transmissivity of heterogeneous media when constrained to late time data. A review of several multiwell pumping tests demonstrates that when drawdown curves from each observation well are interpreted separately, they produce very similar transmissivity T estimates. However, the corresponding estimates for storativity span a broad range. This behavior is verified numerically for several models of formation heterogeneity. A very significant finding of the numerical investigation is that T values estimated using simulated drawdown from individual observation wells are all very close to the effective T value for parallel flow. This was observed even in nonmultiGaussian T fields, where high T zones are well connected and where the effective T is larger than the geometric average of point values. This implies that Jacob's method can be used for estimating effective T values in many, if not most, formations.

On matrix diffusion: formulations, solution methods and qualitative effects

María Jesús Samper — Mon, 16 Mar 2020 17:54:36 +0100

Matrix diffusion has become widely recognized as an important transport mechanism. Unfortunately, accounting for matrix diffusion complicates solute-transport simulations. This problem has led to simplified formulations, partly motivated by the solution method. As a result, some confusion has been generated about how to properly pose the problem. One of the objectives of this work is to find some unity among existing formulations and solution methods. In doing so, some asymptotic properties of matrix diffusion are derived. Specifically, early-time behavior (short tests) depends only on φ m 2 R m D m / L m 2, whereas late-time behavior (long tracer tests) depends only on φ m R m , and not on matrix diffusion coefficient or block size and shape. The latter is always true for mean arrival time. These properties help in: (a) analyzing the qualitative behavior of matrix diffusion; (b) explaining one paradox of solute transport through fractured rocks (the apparent dependence of porosity on travel time); (c) discriminating between matrix diffusion and other problems (such as kinetic sorption or heterogeneity); and (d) describing identifiability problems and ways to overcome them.

Radially convergent flow in heterogeneous media

María Jesús Samper — Mon, 16 Mar 2020 17:43:26 +0100

We present an analytical solution for apparent effective transmissivity under radially convergent steady state flow conditions, produced by constant pumping from a single well of finite radius, rw. Apparent effective transmissivity, Te, is defined as the value that relates the expected values of flow and head gradient at a certain location. The domain is two‐dimensional, of annular shape, and the size of the pumping well is explicitly taken into account. The solution for the steady state heads is obtained by solving the perturbed flow equation and substituting it into Darcy's law to obtain a consistent second‐ order expansion for Te. We show that apparent effective transmissivity is a scalar for any choice of isotropic covariance model, with an expression given in integral form. Our main result is that Te in a heterogeneous, statistically isotropic random field, under radial steady state flow conditions, is a monotonie increasing function of r (distance from the well) that rises from the harmonic mean of the point transmissivity values (close to the well) and tends asymptotically towards the geometric mean (far from the well). The asymptotic value is reached at a distance of a few integral scales (1.5–2 for the Gaussian model and 3–5 for the exponential one). The apparent effective transmissivity versus normalized r curves are in excellent agreement with previously published numerical work carried out using Monte Carlo method

Directional effects on convergent flow tracer tests

María Jesús Samper — Mon, 16 Mar 2020 17:31:36 +0100

Convergent flow tracer tests constitute a convenient way of characterizing hydraulic parameters in an aquifer. Interpretation of tracer breakthrough curves from convergent flow tests normally is made under the assumption of radial symmetry. Nevertheless, these curves may display directional dependence; that is when tracers are injected at several points located at the same distance, both arrival times and estimated dispersivities may be significantly different. This result is why some authors attribute a tensorial nature to porosity or, equivalently, talk about directional porosity when trying to explain the variations in computed porosity depending on the relative orientation of pumping and injection wells. Our main ponit is that this directional effect is nothing but an artifact of an inappropriate selection of a conceptual model, where anisotropy (local of statistical) in hydraulic conductivity is not properly characterized. To illustrate this point, we first consider the situation of a simple homogeneous and anisotropic model of the medium. We prove analytically that this model leads to arrival time being proportional to the square root of directional hydraulic conductivity. Using a stochastic approach, we determine the same directional behavior of arrival time for a locally isotropic hydraulic conductivity field with statistical anisotropy caused by an anisotropic correlation structure. A statistical anisotropic covariance model for hydraulic conductivity is consistent with field evidence.

Field tracer experiment in a low permeability fractured medium: results from El Berrocal site

María Jesús Samper — Mon, 16 Mar 2020 17:08:17 +0100

A modelling experimental activity was developed to characterise the hydraulic behaviour of water-bearing fractures in crystalline rocks.

Three conservative tracers were injected into two packed-off sections of the same well, 69 m deep in a granite formation, and recovered by pumping from an isolated section of a second borehole, 46 m deep, 14 m apart. The concept of this design is to characterise separately an isolated fracture zone intersecting the lower parts of both wells from the fracture network intersecting the bulk of the rock.

Before using the tracers in the field, their behaviour was studied in the laboratory under controlled conditions. Fluorescein, eosin and iodide were finally chosen as the best spikes.

The field experiments were developed under strictly controlled conditions, such as (1) checking the hydraulic pressure in the packed-off sections and in other parts of circuits; (2) mixing the tracer solutions during the injection and checking their homogeneity; (3) performing a continuous and automatic monitoring of tracer concentration in the arrival well.

Iodide and fluorescein were injected in one section, and eosin in the other section. The pumping rate was maintained at 2 1 min−1. The test lasted 27 d after which from 40 to 60% of the injected masses were recovered.

Breakthrough curve analysis considered two conceptual models: radial advective-dispersive transport with and without matrix diffusion: the first model returns thickness-porosity values around 0.2 × 10−1 m and dispersivity around 4 m. Parameters are remarkably consistent for iodide and fluorescein, although fittings can be improved. The matrix diffusion model provides much better fittings by decreasing thickness porosity to 0.8 X 10-Z m. Dispersivities range from 0.5 to 0.9 m and the molecular diffusion term differentiates the behaviour of conservative tracers such as fluorescein and iodide.

Scale effects in transmissivity

María Jesús Samper — Mon, 16 Mar 2020 16:58:29 +0100

Heterogeneity accounts for several paradoxes in groundwater flow and solute transport. One of the most striking observations is the emergence of scale effects in transmissivity, that is, the increase in effective transmissivity (or hydraulic conductivity, for that matter) with increasing scale of observation. Traditional stochastic approaches, where transmissivity is treated as a multilog-normal random function, lead to a large-scale effective transmissivity equal to the geometric average of local measurements.

We present several field cases in which large-scale transmissivities are indeed larger than the geometric average of local tests. This suggests that the assumption of multilog-normality may not be valid in many cases, even if point T values display a log-normal distribution. We conjecture that scale dependence of T may, in part, be a consequence of high T zones being better connected than average or low T zones, a feature which may occur in many geological environments, but which is not consistent with multinormal log-T fields. We go on to generate a suite of log-T fields with a normal distribution for point values but non-multinormal spatial correlation. In all our fields, high T zones show longer correlations than average of low T zones. By simulating flow through these synthetic fields under simple boundary conditions, and estimating their effective transmissivity values, we conclude that these types of departures from the multilog-normality assumption lead consistently to scale effects.

A Synthesis of Approaches to Upscaling of Hydraulic Conductivities

María Jesús Samper — Mon, 16 Mar 2020 16:38:00 +0100

Simulation of flow through heterogeneous media often requires discretizing the flow domain into blocks and assigning an equivalent block conductivity value to each one of them. The process of defining block conductivities from point values is termed upscaling. A number of approaches to upscaling are available, most of which consider the uncertainty associated with any natural property, so that they cast the problem in a stochastic frame. Recently, Indelman and Dagan (1993a, b) provided a general stochastic methodology to upscaling in heterogeneous anisotropic formations by means of the dissipation energy function; unfortunately, they did not provide any “practical” method to compute block values from point ones. The objective of this work is twofold: First, we analyze different practical approaches to compute block conductivities and find that all of them provide very similar results in terms of actual computed values; second, we check that all approaches verify approximately a number of conditions stated by Indelman and Dagan (1993a). Specifically, we show analytically that for regular blocks, the methodologies of both Rubin and Gómez‐Hernández (1990) and Desbarats (1992) (which we call “practical” methodologies) satisfy the condition that the effective conductivity obtained from a field where the elementary conductivities are defined over a certain support (we call this the actual formation) is identical to that obtained from the same field with conductivities defined at a larger support (upscaled formation). The analysis is carried out by working with the logarithm of block conductivities and using a small‐perturbation expansion and thus is strictly valid for small variances. On the other hand, we show numerically that the two methodologies satisfy approximately an important condition stated in terms of the dissipation energy: that block‐averaged dissipation values computed are indeed very close to the true dissipation values in each block. The agreement is even better if we consider statistical moments instead of point values. As an important conclusion we should note that all practical methodologies considered in this work perform equally well and, more important, constitute a simple way to treat an otherwise very complex problem

A discussion on validation of hydrogeological models

María Jesús Samper — Mon, 16 Mar 2020 16:11:21 +0100

Groundwater flow and solute transport are often driven by heterogeneities that elude easy identification. It is also difficult to select and describe the physico-chemical processes controlling solute behavior. As a result, definition of a conceptual model involves numerous assumptions both on the selection of processes and on the representation of their spatial variability. Even if a unique conceptual model could be identified, estimation of its parameters may be highly uncertain. Using a calibrated model for making groundwater predictions involves three types of uncertainties: those associated with the correctness of the conceptual model, which may arise during model construction or during prediction; those related to the accuracy of model parameters; and those corresponding to uncertainties in future stresses. In this context, validating a numerical model by comparing its predictions with actual measurements may not be sufficient for evaluting whether or not it provides a good representation of ‘reality’. Predictions will be close to measurements, regardless of model validity, if these are taken from experiments that stress well-calibrated model modes. On the other hand, predictions will be far from measurements when model parameters are very uncertain, even if the model is indeed a very good representation of the real system. Hence, we contend that ‘classical’ validation of hydrogeological models is not possible. Rather, models should be viewed as theories about the real system. This can be proven wrong, but they cannot be proven right. In this sense, we propose to follow a rigorous modeling approach in which different sources of uncertainty are explicitly recognized. The application of one such approach is illustrated by modeling a laboratory uranium tracer test performed on fresh granite, which was used as Test Case 1b in INTRAVAL.

Contaminación por lavado piezométrico a partir de vertederos enterrados: aplicación a un acuífero aluvial

María Jesús Samper — Mon, 16 Mar 2020 11:30:39 +0100

El vertido incontrolado de residuos industriales y urbanos en acuíferos aluviales constituye una práctica frecuente en el entorno de áreas industrializadas y provoca la contaminación de las aguas subterráneas. En el proceso de contaminación juega un papel primordial el efecto producido por el ascenso y descenso de los niveles piezométricos que provoca un lavado de los residuos, generalmente enterrados en antiguas extracciones de áridos. La modelización de este fenómeno se ha realizado mediante el empleo de un modelo numérico de flujo-no lineal y transporte transitorios (TRNOCONF), que ha permitido reproducir la propagación del ión C1 desde las zonas de vertido. Los resultados obtenidos indican que junto al lavado piezométrico, los factores condicionantes en la formación de los penachos son la recarga procedente de avenidas y la existencia de una red de paleocanales que condiciona la geometría del fondo.

Nonintrusive proper generalised decomposition for parametrised incompressible flow problems in OpenFOAM

María Jesús Samper — Fri, 13 Mar 2020 12:51:46 +0100

The computational cost of parametric studies currently represents the major limitation to the application of simulation-based engineering techniques in a daily industrial environment. This work presents the first nonintrusive implementation of the proper generalised decomposition (PGD) in OpenFOAM, for the approximation of parametrised laminar incompressible Navier–Stokes equations. The key feature of this approach is the seamless integration of a reduced order model (ROM) in the framework of an industrially validated computational fluid dynamics software. This is of special importance in an industrial environment because in the online phase of the PGD ROM the description of the flow for a specific set of parameters is obtained simply via interpolation of the generalised solution, without the need of any extra solution step. On the one hand, the spatial problems arising from the PGD separation of the unknowns are treated using the classical solution strategies of OpenFOAM, namely the semi-implicit method for pressure linked equations (SIMPLE) algorithm. On the other hand, the parametric iteration is solved via a collocation approach. The resulting ROM is applied to several benchmark tests of laminar incompressible Navier–Stokes flows, in two and three dimensions, with different parameters affecting the flow features. Eventually, the capability of the proposed strategy to treat industrial problems is verified by applying the methodology to a parametrised flow control in a realistic geometry of interest for the automotive industry.

Fast solution of elliptic harbor agitation problems under frequency-direction input spectra by model order reduction and NURBS-enhanced FEM

María Jesús Samper — Fri, 13 Mar 2020 12:45:17 +0100

Many harbor applications are based on the solution of linear elliptic agitation problems for many spectral conditions. One of the main goals consists in computing the linear combination of numerous simulations of the harbor agitation problem, using monochromatic waves of different spectral components (i.e. frequency and incoming wave direction). In practice, the standard strategy selects the number of wave components according to a prescribed discretization of the 2D input spectra. The main issue relies on some quantities of interest that are very sensitive to the level of refinement of the spectra, such as the significant wave height at every mesh point or the identification of resonance modes induced by long wave scattering. In many cases, achieving enough quality in these quantities may impose numerous simulations and, consequently, non-practical computer costs. This can drastically limit the final accuracy of results. To overcome this situation, here a new strategy is proposed to efficiently solve a large number of harbor agitation problems derived from dense discretizations of the 2D input spectra. The strategy is based on the combination of two different numerical approaches. Firstly, each required monochromatic simulation is solved via high order NURBS (non-uniform rational B-splines) enhanced finite elements (NEFEM). More precisely, NEFEM captures the exact harbor geometry using large mesh elements that produce accurate solutions and significant savings on the system size, particularly in long wave cases. Secondly, a model order reduction technique is used to approximate the original elliptic harbor model by a so-called surrogate model. The main advantage is that, once the surrogate model is constructed, it can be rapidly evaluated to provide simulations for any value of the spectral components within a range of interest, and without the need of solving any new harbor agitation problem (as the standard strategy does). Thus, this enables the possibility of using any desired discretization of the 2D input spectra with no additional computer cost. The construction of the surrogate model is performed using the proper generalized decomposition method with a novel incremental computation along the frequency dimension. The proposed strategy is discussed, and its superior performance with respect to standard strategies is demonstrated, on two harbor agitation examples with several applications.

Hybrid coupling of CG and HDG discretizations based on Nitsche’s method

María Jesús Samper — Fri, 13 Mar 2020 12:37:04 +0100

A strategy to couple continuous Galerkin (CG) and hybridizable discontinuous Galerkin (HDG) discretizations based only on the HDG hybrid variable is presented for linear thermal and elastic problems. The hybrid CG-HDG coupling exploits the definition of the numerical flux and the trace of the solution on the mesh faces to impose the transmission conditions between the CG and HDG subdomains. The con- tinuity of the solution is imposed in the CG problem via Nitsche’s method, whereas the equilibrium of the flux at the interface is naturally enforced as a Neumann con- dition in the HDG global problem. The proposed strategy does not affect the core structure of CG and HDG discretizations. In fact, the resulting formulation leads to a minimally-intrusive coupling, suitable to be integrated in existing CG and HDG libraries. Numerical experiments in two and three dimensions show optimal global convergence of the stress and superconvergence of the displacement field, locking-free approximation, as well as the potential to treat structural problems of engineering interest featuring multiple materials with compressible and nearly incompressible behaviors. This is a post-peer-review, pre-copyedit version of an article published in Computational mechanics.

A second-order face-centred finite volume method for elliptic problems

María Jesús Samper — Fri, 13 Mar 2020 12:26:49 +0100

A second-order face-centred finite volume method (FCFV) is proposed. Contrary to the more popular cell-centred and vertex-centred finite volume (FV) techniques, the proposed method defines the solution on the faces of the mesh (edges in two dimensions). The method is based on a mixed formulation and therefore considers the solution and its gradient as independent unknowns. They are computed solving an element-by-element problem after the solution at the faces is determined. The proposed approach avoids the need of reconstructing the solution gradient, as required by cell-centred and vertex-centred FV methods. This strategy leads to a method that is insensitive to mesh distortion and stretching. The current method is second-order and requires the solution of a global system of equations of identical size and identical number of non-zero elements when compared to the recently proposed first-order FCFV. The formulation is presented for Poisson and Stokes problems. Numerical examples are used to illustrate the approximation properties of the method as well as to demonstrate its potential in three dimensional problems with complex geometries. The integration of a mesh adaptive procedure in the FCFV solution algorithm is also presented

Solution of geometrically parametrised problems within a CAD environment via model order reduction

María Jesús Samper — Fri, 13 Mar 2020 12:21:35 +0100

The main objective of this work is to describe a general and original approach for computing an off-line solution for a set of parameters describing the geometry of the domain. That is, a solution able to include information for different geometrical parameter values and also allowing to compute readily the sensitivities. Instead of problem dependent approaches, a general framework is presented for standard engineering environments where the geometry is defined by means of NURBS. The parameters controlling the geometry are now the control points characterising the NURBS curves or surfaces. The approach proposed here, valid for 2D and 3D scenarios, allows a seamless integration with CAD preprocessors. The proper generalised decomposition (PGD), which is applied here to compute explicit geometrically parametrised solutions, circumvents the curse of dimensionality. Moreover, optimal convergence rates are shown for PGD approximations of incompressible flows

A regularised-adaptive Proper Generalised Decomposition implementation for coupled magneto-mechanical problems with application to MRI scanners

María Jesús Samper — Fri, 13 Mar 2020 12:14:26 +0100

Latest developments in high-strength Magnetic Resonance Imaging (MRI) scanners with in-built high resolution, have dramatically enhanced the ability of clinicians to diagnose tumours and rare illnesses. However, their high-strength transient magnetic fields induce unwanted eddy currents in shielding components, which result in fast vibrations, noise, imaging artefacts and, ultimately, heat dissipation, boiling off the helium used to super-cool the magnets. Optimum MRI scanner design requires the capturing of complex electro-magneto-mechanical interactions with high fidelity computational tools. During production cycles, this is known to be extremely expensive due to the large number of configurations that need to be tested. There is an urgent need for the development of new cost-effective methods whereby previously performed computations can be assimilated as training solutions of a surrogate digital twin model to allow for real-time simulations. In this paper, a Reduced Order Modelling technique based on the Proper Generalised Decomposition method is presented for the first time in the context of MRI scanning design, with two distinct novelties. First, the paper derives from scratch the offline higher dimensional parametrised solution process of the coupled electro-magneto-mechanical problem at hand and, second, a regularised adaptive methodology is proposed for the circumvention of numerical singularities associated with the ill-conditioning of the discrete system in the vicinity of resonant modes. A series of numerical examples are presented in order to illustrate, motivate and demonstrate the validity and flexibility of the considered approach.

Encapsulated PGD algebraic toolbox operating with high-dimensional data

María Jesús Samper — Fri, 13 Mar 2020 12:05:31 +0100

In its original conception, proper generalized decomposition (PGD) provides explicit parametric solutions, denoted as computational vademecums or digital abacuses, to parametric boundary value problems. The PGD approach is extended here to devise a set of algebraic tools enabling to operate with multidimensional tensor data. These tools are designed to store, compress and perform basic operations (in particular divisions) with tensors in separable format. These tools are directly producing the computational vademecums for the resulting high-dimensional tensor data. Thus, the general methodology enables performing nontrivial operations (storage, compression, division, solving linear systems of equations...) for multidimensional tensor data. The idea is based on the principle of the PGD separation, that produces a separable least squares approximation of any multidimensional function. The PGD compression is a particular case, extensively used in practice to compact the separable solution without loss of accuracy. Here, this concept is applied to algebraic tensor structures that are also seen as functions in multidimensional Cartesian domains. Moreover, a straightforward extension of this concept is devised to operate with multidimensional objects stored in the separable format. That allows creating a toolbox of PGD arithmetic operators that is publicly released at https://git.lacan.upc.edu/zlotnik/algebraicPGDtools. Numerical tests demonstrate the performance and efficiency of the toolbox, both for tensor data handling and operation and also in applications pertaining to the discretized version of boundary value problems.

Multiscale proper generalized decomposition based on the partition of unity

María Jesús Samper — Fri, 13 Mar 2020 11:38:38 +0100

Solutions of partial differential equations could exhibit a multiscale behavior. Standard discretization techniques are constraints to mesh up to the finest scale to predict accurately the response of the system. The proposed methodology is based on the standard proper generalized decomposition rationale; thus, the PDE is transformed into a nonlinear system that iterates between microscale and macroscale states, where the time coordinate could be viewed as a 2D time, representing the microtime and macrotime scales. The macroscale effects are taken into account because of an FEM-based macrodiscretization, whereas the microscale effects are handled with unidimensional parent spaces that are replicated throughout the domain. The proposed methodology can be seen as an alternative route to circumvent prohibitive meshes arising from the necessity of capturing fine-scale behaviors.

A local multiple proper generalized decomposition based on the partition of unity

María Jesús Samper — Fri, 13 Mar 2020 11:30:21 +0100

It is well known that model order reduction techniques that project the solution of the problem at hand onto alow-dimensional subspace present difficulties when this solution lies on a non-linear manifold. To overcomethese difficulties—notably, an undesirable augment in the number of requiredmodesin the solution—severalsolutions have been suggested. Among them we can cite the use of non-linear dimensionality reductiontechniques or, alternatively, the employ of local linear reduced order approaches. These last approachesusually present the difficulty of ensuring continuity between these local models. Here, a new method ispresented that ensures this continuity by resorting to the paradigm of the partition of unity, while employing Proper Generalized Decompositions at each local patch.

Uncertainty propagation using the full second-order approach for probabilistic fatigue crack growth life

Carlos Mallor — Fri, 13 Mar 2020 11:21:36 +0100

Uncertainty propagation of fatigue crack growth life commonly aims to provide the probability distribution of the lifespan needed for probabilistic damage tolerance analysis and for structural integrity assessment. This paper presents a novel methodology for efficiently estimating the parameters of the probability distribution of fatigue lifespan considering the Pearson distribution family. First, the full second-order approach for expected value and variance prediction of probabilistic fatigue crack growth life is extended to predict higher order statistical moments of the underlying distribution. That is, the expected value (first raw moment) and the variance (second central moment) equations are complemented with the probabilistic formulations for the skewness and for the kurtosis (third and fourth central standardized moments, respectively). Then, from these moments, the Pearson distribution type is automatically determined. Finally, the parameters of the particular Pearson distribution type are estimated making the statistical moments of the constructed lifespan distribution match the first four prescribed moments predicted by the probabilistic equations. The validity of the proposed method is verified by a numerical example regarding the fatigue crack growth in a railway axle under random bending loading. It is proven that the probability density function of the lifespan is properly derived by the methodology, without knowing or assuming the output probability distribution beforehand. The methodology presented enables an efficient and an accurate quantification of the lifespan uncertainties via its probabilistic distribution. This probabilistic description of fatigue crack growth life can be subsequently used in reliability studies or in damage tolerance assessment.

Tensor representation of non-linear models using cross approximations

María Jesús Samper — Fri, 13 Mar 2020 11:15:56 +0100

Tensor representations allow compact storage and efficient manipulation of multi-dimensional data. Based on these, tensor methods build low-rank subspaces for the solution of multi-dimensional and multi-parametric models. However, tensor methods cannot always be implemented efficiently, specially when dealing with non-linear models. In this paper, we discuss the importance of achieving a tensor representation of the model itself for the efficiency of tensor-based algorithms. We investigate the adequacy of interpolation rather than projection-based approaches as a means to enforce such tensor representation, and propose the use of cross approximations for models in moderate dimension. Finally, linearization of tensor problems is analyzed and several strategies for the tensor subspace construction are proposed. This is a post-peer-review, pre-copyedit version of an article published in Journal of scientific computing

A simple microstructural viscoelastic model for flowing foams

María Jesús Samper — Fri, 13 Mar 2020 11:06:46 +0100

The numerical modelling of forming processes involving the flow of foams requires taking into account the different problem scales. Thus, in industrial applications a macroscopic approach is suitable, whereas the macroscopic flow parameters depend on the cellular structure: cell size, shape, orientation, etc. Moreover, the shape and orientation of the cells are induced by the flow. A fully microscopic description remains useful to understand the foam behaviour and the topological changes induced by the cell elongation or distortion, however, from an industrial point of view, microscopic simulations remain challenging to address practical applications involving flows in complex 3D geometries. In this paper, we propose a viscoelastic flow model where the foam microstructure is represented from suitable microstructure descriptors whose evolution is governed by the macroscopic flow kinematics. This is a post-peer-review, pre-copyedit version of an article published in International journal of material forming.

A locking-free face-centred finite volume (FCFV) method for linear elastostatics

María Jesús Samper — Thu, 12 Mar 2020 17:15:22 +0100

A face-centred finite volume (FCFV) method is proposed for linear elastostatic problems. The FCFV is a mixed hybrid formulation, featuring a system of first-order equations, that defines the unknowns on the faces (edges in two dimensions) of the mesh cells. The symmetry of the stress tensor is strongly enforced using the well-known Voigt notation and the displacement and stress fields inside each cell are obtained by means of explicit formulas. The resulting FCFV method is robust and locking-free in the nearly incompressible limit. Numerical experiments in two and three dimensions show optimal convergence of the displacement and the stress fields without any reconstruction. Moreover, the accuracy of the FCFV method is not sensitive to mesh distortion and stretching. Classical benchmark tests including Kirch’s plate and Cook’s membrane problems in two dimensions as well as three dimensional problems involving shear phenomenons, pressurised thin shells and complex geometries are presented to show the capability and potential of the proposed methodology.

HDG-NEFEM with degree adaptivity for stokes flows

María Jesús Samper — Thu, 12 Mar 2020 16:53:27 +0100

The NURBS-enhanced finite element method (NEFEM) combined with a hybridisable discontinuous Galerkin (HDG) approach is presented for the first time. The proposed technique completely eliminates the uncertainty induced by a polynomial approximation of curved boundaries that is common within an isoparametric approach and, compared to other DG methods, provides a significant reduction in number of degrees of freedom. In addition, by exploiting the ability of HDG to compute a postprocessed solution and by using a local a priori error estimate valid for elliptic problems, an inexpensive, reliable and computable error estimator is devised. The proposed methodology is used to solve Stokes flow problems using automatic degree adaptation. Particular attention is paid to the importance of an accurate boundary representation when changing the degree of approximation in curved elements. Several strategies are compared and the superiority and reliability of HDG-NEFEM with degree adaptation is illustrated.

A superconvergent HDG method for stokes flow with strongly enforced symmetry of the stress tensor

María Jesús Samper — Thu, 12 Mar 2020 16:17:38 +0100

This work proposes a superconvergent hybridizable discontinuous Galerkin (HDG) method for the approximation of the Cauchy formulation of the Stokes equation using same degree of polynomials for the primal and mixed variables. The novel formulation relies on the well-known Voigt notation to strongly enforce the symmetry of the stress tensor. The proposed strategy introduces several advantages with respect to the existing HDG formulations. First, it remedies the suboptimal behavior experienced by the classical HDG method for formulations involving the symmetric part of the gradient of the primal variable. The optimal convergence of the mixed variable is retrieved and an element-by-element postprocess procedure leads to a superconvergent velocity field, even for low-order approximations. Second, no additional enrichment of the discrete spaces is required and a gain in computational efficiency follows from reducing the quantity of stored information and the size of the local problems. Eventually, the novel formulation naturally imposes physical tractions on the Neumann boundary. Numerical validation of the optimality of the method and its superconvergent properties is performed in 2D and 3D using meshes of different element types.

A superconvergent hybridisable discontinuous Galerkin method for linear elasticity

María Jesús Samper — Thu, 12 Mar 2020 15:34:26 +0100

The first superconvergent hybridisable discontinuous Galerkin method for linear elastic problems capable of using the same degree of approximation for both the primal and mixed variables is presented. The key feature of the method is the strong imposition of the symmetry of the stress tensor by means of the well known and extensively used Voigt notation, circumventing the use of complex mathematical concepts to enforce the symmetry of the stress tensor either weakly or strongly. A novel procedure to construct element by element a superconvergent postprocessed displacement is proposed. Contrary to other hybridisable discontinuous Galerkin formulations, the methodology proposed here is able to produce a superconvergent displacement field for low-order approximations. The resulting method is robust and locking-free in the nearly incompressible limit. An extensive set of numerical examples is utilised to provide evidence of the optimality of the method and its superconvergent properties in two and three dimensions and for different element types

An upwind cell centred Total Lagrangian finite volume algorithm for nearly incompressible explicit fast solid dynamic applications

María Jesús Samper — Thu, 12 Mar 2020 14:50:57 +0100

The paper presents a new computational framework for the numerical simulation of fast large strain solid dynamics, with particular emphasis on the treatment of near incompressibility. A complete set of first order hyperbolic conservation equations expressed in terms of the linear momentum and the minors of the deformation (namely the deformation gradient, its co-factor and its Jacobian), in conjunction with a polyconvex nearly incompressible constitutive law, is presented. Taking advantage of this elegant formalism, alternative implementations in terms of entropy-conjugate variables are also possible, through suitable symmetrisation of the original system of conservation variables. From the spatial discretisation standpoint, modern Computational Fluid Dynamics code “OpenFOAM” [http://www.openfoam.com/] is here adapted to the field of solid mechanics, with the aim to bridge the gap between computational fluid and solid dynamics. A cell centred finite volume algorithm is employed and suitably adapted. Naturally, discontinuity of the conservation variables across control volume interfaces leads to a Riemann problem, whose resolution requires special attention when attempting to model materials with predominant nearly incompressible behaviour (). For this reason, an acoustic Riemann solver combined with a preconditioning procedure is introduced. In addition, a global a posteriori angular momentum projection procedure proposed in Haider et al. (2017) is also presented and adapted to a Total Lagrangian version of the nodal scheme of Kluth and Després (2010) used in this paper for comparison purposes. Finally, a series of challenging numerical examples is examined in order to assess the robustness and applicability of the proposed methodology with an eye on large scale simulation in future works.

A face-centred finite volume method for second-order elliptic problems

María Jesús Samper — Thu, 12 Mar 2020 14:16:28 +0100

This work proposes a novel finite volume paradigm, the face-centred finite volume (FCFV) method. Contrary to the popular vertex (VCFV) and cell (CCFV) centred finite volume methods, the novel FCFV defines the solution on the mesh faces (edges in 2D) to construct locally-conservative numerical schemes. The idea of the FCFV method stems from a hybridisable discontinuous Galerkin (HDG) formulation with constant degree of approximation, thus inheriting the convergence properties of the classical HDG. The resulting FCFV features a global problem in terms of a piecewise constant function defined on the faces of the mesh. The solution and its gradient in each element are then recovered by solving a set of independent element-by-element problems. The mathematical formulation of FCFV for Poisson and Stokes equation is derived and numerical evidence of optimal convergence in 2D and 3D is provided. Numerical examples are presented to illustrate the accuracy, efficiency and robustness of the proposed methodology. The results show that, contrary to other FV methods, the accuracy of the FCFV method is not sensitive to mesh distortion and stretching. In addition, the FCFV method shows its better performance, accuracy and robustness using simplicial elements, facilitating its application to problems involving complex geometries in 3D.

Proper generalized decomposition solutions within a domain decomposition strategy

María Jesús Samper — Thu, 12 Mar 2020 13:56:39 +0100

Domain decomposition strategies and proper generalized decomposition are efficiently combined to obtain a fast evaluation of the solution approximation in parameterized elliptic problems with complex geometries. The classical difficulties associated to the combination of layered domains with arbitrarily oriented midsurfaces, which may require in‐plane–out‐of‐plane techniques, are now dismissed. More generally, solutions on large domains can now be confronted within a domain decomposition approach. This is done with a reduced cost in the offline phase because the proper generalized decomposition gives an explicit description of the solution in each subdomain in terms of the solution at the interface. Thus, the evaluation of the approximation in each subdomain is a simple function evaluation given the interface values (and the other problem parameters). The interface solution can be characterized by any a priori user‐defined approximation. Here, for illustration purposes, hierarchical polynomials are used. The repetitiveness of the subdomains is exploited to reduce drastically the offline computational effort. The online phase requires solving a nonlinear problem to determine all the interface solutions. However, this problem only has degrees of freedom on the interfaces and the Jacobian matrix is explicitly determined. Obviously, other parameters characterizing the solution (material constants, external loads, and geometry) can also be incorporated in the explicit description of the solution.

A multidimensional data-driven sparse identification technique: the sparse proper generalized decomposition

María Jesús Samper — Thu, 12 Mar 2020 13:43:21 +0100

Sparse model identification by means of data is especially cumbersome if the sought dynamics live in a high dimensional space. This usually involves the need for large amount of data, unfeasible in such a high dimensional settings. This well-known phenomenon, coined as the curse of dimensionality, is here overcome by means of the use of separate representations. We present a technique based on the same principles of the Proper Generalized Decomposition that enables the identification of complex laws in the low-data limit. We provide examples on the performance of the technique in up to ten dimensions.

Simulating squeeze flows in multiaxial laminates: towards fully 3D mixed formulations

María Jesús Samper — Thu, 12 Mar 2020 13:25:55 +0100

Thermoplastic composites are widely considered in structural parts. In this paper attention is paid to squeeze flow of continuous fiber laminates. In the case of unidirectional prepregs, the ply constitutive equation is modeled as a transversally isotropic fluid, that must satisfy both the fiber inextensibility as well as the fluid incompressibility. When laminate is squeezed the flow kinematics exhibits a complex dependency along the laminate thickness requiring a detailed velocity description through the thickness. In a former work the solution making use of an in-plane-out-of-plane separated representation within the PGD – Poper Generalized Decomposition – framework was successfully accomplished when both kinematic constraints (inextensibility and incompressibility) were introduced using a penalty formulation for circumventing the LBB constraints. However, such a formulation makes difficult the calculation on fiber tractions and compression forces, the last required in rheological characterizations. In this paper the former penalty formulation is substituted by a mixed formulation that makes use of two Lagrange multipliers, while addressing the LBB stability conditions within the separated representation framework, questions never until now addressed.

MÉTODO NUMÉRICO PARA DETERMINAR EL ÁNGULO ADECUADO EN ESTRUCTURAS CON CUBIERTAS LIGERAS

Julio de la Rosa — Wed, 11 Mar 2020 19:39:02 +0100

El territorio cubano es afectado fuertemente por ciclones tropicalesque causan grandes daños a la población y la economía del país. Uno de los sectores más perjudicadoses el de la vivienda donde resaltan las estructuras que presentan cubiertas ligeras por su alta vulnerabilidad ante el embate de vientos extremos. Esta situación resulta alarmante por el alto número de hogares cubanos que utilizan este tipo de cubiertas ylas grandes pérdidas económicas que se registran anualmente por este concepto. La presente investigación tiene como objetivo elaborar un método para determinar el ángulo adecuado del techo en estructuras con cubiertas ligeras, que permita la construcción de viviendas más resistentes al impacto de vientos extremos. Utilizando la Dinámica de Fluidos Computacional (CFD) para modelar el régimen de viento, se logra determinar la respuesta del techo de la estructura para diferentes inclinaciones de la pendiente.

Vademecum-based GFEM (V-GFEM): optimal enrichment for transient problems

María Jesús Samper — Wed, 11 Mar 2020 16:35:08 +0100

This paper proposes a generalized finite element method based on the use of parametric solutions as enrichment functions. These parametric solutions are precomputed off-line and stored in memory in the form of a computational vademecum so that they can be used on-line with negligible cost. This renders a more efficient computational method than traditional finite element methods at performing simulations of processes. One key issue of the proposed method is the efficient computation of the parametric enrichments. These are computed and efficiently stored in memory by employing proper generalized decompositions. Although the presented method can be broadly applied, it is particularly well suited in manufacturing processes involving localized physics that depend on many parameters, such as welding. After introducing the vademecum-generalized finite element method formulation, we present some numerical examples related to the simulation of thermal models encountered in welding processes.

Editorial Volumen 2, 2020: Ingenieros globalizados

Rodrigo F. Herrera — Wed, 11 Mar 2020 13:55:18 +0100

El equipo editorial de la Revista Iberoamericana de Educación en Ingeniería está muy agradecido de su primer año de publicación el año 2019 en donde tuvimos aportación de alto nivel que fueron aceptadas a través de la revisión por pares y luego publicadas en RIEI. Este año 2020 tenemos la meta de comenzar nuestras indexaciones en distintos buscadores, catálogos e índices, por lo que estaremos muy agradecidos de la divulgación de nuestra revista.

Real-time simulation techniques for augmented learning in science and engineering

María Jesús Samper — Wed, 11 Mar 2020 13:15:44 +0100

In this paper we present the basics of a novel methodology for the development of simulation-based and augmented learning tools in the context of applied science and engineering. It is based on the extensive use of model order reduction, and particularly, of the so-called Proper Generalized Decomposition (PGD) method. This method provides a sort of meta-modeling tool without the need for prior computer experiments that allows the user to obtain real-time response in the solution of complex engineering or physical problems. This real-time capability also allows for its implementation in deployed, touch-screen, handheld devices or even to be immersed into electronic textbooks. We explore here the basics of the proposed methodology and give examples on a few challenging applications never until now explored, up to our knowledge.

Elliptic harbor wave model with perfectly matched layer and exterior bathymetry effects

María Jesús Samper — Wed, 11 Mar 2020 13:06:29 +0100

Standard strategies for dealing with the Sommerfeld condition in elliptic mild-slope models require strong assumptions on the wave field in the region exterior to the computational domain. More precisely, constant bathymetry along (and beyond) the open boundary, and parabolic approximations–based boundary conditions are usually imposed. Generally, these restrictions require large computational domains, implying higher costs for the numerical solver. An alternative method for coastal/harbor applications is proposed here. This approach is based on a perfectly matched layer (PML) that incorporates the effects of the exterior bathymetry. The model only requires constant exterior depth in the alongshore direction, a common approach used for idealizing the exterior bathymetry in elliptic models. In opposition to standard open boundary conditions for mild-slope models, the features of the proposed PML approach include (1) completely noncollinear coastlines, (2) better representation of the real unbounded domain using two different lateral sections to define the exterior bathymetry, and (3) the generation of reliable solutions for any incoming wave direction in a small computational domain. Numerical results of synthetic tests demonstrate that solutions are not significantly perturbed when open boundaries are placed close to the area of interest. In more complex problems, this provides important performance improvements in computational time, as shown for a real application of harbor agitation.

Space‐time NURBS‐enhanced finite elements for free‐surface flows in 2D

María Jesús Samper — Wed, 11 Mar 2020 12:03:34 +0100

The accuracy of numerical simulations of free‐surface flows depends strongly on the computation of geometric quantities like normal vectors and curvatures. This geometrical information is additional to the actual degrees of freedom and usually requires a much finer discretization of the computational domain than the flow solution itself. Therefore, the utilization of a numerical method, which uses standard functions to discretize the unknown function in combination with an enhanced geometry representation is a natural step to improve the simulation efficiency. An example of such method is the NURBS‐enhanced finite element method (NEFEM), recently proposed by Sevilla et al. The current paper discusses the extension of the spatial NEFEM to space‐time methods and investigates the application of space‐time NURBS‐enhanced elements to free‐surface flows. Derived is also a kinematic rule for the NURBS motion in time, which is able to preserve mass conservation over time. Numerical examples show the ability of the space‐time NEFEM to account for both pressure discontinuities and surface tension effects and compute smooth free‐surface forms. For these examples, the advantages of the NEFEM compared with the classical FEM are shown.

Proper generalized decomposition for parameterized Helmholtz problems in heterogeneous and unbounded domains: application to harbor agitation

María Jesús Samper — Wed, 11 Mar 2020 11:50:19 +0100

Solving the Helmholtz equation for a large number of input data in an heterogeneous media and unbounded domain still represents a challenge. This is due to the particular nature of the Helmholtz operator and the sensibility of the solution to small variations of the data. Here a reduced order model is used to determine the scattered solution everywhere in the domain for any incoming wave direction and frequency. Moreover, this is applied to a real engineering problem: water agitation inside real harbors for low to mid-high frequencies. The Proper Generalized Decomposition (PGD) model reduction approach is used to obtain a separable representation of the solution at any point and for any incoming wave direction and frequency. Here, its applicability to such a problem is discussed and demonstrated. More precisely, the contributions of the paper include the PGD implementation into a Perfectly Matched Layer framework to model the unbounded domain, and the separability of the operator which is addressed here using an efficient higher-order projection scheme. Then, the performance of the PGD in this framework is discussed and improved using the higher-order projection and a Petrov-Galerkin approach to construct the separated basis. Moreover, the efficiency of the higherorder projection scheme is demonstrated and compared with the higher-order singular value decomposition.

Real-time monitoring of thermal processes by reduced order modeling

María Jesús Samper — Wed, 11 Mar 2020 11:08:25 +0100

This work presents a simple technique for real-time monitoring of thermal processes. Real-time simulationbased control of thermal processes is a big challenge because high-fidelity numerical simulations are costly and cannot be used, in general, for real-time decision making. Very often, processes are monitored or controlled with a few measurements at some specific points. Thus, the strategy presented here is centered on fast evaluation of the response only where it is needed. To accomplish this, classical harmonic analysis is combined with recent model reduction techniques. This leads to an advanced harmonic methodology, which solves in real-time the transient heat equation at the monitored point. In order to apply the reciprocity principle, harmonic analysis is used in the space-frequency domain. Then, Proper Generalized Decomposition, a reduced order approach, pre-computes a transfer function able to produce the output response for a given excitation. This transfer function is computed offline and only once. The response at the monitoring point can be recovered performing a computationally inexpensive post-processing step. This last step can be performed online for real-time monitoring of the thermal process. Examples show the applicability of this approach for a wide range of problems ranging from fast temperature evaluation to inverse problems.

Hybridizable Discontinuous Galerkin with degree adaptivity for the incompressible Navier-Stokes equations

María Jesús Samper — Wed, 11 Mar 2020 11:01:32 +0100

A degree adaptive Hybridizable Discontinuous Galerkin (HDG) method for the solution of the incompressible Navier-Stokes equations is presented. The key ingredient is an accurate and computationally inexpensive a posteriori error estimator based on the super-convergence properties of HDG. The error estimator drives the local modification of the approximation degree in the elements and faces of the mesh, aimed at obtaining a uniform error distribution below a user-given tolerance in a given output of interest. Three 2D numerical examples are presented. High efficiency of the proposed error estimator is found, and an important reduction of the computational effort is shown with respect to non-adaptive computations, both for steady state and transient simulations.

On the natural stabilization of convection dominated problems using high order Bubnov–Galerkin finite elements

María Jesús Samper — Wed, 11 Mar 2020 10:51:11 +0100

In the case of dominating convection, standard Bubnov–Galerkin finite elements are known to deliver oscillating discrete solutions for the convection–diffusion equation. This paper demonstrates that increasing the polynomial degree (p-extension) limits these artificial numerical oscillations. This is contrary to a widespread notion that an increase of the polynomial degree destabilizes the discrete solution. This treatise also provides explicit expressions as to which polynomial degree is sufficiently high to obtain stable solutions for a given Péclet number at the nodes of a mesh.

Parametric solutions involving geometry: a step towards efficient shape optimization

María Jesús Samper — Wed, 11 Mar 2020 10:24:50 +0100

Optimization of manufacturing processes or structures involves the optimal choice of many parameters (process parameters, material parameters or geometrical parameters). Usual strategies proceed by defining a trial choice of those parameters and then solving the resulting model. Then, an appropriate cost function is evaluated and its optimality checked. While the optimum is not reached, the process parameters should be updated by using an appropriate optimization procedure, and then the model must be solved again for the updated process parameters. Thus, a direct numerical solution is needed for each choice of the process parameters, with the subsequent impact on the computing time. In this work we focus on shape optimization that involves the appropriate choice of some parameters defining the problem geometry. The main objective of this work is to describe an original approach for computing an off-line parametric solution. That is, a solution able to include information for different parameter values and also allowing to compute readily the sensitivities. The curse of dimensionality is circumvented by invoking the Proper Generalized Decomposition (PGD) introduced in former works, which is applied here to compute geometrically parametrized solutions

High-order continuous and discontinuous Galerkin methods for wave problems

María Jesús Samper — Wed, 11 Mar 2020 10:12:32 +0100

Three Galerkin methods-continuous Galerkin, Compact Discontinuous Galerkin, and hybridizable discontinuous Galerkin-are compared in terms of performance and computational efficiency in 2-D scattering problems for low and high-order polynomial approximations. The total number of DOFs and the total runtime are used for this correlation as well as the corresponding precision. The comparison is carried out through various numerical examples. The superior performance of high-order elements is shown. At the same time, similar capabilities are shown for continuous Galerkin and hybridizable discontinuous Galerkin, when high-order elements are adopted, both of them clearly outperforming compact discontinuous Galerkin. hree Galerkin methods—continuous Galerkin, Compact Discontinuous Galerkin, and hybridizable discontinuous Galerkin—are compared in terms of performance and computational efficiency in 2-D scattering problems for low and high-order polynomial approximations. The total number of DOFs and the total runtime are used for this correlation as well as the corresponding precision. The comparison is carried out through various numerical examples. The superior performance of high-order elements is shown. At the same time, similar capabilities are shown for continuous Galerkin and hybridizable discontinuous Galerkin, when high-order elements are adopted, both of them clearly outperforming compact discontinuous Galerkin

Efficiency of high-order elements for continuous and discontinuous Galerkin methods

María Jesús Samper — Wed, 11 Mar 2020 10:07:19 +0100

To evaluate the computational performance of high-order elements, a comparison based on operation count is proposed instead of runtime comparisons. More specifically, linear versus high-order approximations are analyzed for implicit solver under a standard set of hypotheses for the mesh and the solution. Continuous and discontinuous Galerkin methods are considered in two-dimensional and three-dimensional domains for simplices and parallelotopes. Moreover, both element-wise and global operations arising from different Galerkin approaches are studied. The operation count estimates show, that for implicit solvers, high-order methods are more efficient than linear ones.

Stability of anchored sheet wall in cohesive-frictional soils by FE limit analysis

María Jesús Samper — Wed, 11 Mar 2020 09:47:12 +0100

This study extends the limit analysis techniques used for the computation of strict bounds of the load factors in solids to stability problems with interfaces, anchors and joints. The cases considered include the pull-out capacity of multibelled anchors and the stability of retaining walls for multiple conditions at the anchor/soil and wall/soil interfaces. Three types of wall supports are examined: free standing wall, simply supported wall and anchored wall. The results obtained are compared against available experimental and numerical data. The conclusion drawn confirms the validity of numerical limit analysis for the computation of accurate bounds on limit loads and capturing failure modes of structures with multiple inclusions of complex interface and support conditions.

Dimensionless analysis of HSDM and application to simulation of breakthrough curves of highly adsorbent porous media

María Jesús Samper — Wed, 11 Mar 2020 09:41:13 +0100

The homogeneous surface diffusion model (HSDM) is widely used for adsorption modeling of aqueous solutions. The Biot number is usually used to characterize model behavior. However, some limitations of this characterization have been reported recently, and the Stanton number has been proposed as a complement to be considered. In this work, a detailed dimensionless analysis of HSDM is presented and limit behaviors of the model are characterized, confirming but extending previous results. An accurate and efficient numerical solver is used for these purposes. The intraparticle diffusion equation is reduced to a system of two ordinary differential equations, the transport-reaction equation is discretized by using a discontinuous Galerkin method, and the overall system evolution is integrated with a time-marching scheme. This approach facilitates the simulation of HSDM with a wide range of dimensionless numbers and with a correct treatment of shocks, which appear with nonlinear adsorption isotherms and with large Biot numbers and small surface diffusivity modulus. The approach is applied to simulate the breakthrough curves of granular ferric hydroxide. Published experimental data is adequately simulated.

PGD-Based computational vademecum for efficient design, optimization and control

María Jesús Samper — Wed, 11 Mar 2020 09:31:18 +0100

In this paper we are addressing a new paradigm in the field of simulation-based engineering sciences (SBES) to face the challenges posed by current ICT technologies. Despite the impressive progress attained by simulation capabilities and techniques, some challenging problems remain today intractable. These problems, that are common to many branches of science and engineering, are of different nature. Among them, we can cite those related to high-dimensional problems, which do not admit mesh-based approaches due to the exponential increase of degrees of freedom. We developed in recent years a novel technique, called Proper Generalized Decomposition (PGD). It is based on the assumption of a separated form of the unknown field and it has demonstrated its capabilities in dealing with high-dimensional problems overcoming the strong limitations of classical approaches. But the main opportunity given by this technique is that it allows for a completely new approach for classic problems, not necessarily high dimensional. Many challenging problems can be efficiently cast into a multidimensional framework and this opens new possibilities to solve old and new problems with strategies not envisioned until now. For instance, parameters in a model can be set as additional extra-coordinates of the model. In a PGD framework, the resulting model is solved once for life, in order to obtain a general solution that includes all the solutions for every possible value of the parameters, that is, a sort of computational vademecum. Under this rationale, optimization of complex problems, uncertainty quantification, simulation-based control and real-time simulation are now at hand, even in highly complex scenarios, by combining an off-line stage in which the general PGD solution, the vademecum, is computed, and an on-line phase in which, even on deployed, handheld, platforms such as smartphones or tablets, real-time response is obtained as a result of our queries.

Hybridizable discontinuous Galerkin p-adaptivity for wave propagation problems

María Jesús Samper — Wed, 11 Mar 2020 09:25:42 +0100

A p-adaptive hybridizable discontinuous Galerkin method for the solution of wave problems is presented in a challenging engineering problem. Moreover, its performance is compared with a high-order continuous Galerkin. The hybridization technique allows to reduce the coupled degrees of freedom to only those on the mesh element boundaries, whereas the particular choice of the numerical fluxes opens the path to a superconvergent postprocessed solution. This superconvergent postprocessed solution is used to construct a simple and inexpensive error estimator. The error estimator is employed to obtain solutions with the prescribed accuracy in the area (or areas) of interest and also drives a proposed iterative mesh adaptation procedure. The proposed method is applied to a nonhomogeneous scattering problem in an unbounded domain. This is a challenging problem because, on the one hand, for high frequencies, numerical difficulties are an important issue because of the loss of the ellipticity and the oscillatory behavior of the solution. And on the other hand, it is applied to real harbor agitation problems. That is, the mild slope equation in frequency domain (Helmholtz equation with nonconstant coefficients) is solved on real geometries with the corresponding perfectly matched layer to damp the diffracted waves. The performance of the method is studied on two practical examples. The adaptive hybridizable discontinuous Galerkin method exhibits better efficiency compared with a high-order continuous Galerkin method using static condensation of the interior nodes.

PGD-based “Computational Vademecum” for efficient design, optimization and control

María Jesús Samper — Wed, 11 Mar 2020 09:14:25 +0100

D espite the impressive progresses attained by simulation capabilities and techniques, some challenging problems remain today intractable. These prob- lems, that are common to many branches of science and engineering, are of differ- ent nature. Among them, we can cite those related to high-dimensional models, on which mesh-based approaches fail due to the exponential increase of degrees of freedom. Other challenging scenarios concern problems requiring many direct solutions (optimization, inverse identifica- tion, uncertainty quantification ! ) or those needing very fast solutions (real time simulation, simulation based control ! ).

Dynamic model and numerical simulation for a new eccentric rotary multiphase pump

Fei Wang — Wed, 11 Mar 2020 04:29:26 +0100

In order to simplify the manufacture of multiphase pump and improve the operating flexibility for gas void fraction (GVF) of the multiphase fluids that the pump transported, an eccentric rotary multiphase pump (ERMP) is presented. In this study, the structural characteristics and working principle of the ERMP are presented first. Then, the kinematic and force models are established for the key components- sliding vane and rotor. The velocity, acceleration, and force equations with shaft rotation angle are derived for each component. Based on the established models, simulations are performed for an ERMP prototype. The simulated results show that the areas opposite the sliding vane and apart from the center of the rotor have larger velocities and wear problem. Moreover, the binding force, pressure difference induced force and the normal force exercise a negative effect on the friction at the sliding vane sides and rotor. Lower shaft speed and smaller eccentric distance of the crankshaft are helpful to reduce this effect. The findings confirm that the proposed ERMP is suitable for multiphase transportation and has a higher mechanical efficiency for its advanced structure and working principle.

Estimation of crack opening from a two-dimensional continuum-based finite element computation

María Jesús Samper — Tue, 10 Mar 2020 16:26:22 +0100

Damage models are capable of representing crack initiation and mimicking crack propagation within a continuum framework. Thus, in principle, they do not describe crack openings. In durability analyses of concrete structures however, transfer properties are a key issue controlled by crack propagation and crack opening. We extend here a one dimensional approach for estimating a crack opening from a continuum based fi nite element calculation to two dimensional cases. The technique operates in the case of mode I cracking described in a continuum setting by a nonlocal isotropic damage model. We used the global tracking method to compute the idealized crack location as a post treatment procedure. The orig inal one dimensional problem devised in Dufour et al . [4] is recovered as pro fi les of deformation orthog onal to the idealized crack direction are computed. An estimate of the crack opening and an error indicator are computed by comparing fi nite element deformation pro fi les and theoretical pro fi les corresponding to a displacement discontinuity. Two estimates have been considered: In the strong approach, the maxima of the pro fi les are assumed to be equal; in the weak approach, the integrals of each pro fi le are set equal. Two dimensional numerical calculations show that the weak estimates perform better than do the strong ones. Error indicators, de fi ned as the distance between the numerical and theoretical pro fi les, are less than a few percentages. In the case of a three point bending, test results are in good agreement with experimental data, with an error lower than 10% for widely opened crack ( > 40 m m )

High-order implicit time integration for unsteady incompressible flows

María Jesús Samper — Tue, 10 Mar 2020 16:20:45 +0100

The spatial discretization of unsteady incompressible Navier–Stokes equations is stated as a system of differential algebraic equations, corresponding to the conservation of momentum equation plus the constraint due to the incompressibility condition. Asymptotic stability of Runge–Kutta and Rosenbrock methods applied to the solution of the resulting index-2 differential algebraic equations system is analyzed. A critical comparison of Rosenbrock, semi-implicit, and fully implicit Runge–Kutta methods is performed in terms of order of convergence and stability. Numerical examples, considering a discontinuous Galerkin formulation with piecewise solenoidal approximation, demonstrate the applicability of the approaches and compare their performance with classical methods for incompressible flows.

A note on upper bound formulations in limit analysis

María Jesús Samper — Tue, 10 Mar 2020 15:34:16 +0100

In this paper we study some recent formulations for the computation of upper bounds in limit analysis. We show that a previous formulation presented by the authors does not guarantee the strictness of the upper bound, nor does it provide a velocity field that satisfies the normality rule everywhere. We show that these deficiencies are related to the quadrature employed for the evaluation of the dissipation power. We derive a formulation that furnishes a strict upper bound of the load factor, which in fact coincides with a formulation reported in the literature. From the analysis of these formulations we propose a post-process which consists in computing exactly the dissipation power for the optimum upper bound velocity field. This post-process may further reduce the strict upper bound of the load factor in particular situations. Finally, we also determine the quadratures that must be used in the elemental and edge gap contributions so that they are always positive and their addition equals the global bound gap.

A simple shock-capturing technique for high-order discontinuous Galerkin methods

María Jesús Samper — Tue, 10 Mar 2020 15:22:01 +0100

This article presents a novel shock-capturing technique for the discontinuous Galerkin (DG) method. The technique is designed for compressible flow problems, which are usually characterized by the presence of strong shocks and discontinuities. The inherent structure of standard DG methods seems to suggest that they are especially adapted to capture shocks because of the numerical fluxes based on suitable approximate Riemann solvers, which, in practice, introduces some stabilization. However, the usual numerical fluxes are not sufficient to stabilize the solution in the presence of shocks for large high-order elements. Here, a new basis of shape functions is introduced. It has the ability to change locally between a continuous or discontinuous interpolation depending on the smoothness of the approximated function. In the presence of shocks, the new discontinuities inside an element introduce the required stabilization because of numerical fluxes. Large high-order elements can therefore be used and shocks captured within a single element, avoiding adaptive mesh refinement and preserving the locality and compactness of the DG scheme. Several numerical examples for transonic and supersonic flows are studied to demonstrate the applicability of the proposed approach.

One-dimensional shock-capturing for high-order discontinuous Galerkin methods

María Jesús Samper — Tue, 10 Mar 2020 15:12:18 +0100

Discontinuous Galerkin methods have emerged in recent years as an alternative for nonlinear conservation equations. In particular, their inherent structure (a numerical flux based on a suitable approximate Riemann solver introduces some stabilization) suggests that they are specially adapted to capture shocks. However, numerical fluxes are not sufficient to stabilize the solution in the presence of shocks. Thus, slope limiter methods, which are extensions of finite volume methods, have been proposed. These techniques require, in practice, mesh adaption to localize the shock structure. This is is more obvious for large elements typical of high-order approximations. Here, a new approach based on the introduction of artificial diffusion into the original equations is presented. The order is not systematically decreased to one in the presence of the shock, large high-order elements can be used, and several linear and nonlinear tests demonstrate the efficiency of the proposed methodology.

Are High-order and Hybridizable Discontinuous Galerkin methods competitive?

María Jesús Samper — Tue, 10 Mar 2020 15:05:23 +0100

The talk covered several issues motivated by a practical engineering wave propagation problem: real-time evaluation of wave agitation in harbors. The first part, presented the application of a reduced order model in the framework of a Helmholtz equation with non-constant coefficients in an unbounded domain. This problem requires large numbers of degrees of freedom (ndof) because relatively high frequencies with small (compared with the domain size) geometric features must be considered

Interactive simulation on a smart Phone

María Jesús Samper — Tue, 10 Mar 2020 14:58:13 +0100

Traditionally, Simulationbased Engineering Sciences (SBES) made use of static data inputs to perform the simulations. Namely parameters of the model, boundary conditions, etc. were traditionally obtained by experimentation and could not be modified during the course of the simulation. More recently, large efforts have been invested in developing dynamic datadriven application systems (DDDAS): systems in which measurements and simulations are continuously influencing each other in a symbiotic manner. It should be understood that measurements should be incorporated in real time to the simulations, while simulations could eventually control the way in which measurements are done.

Proper generalized decomposition based dynamic data-driven control of material forming processes

María Jesús Samper — Tue, 10 Mar 2020 14:51:58 +0100

Dynamic Data-Driven Application Systems—DDDAS—appear as a new paradigm in the field of applied sciences and engineering, and in particular in Simulation-based Engineering Sciences. By DDDAS we mean a set of techniques that allow to link simulation tools with measurement devices for real-time control of systems and processes. In this paper a novel simulation technique is developed with an eye towards its employ in the field of DDDAS. The main novelty of this technique relies in the consideration of parameters of the model as new dimensions in the parametric space. Such models often live in highly multidimensional spaces suffering the so-called curse of dimensionality. To avoid this problem related to mesh-based techniques, in this work an approach based upon the Proper Generalized Decomposition—PGD—is developed, which is able to circumvent the redoubtable curse of dimensionality. The approach thus developed is composed by a marriage of DDDAS concepts and a combination of PGD “off-line” computations, linked to “on-line” post-processing. In this work we explore some possibilities in the context of process control, malfunctioning identification and system reconfiguration in real time, showing the potentialities of the technique in real engineering contexts.

NURBS-Enhanced Finite Element Method (NEFEM)

María Jesús Samper — Tue, 10 Mar 2020 14:36:23 +0100

The development of NURBS-Enhanced Finite Element Method (NEFEM) is revisited. This technique allows a seamless integration of the CAD boundary representation of the domain and the finite element method (FEM). The importance of the geometrical model in finite element simulations is addressed and the benefits and potential of NEFEM are discussed and compared with respect to other curved finite element techniques.

3D NURBS-enhanced finite element method (NEFEM)

María Jesús Samper — Tue, 10 Mar 2020 14:28:25 +0100

This paper presents the extension of the recently proposed NURBS-enhanced finite element method (NEFEM) to 3D domains. NEFEM is able to exactly represent the geometry of the computational domain by means of its CAD boundary representation with non-uniform rational B-splines (NURBS) surfaces. Specific strategies for interpolation and numerical integration are presented for those elements affected by the NURBS boundary representation. For elements not intersecting the boundary, a standard finite element rationale is used, preserving the efficiency of the classical FEM. In 3D NEFEM special attention must be paid to geometric issues that are easily treated in the 2D implementation. Several numerical examples show the performance and benefits of NEFEM compared with standard isoparametric or cartesian finite elements. NEFEM is a powerful strategy to efficiently treat curved boundaries and it avoids excessive mesh refinement to capture small geometric features.

Comparison of high-order curved finite elements

María Jesús Samper — Tue, 10 Mar 2020 14:15:09 +0100

Several finite element techniques used in domains with curved boundaries are discussed and compared, with particular emphasis in two issues: the exact boundary representation of the domain and the consistency of the approximation. The influence of the number of integration points on the accuracy of the computation is also studied. Two-dimensional numerical examples, solved with continuous and discontinuous Galerkin formulations, are used to test and compare all these methodologies. In every example shown, the recently proposed NURBS-enhanced finite element method (NEFEM) provides the maximum accuracy for a given spatial discretization, at least one order of magnitude more accurate than classical isoparametric finite element method (FEM). Moreover, NEFEM outperforms Cartesian FEM and p-FEM, stressing the importance of the geometrical model as well as the relevance of a consistent approximation in finite element simulations.

Discontinuous Galerkin methods for the Navier–Stokes equations using solenoidal approximations

María Jesús Samper — Tue, 10 Mar 2020 14:00:24 +0100

An interior penalty method and a compact discontinuous Galerkin method are proposed and compared for the solution of the steady incompressible Navier–Stokes equations. Both compact formulations can be easily applied using high-order piecewise divergence-free approximations, leading to two uncoupled problems: one associated with velocity and hybrid pressure, and the other one only concerned with the computation of pressures in the elements interior. Numerical examples compare the efficiency and the accuracy of both proposed methods.

A new least-squares approximation of affine mappings for sweep algorithms

María Jesús Samper — Tue, 10 Mar 2020 13:51:57 +0100

This paper presents a new algorithm to generate hexahedral meshes in extrusion geometries. Several algorithms have been devised to generate hexahedral meshes by projecting the cap surfaces along a sweep path. In all of these algorithms the crucial step is the placement of the inner layer of nodes. That is, the projection of the source surface mesh along the sweep path. From the computational point of view, sweep methods based on a least-squares approximation of an affine mapping are the fastest alternative to compute these projections. Several functionals have been introduced to perform the least-squares approximation. However, for very simple and typical geometrical configurations they may generate low-quality projected meshes. For instance, they may induce skewness and flattening effects on the projected discretizations. In addition, for these configurations the minimization of these functionals may lead to a set of normal equations with singular system matrix. In this work we analyze previously defined functionals. Based on this analysis we propose a new functional and show that its minimization overcomes these drawbacks. Finally, we present several examples to assess the properties of the proposed functional.