Scipedia: Eugenio Oñate's Monographs

Direct computation of instability points with inequality constraints using the Finite Element Method

María Jesús Samper — Thu, 01 Feb 2018 12:08:37 +0100

The objective of this monograph is to apply the computation methods for critical points to more complex mechanical problems involving inequality constraints. Prior to this extension to a new class of problems appropriate methods among the existing ones for the critical point detection are chosen. Therefore the CDM and the extended system as the most primising techniques will be compared and evaluated.

A one step prediction of the critical load based on the extended system will be developed that enables a better evaluation. The possibilities of a combination of both methods will be examined. A conceivable combination is to use the prediction of a CDM computation as starting value for the extended system and enhance the convergence of the latter.

In a second step critical point detection methods are extended to problems that involve inequality constraints. In this context constitutive damage models and contact problems are studied.

Tratamiento numérico de los Materiales Compuestos

María Jesús Samper — Tue, 22 May 2018 14:46:15 +0200

La principal dificultad que se encuentra en el momento de diseñar estructuras
con materiales compuestos es la falta de modelos constitutivos que permitan si- mular su
comportamiento. Las técnicas analíticas convencionales utilizadas para el estudio de materiales
simples isótropos no resultan adecuadas para el análisis de materiales compuestos. Tampoco ha
resultado satisfactoria la representación de un compuesto mediante un único material ortótropo con
propiedades del conjunto. Puede observarse en distintas referencias los intentos que ha habido para
modelar el comportamiento de materiales compuestos, utilizando la técnica de elementos fi- nitos
para el análisis y diseño de estructuras, donde la correlación entre los análisis y los resultados
experimentales no resulta satisfactoria (Ali, 1996) (Klintworth y Macmillian, 1992). El proceso de
diseño de componentes en materiales compuestos se ha basado, principalmente, en métodos empíricos,
observándose en la literatura la ausencia de análisis o simulaciones del comportamiento de
materiales compuestos sometidos a niveles de esfuerzos que sobrepasan el límite elástico.

Métodos evolutivos en la optimización topológica

María Jesús Samper — Mon, 28 May 2018 13:39:22 +0200

En este trabajo se desarrollan diferentes métodos evolutivos para la optimización topológica de estructuras resistentes: Algoritmo Genético, Estrategias Evolutivas, Método de Escalada, Método de Baluja, Métodos de Segag y Schoenauer, Recocido Simulado

Cálculo del comportamiento de la mampostería mediante elementos finitos

María Jesús Samper — Mon, 28 May 2018 13:46:21 +0200

La mampostería es uno de los materiales de construcción con mayor abanico de usos, ya
sea en el pasado como en el presente, así es como hoy en día también se puede encontrar
en la construcción de edificaciones modernas. Los materiales utilizados a lo largo de la
historia como elementos componentes de la mampostería han sido muchos y muy
variados: desde la simple roca unida con mortero de cal (sillería), pasando por los
enormes bloques de mármol usados en la construcción de los grandes monumentos del
apogeo de la arquitectura del Renacimiento, hasta llegar a elementos cerámicos
refractarios como los que se utilizan para la construcción de hornos, centrales nucleares e
incluso como aislante térmico de naves espaciales.

Los métodos de cálculo avanzado (modelos constitutivos de la mecánica del medio
continuo) deben ser el pilar sobre el que desarrollar elementos más objetivos de análisis
estructural de la mampostería. Los elementos finitos son una herramienta potente en la que apoyar
el cálculo de la obra de fábrica pero, debido a que ésta tiene un tamaño pequeño respecto a las
dimensiones globales de la estructura, se hacen inviables desde el punto de vista computacional.

La necesidad de encontrar un método que equilibre sencillez, objetividad y rapidez de cálculo es la
que motiva el desarrollo de formulaciones con tratamiento al nivel de macromodelo de la
mampostería. La inquietud por conseguir este equilibrio hace a Jacob Lubliner y Sergio Oller
sentar las bases que permitirán el desarrollo del modelo
constitutivo homogeneizado que se presenta en este trabajo.

Finite element methods for advection-diffusion-absorption and fluid flow problems

María Jesús Samper — Wed, 15 Sep 2021 12:36:26 +0200

The objective of the work is to develop a numerical tool to describe how the concentration of one or more substances distributed in a fluid environment changes under the effect of three transport processes: advection, diffusion and absorption. For that purpose, it is essential to know the interaction of the transported substance with the fluid medium.

The work aims to develop stabilized numerical methods for solving the transport and fluid flow equations in a coupled manner for greater accuracy, efficiency and speed when predicting the motion of the transported substances in the fluid. Emphasis is put in the transport of substances in fluids at high P\'eclet numbers.

The practical motivation of the work is predicting the transport of a pollutant in air in urban environments.

The work document summarizes the research published in three papers published in JCR journals of high impact. The author of the work is also the first author in the three papers. The papers are attached to the document in the corresponding chapters.

The description of the work developments has been organized as follows. First, we present the research carried out in the work for the development of a generalized stabilized Finite Increment Calculus-Finite Element Method (FIC--FEM) formulation for solving the multidimensional transient advection-diffusion-absorption equation. The starting point of the developments are the governing equations for the multidimensional steady advection-diffusion-absorption and the unidimensional transient advection-diffusion-absorption problems obtained via the FIC procedure. The good behaviour of the new FIC--FEM formulation is shown in several examples of application. This work was published in the first of the three papers mentioned.

In the following chapter we present an innovative numerical method for solving transport problems with high values of advection and / or absorption. A Lagrangian approach based on the updated version of the classical Particle Finite Element Method (PFEM) has been developed to calculate the advection of substances in fluids, while a Eulerian strategy based on the stabilized FIC--FEM formulation is adopted to compute diffusion and absorption effects. The new semi-Lagrangian approach has been validated in its application of a series of academic examples of transport of substances for different values of the P\'eclet and Damk\"ohler numbers.

Finally, we derive a procedure for coupling the fluid and transport equations to model the distribution of a pollutant in a street canyon. In our case, we have considered black carbon (BC) as the pollutant. The evolution of the fluid flow is calculated with a standard stabilized finite element method using the Quasi-Static Variational Multiscale (QS-VMS) technique. For the temperature and pollutant transport we use the semi-Lagrangian procedure developed in the work.

Several examples of application have been solved to illustrate the accuracy and practicability of the proposed numerical tool for predicting the transport of a pollutant in air in urban environments. One of the examples are presented in the third paper, while another academic one is presented in the appendix of this document.

A fully Lagrangian formulation for fluid-structure interaction between free-surface flows and multi-fracturing solids and structures

María Jesús Samper — Wed, 03 Feb 2021 16:15:49 +0100

It is well known that in civil engineering structures are designed so that
they remain, whenever possible, in an elastic regime and with their mechanical
properties intact. The truth is that in reality there are uncertainties
either in the execution of the work (geometric errors or material quality) or
during its subsequent use (loads not contemplated or its value has been
estimated incorrectly) that can lead to the collapse of the structure. This
is why the study of the failure of structures is inherently interesting and,
once is known, its design can be improved to be the less catastrophic as
possible or to dissipate the maximum energy before collapsing. Another
area of application of fracture mechanics is that of processes of which
interest lies in the breakage or cracking of a medium. Within the mining
engineering we can enumerate several processes of this nature, namely:
hydraulic fracture processes or fracking, blasting for tunnels, explosion of
slopes in open pit mines, among others. Equally relevant is the analysis of
structural failures due to natural disasters, such as large avenues or even
tsunamis impacting protection structures such as walls or dikes. In this
work numerous implementations and studies have been made in relation
to the mentioned processes.
That said, the objective of this work is to develop an advanced numerical
method capable of simulating multi-fracture processes in materials and
structures. The general approach of the proposed method can be seen in
various publications made by the author and directors of this work. This
methodology is meant to cover the maximum spectrum of engineering
applications possible. For this purpose, a coupled formulation of the Finite
Element Method (FEM) and the Discrete Element Method (DEM) is used,
which employs an isotropic damage constitutive model to simulate the
initial degradation of the material and, once the strength of the material
has been completely exhausted, those Finite Element (FE) are removed
from the FEM mesh and a set of Discrete Element (DE) are generated
at its nodes. In addition to ensure the conservation of the mass of the
system, these DE prevent the indentation between the fissure planes
thanks to the frictional repulsive forces calculated by the DEM, if any.
Additionally, in this work it has been studied how the proposed coupled
method named FEM-DEM together with the smoothing of stresses based on the super-convergent patch is able to obtain reasonably meshindependent
results but, as one can imagine, the crack width is directly
related to the size of the elements that have been removed. This favours
the inclusion of an adaptive remeshing technique that will refine the mesh
where it is required (according to the Hessian of a nodal indicator of interest)
thus improving the discretization quality of the crack obtained and
thereby optimizing the simulation cost. In this sense, the procedures for
mapping nodal and internal variables as well as the calculation of the
nodal variable of interest will be discussed.
As far as the studies of natural disasters are concerned, especially
those related to free-surface water flows such as tsunamis, one more
level of coupling between the aforementioned method FEM-DEM and one
Computational Fluid Dynamics (CFD) formulation commonly referred to as
Particle Finite Element Method (PFEM) has been implemented. With this
strong coupled formulation, many cases of wave impacts and fluid flows
have been simulated against solid structures such as walls and dikes,
among others.

Innovative mathematical and numerical models for studying the deformation of shells during industrial forming processes with the Finite Element Method

María Jesús Samper — Wed, 28 Oct 2020 13:10:16 +0100

This document contains the result resulting from the work in the doctoral thesis Innovative mathematical
and numerical models for studying the deformation of shells during industrial forming processes with the
Finite Element Method. The objective of this thesis is to contribute to the development of finite element
methods for the analysis of the stamping processes, an area of problems with a very clear industrial
application. Indeed these kinds of problems involve multiple disciplines and require the understanding
of different mechanical problems, being the most relevant disciplines the continuous mechanics, the
plasticity, contact problems, among others, depending of the problematic of study.

Towards the Virtual Wind Tunnel for civil engineering applications

María Jesús Samper — Tue, 06 Oct 2020 14:19:06 +0200

This monograph develops a numerical tool (the Virtual Wind Tunnel, VWT) for the
reso-lution of problems involving fluid flow around structures. Due to the limitations
that traditional methods may have in this context, the VWT is based on the use of fixed
mesh technologies (CutFEM-type) combined with an implicit representation of the
embedded bodies.
One of the main contributions of the monograph is the use of such fixed mesh methods to
solve lightweight thin-walled structures problems. Hence, two embedded formulations
capable of representing the flow around bodies with and without internal volume are
proposed. The first one results in a simpler implementation and lower computational
effort but can only represent a slip behavior of the wall. The second one gets rid of such
limitation by including a Nitsche imposition of the Navier-slip condition, thus allowing
modelling any wall behavior as a wall law would do.
The applicability range of the VWT includes the fluid–structure i nteraction problem
(FSI). To that purpose an improvement for the boundary condition imposition of the
FM-ALE algorithm mesh motion problem is also proposed. Moreover, the implementation,
which has been conceived to be easily extended to any other coupled problem, is
also treated.
The validation of the technologies within the VWT includes multiple theoretical test
cases as well as feasible industrial applications. Among these, the FSI analysis of a
4-point tent during a strong wind episode deserves to be highlighted as it showcases the
achievement of the initial objective of the monograph.

Discrete-continuum hybrid modelling of flowing and static regimes

María Jesús Samper — Tue, 04 Feb 2020 09:34:50 +0100

Bulk handling, transport and processing of granular materials and powders are fundamental
operations in a wide range of industrial processes and geophysical phenomena. Particulate materials,
which can be found in nature, are usually characterized by a grain size which can range across several
scales: from nanometre to the order of metre. Depending on the volume fraction and on the shear strain
conditions, granular materials can have different behaviours and often can be expressed as a new state
of matter with properties of solids, liquids and gases. For the above reasons, both the experimental
and the numerical analysis of granular media is still a difficult task and the prediction of their dynamic
behaviour still represents, nowadays, an important challenge. The main goal of the current monograph
is the development of a numerical strategy with the objective of studying the macroscopic behaviour
of dry granular flows in quasi-static and dense flow regime. The problem is defined in a continuum
mechanics framework and the balance laws, which govern the behaviour of a solid body, are solved by
using a Lagrangian formalism. The Material Point Method (MPM), a particle-based method, is chosen
due to its features which make it very suitable for the solution of large deformation problems involving
complex history-dependent constitutive laws. An irreducible formulation using a Mohr-Coulomb
constitutive law, which takes into account geometric non-linearities, is implemented within the MPM
framework. The numerical strategy is verified and validated against several benchmark tests and
experimental results, available in the literature. Further, a mixed formulation is implemented for the
solution of granular flows that undergo undrained conditions. Finally, the developed MPM strategy is
used and tested against the experimental study performed for the characterization of the flowability of
several types of sucrose. The capabilities and limitations of this numerical strategy are observed and
discussed and the bases for future research are outlined.

A framework for developing finite element codes for multi- disciplinary applications

María Jesús Samper — Wed, 27 Nov 2019 14:45:43 +0100

The world of computing simulation has experienced great progresses in recent years and requires
more exigent multidisciplinary challenges to satisfy the new upcoming demands. Increasing the
importance of solving multi-disciplinary problems makes developers put more attention to these
problems and deal with difficulties involved in developing software in this area.
Conventional finite element codes have several difficulties in dealing with multi-disciplinary
problems. Many of these codes are designed and implemented for solving a certain type of problems,
generally involving a single field. Extending these codes to deal with another field of analysis
usually consists of several problems and large amounts of modifications and implementations.
Some typical difficulties are: predefined set of degrees of freedom per node, data structure with
fixed set of defined variables, global list of variables for all entities, domain based interfaces, IO
restriction in reading new data and writing new results and algorithm definition inside the code.
A common approach is to connect different solvers via a master program which implements the
interaction algorithms and also transfers data from one solver to another. This approach has been
used successfully in practice but results duplicated implementation and redundant overhead of
data storing and transferring which may be significant depending to the solvers data structure.
The objective of this work is to design and implement a framework for building multi-disciplinary
finite element programs. Generality, reusability, extendibility, good performance and memory efficiency
are considered to be the main points in design and implementation of this framework.
Preparing the structure for team development is another objective because usually a team of experts
in different fields are involved in the development of multi-disciplinary code.
Kratos, the framework created in this work, provides several tools for easy implementation
of finite element applications and also provides a common platform for natural interaction of its
applications in different ways. This is done not only by a number of innovations but also by
collecting and reusing several existing works.
In this work an innovative variable base interface is designed and implemented which is used
at different levels of abstraction and showed to be very clear and extendible. Another innovation
is a very efficient and flexible data structure which can be used to store any type of data in a
type-safe manner. An extendible IO is also created to overcome another bottleneck in dealing with
multi-disciplinary problems. Collecting different concepts of existing works and adapting them
to coupled problems is considered to be another innovation in this work. Examples are using an
interpreter, different data organizations and variable number of dofs per node. The kernel and
application approach is used to reduce the possible conflicts arising between developers of different
fields and layers are designed to reflect the working space of different developers also considering
their programming knowledge. Finally several technical details are applied in order to increase the
performance and efficiency of Kratos which makes it practically usable.
This work is completed by demonstrating the framework’s functionality in practice. First some
classical single field applications like thermal, fluid and structural applications are implemented and
used as benchmark to prove its performance. These applications are used to solve coupled problems
in order to demonstrate the natural interaction facility provided by the framework. Finally some
less classical coupled finite element algorithms are implemented to show its high flexibility and
extendibility.

Regularized maxwell equations and nodal finite elements for electromagnetic field computations in frequency domain

María Jesús Samper — Tue, 26 Nov 2019 12:05:24 +0100

In this work we present an alternative approach to the usual finite element formulation based on edge elements and double-curl Maxwell equations. This alternative approach is based on nodal elements and regularized Maxwell equations. The advantages are that, without adding extra unknowns (such as Lagrange multipliers), it provides spurious-free solutions and well-conditioned matrices. Besides, its integral representation involves a less singular kernel (order 1 instead of 3), which makes this approach best suited to hybridization with integral numerical techniques. On the other hand, a new set of difficulties arises that were not present in the classical formulation. The main drawback is that a globally wrong solution is obtained when the electromagnetic field has a singularity in the problem domain. Also, boundary conditions and field discontinuities are more laborious to implement. This work explains how to overcome these difficulties and demonstrates that accurate solutions can be obtained with nodal elements and the regularized formulation.
We also present ERMES, the C++ implementation of the finite element approach depicted above and the main deliverable of this work. We compute with ERMES the scattering parameters of microwave filters and the specific absorption rate induced in a body when exposed to electromagnetic fields. ERMES is also the computational tool used in two novel numerical models introduced in this work. The first one characterizes electromagnetic metal forming processes and the second one the transfer impedance of cable shields.
The electromagnetic metal forming model calculates the driving Lorentz force and estimates the optimum frequency at which it is attained the maximum workpiece deformation. The main advantage of the approach is that it provides an explicit relation between the capacitance of the capacitor bank and the frequency of the discharge, which is a key parameter in the design of an electromagnetic forming system. The successful application of the regularized formulation in this model reveals its excellent behavior in the low-frequency (quasi-static) regime.
The second numerical model introduced in this work computes the transfer impedance of cable shields. The model reproduces the high frequency behavior of the transfer impedance more accurately than the approaches found in the literature and, moreover, it is able to analyze a wider variety of geometries and materials.

Numerical simulation of industrial sheet forming processes

María Jesús Samper — Fri, 22 Nov 2019 13:19:11 +0100

This monograph presents different finite element based mathematical models and computational methods for numerical simulation of industrial sheet metal forming processes.

II International Workshop. Information Technologies and Computing Techniques for the Agro-Food Sector

María Jesús Samper — Fri, 22 Nov 2019 12:50:08 +0100

This monographs of proceedings includes all extended abstracts, which will be presented during the AfoT. These presentations will cover a wide range of topics:

- Modelling and simulation operations and process plants.
- Food process optimisation, scheduling and control.
- Food properties measurements and quality control.
- Simulation of complex processes, for example those requiring computational fluid dynamics, CFD.
- The use of new information technologies to develop decision support sytems.

Métodos avanzados de cálculo de estructuras de materiales compuestos

María Jesús Samper — Fri, 22 Nov 2019 12:34:23 +0100

Se presenta una panorámica del estado del arte de los métodos más actuales para análisis de estructuras con materiales compuestos, incidiendo particularmente en los métodos para análisis de vehículos industriales como materiales compuestos

Simulación numérica de la aerodinámica de vehículos

María Jesús Samper — Fri, 22 Nov 2019 12:19:10 +0100

Este trabajo analiza las posibilidades de simulación numérica del flujo aerodinámico alrededor de vehículos automotores, desde un doble punto de vista: metodología a utilizar y desarrollo de las aplicaciones que tal tipo de estudios tienen en los vehículos automotores.

A lo largo del desarrollo del mismo, quedan patentes una serie de herramientas mediante las cuales es posible realizar tal tipo de simulación numérica. Dichos estudios revisten una gran importancia si se quiere conocer el comportamiento de los vehículos automotores en condiciones de operación, afectando a aspectos tan importantes como seguridad, ruido, estabilidad, consumo de combustible, ventilación, etc.

Discrete Volume Method. A variational approach for brittle fracture

María Jesús Samper — Tue, 28 May 2019 14:18:09 +0200

The Discrete Element Method has been used to simulate fracture dynamics beacuse its inherent capacity to reproduce multi-body interaction, but in the case of elasticity mechanics the microparameters of the numerical model, required to replicate the properties of the material, are difficult to calibrate. On the other hand, damage models based on finite element strategies can easily reproduce the properties of the media but they can not simulate the dynamics of multiple fractures.

We propose a numerical approach, the Discrete Volume Method, to simulate fracture of brittle materials without the disadvantages mentioned, by combining the benefits of variational formulations and the numerical convenience of discrete element method to capture the dynamics of cracks. The Discrete Volume Method does not have microparameters, since the displacements are computed using the material properties and the fracture mechanism is controlled by an auxiliary damage field.

Within this work we discuss a numerical strategy to solve the elasticity problem upon unstructured and non conforming meshes, allowing all kinds of flat-faced elements (polygons in 2D and polyhedra in 3D). The core of the formulation relies on two numerical procedures the Control Volume Function Approximation (CVFA), and the polynomial interpolation in the neighborhood of the control volumes, which is used to solve the surface integrals resulting from applying the divergence theorem. By comparing the estimated stress against the analytical stress field of the well known test of an infinite plate with a hole, we show that this conservative approach is robust and accurate. A similar strategy is used to get the damage field solution.

In order to coupling both fields, displacement and damage, we use a finite increment arrangement for reducing the resdidual of elastic equation within each time step.

We develop a numerical formulation for time discretization based on the analytical solution of the differential equation resulting from assuming a continuous variation of internal forces of the system between time steps.

Finally, we show the effectiveness of the methodology by performing numerical experiments and comparing the solutions with published results.

Estudio de estimación de parámetros constitutivos en el método de elementos discretos o de partículas

María Jesús Samper — Fri, 17 May 2019 14:45:36 +0200

Se presenta un modelo numérico que emplea elementos discretos esféricos o también denominados elementos distintos. Este modelo se aplica en la simulación de rocas, suelos, medios granulares y otros materiales. El movimiento de elementos esféricos se describe por medio de las ecuaciones de dinámica del cuerpo rígido. Se emplea en la formulación una integración explícita, la cual, brinda una buena eficiencia computacional.

Numerical simulation of multifluid flows with the particle finite element method

María Jesús Samper — Fri, 17 May 2019 14:19:56 +0200

In this monograph we have focused on understanding the basic physical principles of multi-fluid flows and the difficulties that arise in their numerical simulation. We have extended the Particle Finite Element Method to problems involving several different fluids with the aim of exploiting the fact that Lagrangian methods are specially well suited for tracking any kind of interfaces. We have developed a numerical scheme able to deal with large jumps in the physical properties (density and viscosity), include surface tension, and accurately represent all types of discontinuities in the flow variables at the interface. The scheme is based on
decoupling the nodes position, velocity and pressure variables through the Picard linearization and a pressure segregation method which takes into account the interface conditions. The interface has been defined to be aligned with the moving mesh, so that it remains sharp along time. Furthermore, pressure degrees of freedom have been duplicated at the interface nodes to represent the discontinuity of this variable due to surface tension and variable viscosity, and the mesh has been refined in the vicinity of the interface to improve the accuracy of the computations.

Computational model of the human urinary bladder

María Jesús Samper — Fri, 17 May 2019 13:54:32 +0200

The proposal of an artificial bladder is still a challenge to overcome. Bladder cancer is among the most frequent cases of oncologic diseases in United States and Europe. It is considered a major medical problem once this disease has high rates of reoccurrence, often leading to the extirpation of this organ. The most refined solution to replace this organ is the ileal bladder, which consists of a neobladder made of the patient’s intestinal tissue. Unfortunately this solution presents not only functional mechanical problems, described on the literature as voiding and leaking problems, but also biological ones (i.e. bone loss, given the absorption by the intestine of substances that should be eliminated from the organism). Urged by the urological community of the Hospital Clinic de Barcelona and backgrounded by its experience in the numerical simulation of biomedical structures, the Center of Numerical Methods in Engineering (CIMNE) had the initiative to provide the research of the mechanics of the urinary bladder and the simulation of fluid structure interaction (FSI) to account for the filling and voiding of this organ with urine. The Finite Element Method (FEM) simulation of the real bladder and the comprehensive understanding of the mechanics of this organ and its interaction with urine will give the possibility to propose geometrical improvements and study suitable materials for an artificial solution to address the cases on which the bladder needs to be removed. To reach this goal, first we proceeded to the bibliographic review of mathematical models of the urinary apparatus and to a comprehensive study of the physiology and dynamics of the bladder. A review of the major urological structures, kidney, ureter and urethra, takes place. To consider boundary conditions other surrounding structures to the urinary system are also studied. In the second part of the thesis, we propose the numerical model to study the human urinary bladder. The behavior of the detrusor muscle during filling and voiding of the bladder with urine and its ability to promote the storage of urine under low pressure need to be accurately represented, requiring the implementation of a non-linear constitutive model. The mathematical model needs to be capable to simulate the mechanical variables that govern this organ and the properties of the urine. The nonlinear behavior of living tissues is implemented and validated with examples from the literature. The quasi-incompressibility property of urine and the navierstokes equations for the fluid are taken into account. The geometry of the bladder needs to be taken into account, and the implementation of a 3D computational model obtained from the computerized tomography of a cadaver male adult is considered. The data has been treated to consider boundary conditions. Two models have been conceived: one meshed with four nodes tetrahedral and another meshed with shell elements. FSI must work for the simulation of filling and voiding of the bladder. Due to the close densities of the materials the scheme used to solve fluid-structure needs to be carefully selected. The proposed numerical model and the filling and voiding analysis are finally validated with standardized urodynamic tests. The final part of the thesis, the simulation of a neobladder is presented, being the first step to simulate numerically artificial materials for bladder replacement.

Development and applications of the finite point method to compressible aerodynamics problems

María Jesús Samper — Fri, 17 May 2019 13:40:14 +0200

This work deals with the development and application of the Finite Point
Method (FPM) to compressible aerodynamics problems. The research focuses
mainly on investigating the capabilities of the meshless technique to address
practical problems, one of the most outstanding issues in meshless methods.
The FPM spatial approximation is studied firstly, with emphasis on aspects of
the methodology that can be improved to increase its robustness and accuracy.
Suitable ranges for setting the relevant approximation parameters and the
performance likely to be attained in practice are determined. An automatic
procedure to adjust the approximation parameters is also proposed to simplify
the application of the method, reducing problem- and user-dependence
without affecting the flexibility of the meshless technique.
The discretization of the flow equations is carried out following wellestablished
approaches, but drawing on the meshless character of the methodology. In order to meet the requirements of practical applications, the procedures are designed and implemented placing emphasis on robustness and efficiency (a simplification of the basic FPM technique is proposed to this end). The flow solver is based on an upwind spatial discretization of the convective fluxes (using the approximate Riemann solver of Roe) and an explicit time integration scheme. Two additional artificial diffusion schemes are also proposed to suit those cases of study in which computational cost is a major concern. The performance of the flow solver is evaluated in order to determine the potential of the meshless approach. The accuracy, computational cost and parallel scalability of the method are studied in
comparison with a conventional FEM-based technique.
Finally, practical applications and extensions of the flow solution scheme are
presented. The examples provided are intended not only to show the
capabilities of the FPM, but also to exploit meshless advantages. Automatic hadaptive procedures, moving domain and fluid-structure interaction problems,
as well as a preliminary approach to solve high-Reynolds viscous flows, are a
sample of the topics explored.
All in all, the results obtained are satisfactorily accurate and competitive in
terms of computational cost (if compared with a similar mesh-based
implementation). This indicates that meshless advantages can be exploited
with efficiency and constitutes a good starting point towards more challenging
applications.