Julio García-Espinosa's papers in WoS journals

Julio García-Espinosa's papers in WoS journals is an online self-archive aimed at collecting, preserving, and disseminating digital copies of pre-prints and open access papers published on international journals included in the Journal Citation Reports, and ... show more

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Fully 3D ship hydroelasticity: monolithic versus partitioned strategies for tight coupling
B. Servan Camas, D. Di Capua, J. García-Espinosa, D. Sá

Marine Structures (2021). Volume 80, 103098

Abstract
This paper analyzes the partitioned and monolithic strategies to simulate tightly coupled hidroelastic problems. The seakeeping hydrodynamics solver used is based on a first-order linear time-domain FEM model with forward speed and double-body linearization. The structural dynamics solver is based on a full 3D time-domain FEM with corotational shell elements accounting for the geometric non-linearity. Both solvers are implemented under the same programming framework, which allows to implement the monolithic strategy, and to minimize the communication overheads of the partitioned strategy. Two case studies are used to test and compare the partitioned and monolithic coupling: a flexible catamaran in oblique waves, and a large floating reticulated structure made of fiber reinforced plastic. In both cases, the monolithic strategy is between three and four times faster than the partitioned strategy. This project has been developed under the H2020 project FIBRESHIP aimed at developing the technology to design and build the structure of large-length vessels in fiber reinforced polymers.
Abstract
This paper analyzes the partitioned and monolithic strategies to simulate tightly coupled hidroelastic problems. The seakeeping hydrodynamics solver used is based on a first-order [...]
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A time-domain second-order FEM model for the wave diffraction-radiation problem. Validation with a semisubmersible platform
B. Servan Camas, J. Gutiérrez Romero, J. García-Espinosa

Marine Structures (2018). Volume 58, Pages 278-300

Abstract
A finite element method for the solution of the up-to-second-order wave diffraction-radiation problem in the time-domain is proposed. The solver has been verified against available analytical solutions, and validated against experimental data available for the HiPRWind semisubmersible platform (designed for floating wind turbines). To perform the validation, the wave diffraction-radiation solver is coupled to a body dynamics and mooring solvers in the time-domain. The HiPRWind movements and mooring forces have been compared for a large number of test cases, including decay tests, monochromatic waves, and bichromatic waves obtaining good agreement for both, body movements and mooring forces.
Abstract
A finite element method for the solution of the up-to-second-order wave diffraction-radiation problem in the time-domain is proposed. The solver has been verified against [...]
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A Second Order Semi-Lagrangian Particle Finite Element Method for Fluid Flows
J. Colom Cobb, J. García-Espinosa, B. Servan Camas, P. Nadukandi

Computational Particle Mechanics (2020). 7, 3–18

Abstract
In this paper, a second order SL-PFEM scheme for solving the incompressible Navier-Stokes equations is presented. This scheme is based on the second order velocity Verlet algorithm, which uses an explicit integration for the particle’s trajectory and an implicit integration for the velocity. The algorithm is completed with a predictor-multicorrector scheme for the integration of the velocity correction using the Finite Element Method. A second order projector based on least squares is used to transfer the intrinsic variables information from the particles onto the background mesh, while a second order interpolation scheme is used to transfer the accelerations from the mesh to the particles. Convergence analyses are carried out to assess the second order convergence.
Abstract
In this paper, a second order SL-PFEM scheme for solving the incompressible Navier-Stokes equations is presented. This scheme is based on the second order velocity Verlet [...]
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Seakeeping with the semi-Lagrangian particle finite element method
P. Nadukandi, B. Servan Camas, P. Becker, J. García-Espinosa

Comp. Part. Mech. (2016). 4: 321-329 (preprint)

Abstract
The application of the semi-Lagrangian particle finite element method (SL–PFEM) for the seakeeping simulation of the wave adaptive modular vehicle under spray generating conditions is presented. The time integration of the Lagrangian advection is done using the explicit integration of the velocity and acceleration along the streamlines (X-IVAS). Despite the suitability of the SL–PFEM for the considered seakeeping application, small time steps were needed in the X-IVAS scheme to control the solution accuracy. A preliminary proposal to overcome this limitation of the X-IVAS scheme for seakeeping simulations is presented.
Abstract
The application of the semi-Lagrangian particle finite element method (SL–PFEM) for the seakeeping simulation of the wave adaptive modular vehicle under spray generating [...]
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A real-time decision support system for the adjustment of sailboat rigging
I. Ortigosa, J. García-Espinosa

Brodogradnja (2015). 66 (4), 39-56

Abstract
The operational complexity and performance requirements of modern racing yachts demand the use of advanced applications, such as a decision support system (DSS) able to assist crew members during navigation. In this article, the authors describe a near-time computational solver as the main piece of a DSS which analyses and monitors the behaviour of sails and rigging. The solver is made up of two different interconnected tools: an iterative FluidStructure Interaction algorithm and an advanced Wireless Sensor Network to monitor rigging. The real-time DSS quantifies crew manoeuvres in physical terms, which are reproduced by a simulation program. It can be used in the design phase of sailing yachts and as an aid for realtime boat performance optimisation and accident prevention. This novel DSS is a useful tool for navigation, especially in races.
Abstract
The operational complexity and performance requirements of modern racing yachts demand the use of advanced applications, such as a decision support system (DSS) able to assist [...]
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Tool development based on FAST for performing design optimization of offshore wind turbines: FASTLognoter
J. Gutiérrez Romero, B. Zamora, J. García-Espinosa, M. Peyrau

Renewable Energy (2012). 55, 69-78, 2012

Abstract
The new engineering FASTLognoter software is presented. This code is essentially the result of the integration of two tools, along with some additional features. Theﬁrst basis tool is FAST (developed by NREL), a comprehensive aeroelastic simulator code for wind turbines. The second basis tool is Lognoter (developed by CompassIS), a general-purpose commercial software for managing and creating engineering forms. The integration of FAST and Lognoter gives a useful, comprehensive and versatile toolkit, which is veriﬁed in this work by means of bibliographic documented cases. An important advantage of the tool presented is the parametric design capability, allowing the user of FAST/AeroDyn/HydroDyn codes to analyze a massive group of cases; therefore, optimal design can be carried out.
Abstract
The new engineering FASTLognoter software is presented. This code is essentially the result of the integration of two tools, along with some additional features. Theﬁrst [...]
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On the interpolation of normal vectors for triangle meshes
P. Ubach de Fuentes, C. Estruch, J. García-Espinosa

International journal for numerical methods in engineering (2013). 96 (4), 247-268

Abstract
This paper analyzes the problem arising from the need to assign information about the normal vectors to the surface at the nodes of a mesh of triangles. Meshes of triangles do not have normals uniquely defined at the nodes. A widely used technique to compute the normal direction at any given node is to compute the weighted average of the normals of each surrounding triangle. The present study proposes new weighting factors to compute the normal directions at the nodes of the mesh of triangles of a general surface. Previous weights found in the literature used the geometric dimensions of the triangles themselves to design the weighting factors. The new factors are proposed using the triangles’ circumscribed circles dimensions. The new weights provide superior results than the ones obtained by previous best practices for a wide range of surfaces. An advanced framework based on the approachability of smooth surfaces by quadrics is presented and used. This framework helps to understand the improved performance of the presented factors with respect to other factors found in the literature. A comprehensive numerical comparison analysis is performed, and the most precise of all factors is clearly identified.
Abstract
This paper analyzes the problem arising from the need to assign information about the normal vectors to the surface at the nodes of a mesh of triangles. Meshes of triangles [...]
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Simulation of Water Circulation over a Model of a Submarine Canyon by Using FIC-FEM Numerical Model
A. German, J. García-Espinosa, M. Espino, M. Maidana Silanes

Journal of Waterway, Port, Coastal, and Ocean Engineering (2011). 138 (1), 21-29

Abstract
A set of numerical model experiments has been conducted to simulate the circulation driven by oscillatory forcing over a theoretical continental slope configuration used previously in laboratory experiments. The test case considered was the numerical simulation of the flow over a model of a submarine canyon, and the numerical model used in the analysis was a coastal ocean model version based on an adaptation of the finite-calculus–finite-element method (FIC-FEM) approach implemented in the commercial package Tdyn. Two cases were analyzed involving changes in fluid density. Structured and unstructured finite-element spatial discretizations were generated for the same study domain to compare the resulting velocity field with outputs from the laboratory experiments and to assess which mesh provided a better representation of the complex geometry of the channel model and the water circulation process. The comparison between the laboratory results from the reference article and the output of the numerical model showed good agreement in the structure and magnitude of the phaseaveraged and residual velocity fields.
Abstract
A set of numerical model experiments has been conducted to simulate the circulation driven by oscillatory forcing over a theoretical continental slope configuration used previously [...]
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Analysis of a consistency recovery method for the 1D convection–diffusion equation using linear finite elements
P. Nadukandi, E. Oñate, J. García-Espinosa

International Journal for Numerical Methods in Fluids (2008). 57 (9), 1291-1320, 2008

Abstract
For residual-based stabilization methods such as streamline-upwind Petrov–Galerkin (SUPG) and ﬁnite calculus (FIC), the higher-order derivatives of the residual that appear in the stabilization term vanish when simplicial elements are used. The sub-grid scale method using orthogonal sub-scales (OSS) attempts to recover the lost consistency by using a ﬁne-scale projected residual in the stabilization term. The FIC method may also be cast into an OSS form with very little manipulation using an auxiliary convective projection equation. This paper discusses the gain/loss by recovering the consistency of the discrete residual in the stabilization terms via the form that includes the convective projection (as in the OSS method). We present the von Neumann analysis of the FIC method with recovered consistency (FIC RC) for the 1D convection–diffusion problem and we compare it with the standard Bubnov–Galerkin linear ﬁnite element method and FIC/SUPG methods. The transient analysis is done by examining the discrete dispersion relation of the stabilization methods. The spectral results for the semi-discrete and fully discrete problem are presented with time integration done by the trapezoidal and second-order backward differencing formula schemes. The effect of lumping the effective mass matrix T is considered relative to using a consistent form. The effect of reﬁnement in space and time is also discussed. Finally, an optimal expression for the stabilization parameter for the FIC RC method on a uniform grid and for the steady state is given and its performance in the transient mode is discussed.
Abstract
For residual-based stabilization methods such as streamline-upwind Petrov–Galerkin (SUPG) and ﬁnite calculus (FIC), the higher-order derivatives of the residual that [...]
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Computation of turbulent flows using a finite calculus–finite element formulation
E. Oñate, A. Valls, J. García-Espinosa

International journal for numerical methods in fluids (2007). 54 (6‐8), 609-637, 2007

Abstract
We present a formulation for analysis of turbulent incompressible flows using a stabilized finite element method (FEM) based on the finite calculus (FIC) procedure. The stabilization terms introduced by the FIC approach allow to solve a wide range of fluid flow problems at different Reynolds numbers, including turbulent flows, without the need of a turbulence model. Examples of application of the FIC/FEM formulation to the analysis of 2D and 3D incompressible flows at large Reynolds numbers exhibiting turbulence features are presented.
Abstract
We present a formulation for analysis of turbulent incompressible flows using a stabilized finite element method (FEM) based on the finite calculus (FIC) procedure. The stabilization [...]
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Modeling incompressible flows at low and high Reynolds numbers via a finite calculus–finite element approach
E. Oñate, A. Valls, J. García-Espinosa

Journal of Computational Physics (2007). 224 (1), 332-351

Abstract
We present a formulation for incompressible ﬂows analysis using the ﬁnite element method (FEM). The necessary stabilization for dealing with convective eﬀects and the incompressibility condition is modeled via the ﬁnite calculus (FIC) method. The stabilization terms introduced by the FIC formulation allow to solve a wide range of ﬂuid ﬂow problems for low and high Reynolds numbers ﬂows without the need for a turbulence model. Examples of application of the FIC/FEM formulation to the analysis of 2D and 3D incompressible ﬂows with moderate and large Reynolds numbers are presented.
Abstract
We present a formulation for incompressible ﬂows analysis using the ﬁnite element method (FEM). The necessary stabilization for dealing with convective eﬀects and the [...]
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Finite calculus formulations for finite element analysis of incompressible flows. Eulerian, ALE and Lagrangian approaches
E. Oñate, J. García-Espinosa, S. Idelsohn, F. Pin

Computer methods in applied mechanics and engineering (2006). 195 (23), 3001-3037

Abstract
We present a general formulation for incompressible ﬂuid ﬂow analysis using the ﬁnite element method (FEM). The standard Eulerian formulation is described ﬁrst. The necessary stabilization for dealing with convective eﬀects and the incompressibility condition are introduced via the ﬁnite calculus (FIC) method. A simple extension of the ﬂuid ﬂow equations to an arbitrary Lagrangian–Eulerian (ALE) frame adequate for treating ﬂuid–structure interaction problems is brieﬂy presented. A fully Lagrangian formulation called the particle ﬁnite element method (PFEM) is also described. The PFEM is particularly attractive for ﬂuid–structure interaction problems involving large motions of the free surface and breaking waves. Examples of application of the Eulerian, the ALE and the fully lagrangian PFEM formulations are presented.
Abstract
We present a general formulation for incompressible ﬂuid ﬂow analysis using the ﬁnite element method (FEM). The standard Eulerian formulation is described ﬁrst. The [...]
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An unstructured finite element solver for ship hydrodynamics problems
J. García-Espinosa, E. Oñate

Journal of Applied Mechanics (2003). 70(1): 18-26

Abstract
A stabilized semi-implicit fractional step algorithm based on the ﬁnite element method for solving ship wave problems using unstructured meshes is presented. The stabilized gov-erning equations for the viscous incompressible ﬂuid and the free surface are derived at a differential level via a ﬁnite calculus procedure. This allows us to obtain a stabilized numerical solution scheme. Some particular aspects of the problem solution, such as the mesh updating procedure and the transom stern treatment, are presented. Examples of the efﬁciency of the semi-implicit algorithm for the analysis of ship hydrodynamics problems are presented.
Abstract
A stabilized semi-implicit fractional step algorithm based on the ﬁnite element method for solving ship wave problems using unstructured meshes is presented. The stabilized [...]
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A finite element method for fluid-structure interaction with surface waves using a finite calculus formulation
E. Oñate, J. García-Espinosa

Comput. Methods Appl. Mech. Engrg. (2001). 191, 635-660

Abstract
A stabilized semi-implicit fractional step finite element method (FEM) for solving coupled fluid-structure interaction problems involving free surface waves is presented. The stabilized governing equations for the viscous incompressible fluid and the free surface are derived at a differential level via a finite calculus (FIC) procedure. A mesh updating technique based on solving a fictitious elastic problem on the moving mesh is described. Examples of the efficiency of the stabilized semi-implicit algorithm for the analysis of fluid-structure interaction problems in totally or partially submerged bodies is presented.
Abstract
A stabilized semi-implicit fractional step finite element method (FEM) for solving coupled fluid-structure interaction problems involving free surface waves is presented. [...]
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A FEM fluid-structure interaction algorithm for analysis of the seal dynamics of a Surface-Effect Ship
J. García-Espinosa, B. Servan Camas, E. Oñate, D. Di Capua, P. Ubach de Fuentes

Comp. Meth. App. Mech. Eng. (2015). 295, 290-304 (preprint)

Abstract
This paper shows the recent work of the authors in the development of a time-domain FEM model for evaluation of the seal dynamics of a surface effect ship. The fluid solver developed for this purpose, uses a potential flow approach along with a stream-line integration of the free surface. The paper focuses on the free surface-structure algorithm that has been developed to allow the simulation of the complex and highly dynamic behavior of the seals in the interface between the air cushion, and the water. The developed fluid-structure interaction solver is based, on one side, on an implicit iteration algorithm, communicating pressure forces and displacements of the seals at memory level and, on the other side, on an innovative wetting and drying scheme able to predict the water action on the seals. The stability of the iterative scheme is improved by means of relaxation, and the convergence is accelerated using Aitken’s method. Several validations against experimental results have been carried out to demonstrate the developed algorithm.
Abstract
This paper shows the recent work of the authors in the development of a time-domain FEM model for evaluation of the seal dynamics of a surface effect ship. The fluid solver [...]
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Time domain simulation of coupled sloshing–seakeeping problems by SPH–FEM coupling
B. Servan Camas, J. Cercós-Pita, J. Colom Cobb, J. García-Espinosa, A. Souto-Iglesias

Ocean Engineering (2016). 123, 383-396 (preprint)

Abstract
The aim of this work is to carry out numerical simulations in the time domain of seakeeping problems taking into account internal flow in tanks, including sloshing. To this aim, a Smooth Particle Hydrodynamics (SPH) solver for simulating internal flows in tanks is coupled in the time domain to a Finite Element Method (FEM) diffraction-radiation solver developed for seakeeping problems. Validations are carried out comparing against available experimental data. Good agreement between obtained numerical results and experimental data is found.
Abstract
The aim of this work is to carry out numerical simulations in the time domain of seakeeping problems taking into account internal flow in tanks, including sloshing. To this [...]
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Computer Programming of free GUIs for the Analysis of the Behaviour of Marine Structures
J. Gutiérrez Romero, Z. B, J. García-Espinosa

Ships and Offshore Structures (2015). 11:5, 471-481 (preprint)

Abstract
This work presents the development of two free Graphical User Interfaces (GUI), called ''FASTLognoter'' and ''MorisonForm'', both focused on the analysis of the behaviour of offshore structures, especially of offshore wind turbines. The first one is related to the aeroelastic analysis of wind turbines, and the second is concerned with the seakeeping of marine structures. The development of these tools has been carried out using a powerful software called ''Lognoter''. This tool is free software for Knowledge Management in Technology (KMT), which integrates computer programming for allowing the development of GUIs. These GUIs give an open platform for conducting a parametric study of the structural and dynamic behaviour of marine structures. Their coupling permits the user to set a suitable way to evaluate new concepts in marine structures. Finally, an application for the intensive analysis of offshore wind turbines is shown.
Abstract
This work presents the development of two free Graphical User Interfaces (GUI), called ''FASTLognoter'' and ''MorisonForm'', both focused on [...]
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Desarrollo de un sistema de apoyo a la decisión para optimizar el comportamiento de barcos de vela
J. García-Espinosa, I. Ortigosa, A. Fernández

Rev. int. métodos numér. cálc. diseño ing. (2015). Vol. 31, (3)

Abstract
In this paper, the conception and design of a new monitoring system for a racing yachts rig is presented. The sensors developed are able to process the measured strain data, by applying artificial neural networks (ANN) algorithms, and then evaluate the load acting on an element and identify the direction of the action of that force. This way, it is possible to identify the actual operating conditions of the yacht rig. The required data for ANN training is generated from the results obtained from different finite element method (FEM) computational models of the device. Furthermore, during the design phase of the system, different experimental campaigns were carried out. The experimental tests were designed to serve as proof of concept, as well as to validate the different procedures used in the system development and application. The developed monitoring system is wireless, low-intrusive and easily adaptable to any yacht configuration. This work also presents the integration of the monitoring system into a coupled fluid-structure computation model for the sails and rig of a boat. The resulting system is an efficient tool for evaluating performance and decision support in the adjustment of a sailboat rig.
Abstract
In this paper, the conception and design of a new monitoring system for a racing yachts rig is presented. The sensors developed are able to process the measured strain data, [...]
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Accelerated 3D multi-body seakeeping simulations using unstructured finite elements
B. Servan Camas, J. García-Espinosa

Journal of Computational Physics (2013). 252:382-403 (preprint)

Abstract
Being capable of predicting seakeeping capabilities in the time domain is of great interest for the marine and offshore industry. However, most computer programs used in the industry work in the frequency domain, with the subsequent limitation in the accuracy of their model predictions. The main objective of this work is the development of a time domain solver based on the finite element method capable of solving multi-body seakeeping problems on unstructured meshes. In order to achieve such an objective, several techniques are combined: the use of an efficient algorithm for the free surface boundary conditions, the use of deflated conjugate gradients, and the use of a graphic processing unit for speeding up the linear solver. The results obtained results by the developed model showed good agreement with analytical solutions, experimental data for an actual offshore structure model, as well as numerical solutions obtained by other numerical method. Also, a simulation with sixteen floating bodies was carried out in a affordable CPU time, showing the potential of this approach for multi-body simulation.
Abstract
Being capable of predicting seakeeping capabilities in the time domain is of great interest for the marine and offshore industry. However, most computer programs used in the [...]
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A non-linear finite element method on unstructured meshes for added resistance in waves
J. García-Espinosa, B. Servan Camas

Ships and offshore structures (2018). 14:2, 153-164 (preprint)

Abstract
In this work a finite element method (FEM) is proposed to solve the problem of estimating the added resistance of a ship in waves in the time domain and using unstructured meshes. Two different schemes are used to integrate the corresponding free surface kinematic and dynamic boundary conditions: the first one based on streamlines integration (SLI); and the second one based on the Streamline-Upwind Petrov-Galerking (SUPG) stabilization. The proposed numerical schemes have been validated in different test cases, including towing tank tests with monochromatic waves. The results obtained in this work show the suitability of the present method to estimate added resistance in waves in a computationally affordable manner.
Abstract
In this work a finite element method (FEM) is proposed to solve the problem of estimating the added resistance of a ship in waves in the time domain and using unstructured [...]
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Computation of the stabilization parameter for the finite element solution of advective–diffusive problems
E. Oñate, J. García-Espinosa, S. Idelsohn

Int. J. for Num. Meths. in Fluids (1997). Vol. 25, pp. 1387-1407

Abstract
In a previous paper a general procedure for deriving stabilized finite element schemes for advective type problems based on invoking higher order balance laws over finite size domains was presented. This provides an expression for the element stabilization parameter in terms of the solution residual and its first derivatives in a kind of iterative or adaptative manner. Details of the application of this procedure to 1D and 2D advective- diffusive problems are given. Some examples of applications showing the potential of the new approach are presented.
Abstract
In a previous paper a general procedure for deriving stabilized finite element schemes for advective type problems based on invoking higher order balance laws over finite [...]
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Error estimation and mesh adaptivity in incompressible viscous flows using a residual power approach
E. Oñate, J. Arteaga, J. García-Espinosa, R. Flores

Comput. Methods Appl. Mech. Engrg., (2006). Vol. 195, pp. 339-362

Abstract
A methodology for error estimation and mesh adaptation for finite element (FE) analysis of incompressible viscous flow is presented. The error estimation method is based on the evaluation of the energy rate (the power) of the FE residuals of the momentum and incompressibility equations. The residuals are computed using recovered values of the derivatives of the velocity and pressure variable obtained via a nodal derivative recovery technique. Two mesh adaptation procedures based on: a) the equi-distribution of the residual power among the elements in the mesh and b) the equi-distribution of the density of the total residual power are presented. The stabilized form of the Navier-Stokes equations using a finite calculus (FIC) formulation is solved with a fractional step FE scheme. This allows the use of linear triangles and tetrahedra with an equal order interpolation for the velocity and pressure variables. A nodal-based approach is used for computing the residual power integrals. The examples show the ability of the error estimation and the mesh adaptation process to capture the high gradients of the solution in the vecinity of boundary layers and in zones of high vorticity of the fluid for both steady state and transient flow situations.
Abstract
A methodology for error estimation and mesh adaptation for finite element (FE) analysis of incompressible viscous flow is presented. The error estimation method is based on [...]
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ODDLS: A new unstructured mesh finite element method for the analysis of free surface flow problems
J. García-Espinosa, A. Valls, E. Oñate

Int. J. Numer. Meth. Engng. (2008). Vol 76 (9), pp. 1297-1327

Abstract
This paper introduces a new stabilized finite element method based on the finite calculus (Comput. Methods Appl. Mech. Eng. 1998; 151:233–267) and arbitrary Lagrangian–Eulerian techniques (Comput. Methods Appl. Mech. Eng. 1998; 155:235–249) for the solution to free surface problems. The main innovation of this method is the application of an overlapping domain decomposition concept in the statement of the problem. The aim is to increase the accuracy in the capture of the free surface as well as in the resolution of the governing equations in the interface between the two fluids. Free surface capturing is based on the solution to a level set equation. The Navier–Stokes equations are solved using an iterative monolithic predictor–corrector algorithm (Encyclopedia of Computational Mechanics. Wiley: New York, 2004), where the correction step is based on imposing the divergence‐free condition in the velocity field by means of the solution to a scalar equation for the pressure. Examples of application of the ODDLS formulation (for overlapping domain decomposition level set) to the analysis of different free surface flow problems are presented. Copyright © 2008 John Wiley & Sons, Ltd.
Abstract
This paper introduces a new stabilized finite element method based on the finite calculus (Comput. Methods Appl. Mech. Eng. 1998; 151:233–267) and arbitrary [...]
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A fourth‐order compact scheme for the Helmholtz equation: Alpha‐interpolation of FEM and FDM stencils
P. Nadukandi, E. Oñate, J. García-Espinosa

Int. J. Numer. Meth. Engng. (2011). Vol. 86 (1), pp. 18-46

Abstract
We propose a fourth‐order compact scheme on structured meshes for the Helmholtz equation given by R(φ):=f(x)+Δφ+ξ2φ=0. The scheme consists of taking the alpha‐interpolation of the Galerkin finite element method and the classical central finite difference method. In 1D, this scheme is identical to the alpha‐interpolation method (J. Comput. Appl. Math. 1982; 8(1):15–19) and in 2D making the choice α=0.5 we recover the generalized fourth‐order compact Padé approximation (J. Comput. Phys. 1995; 119:252–270; Comput. Meth. Appl. Mech. Engrg 1998; 163:343–358) (therein using the parameter γ=2). We follow (SIAM Rev. 2000; 42(3):451–484; Comput. Meth. Appl. Mech. Engrg 1995; 128:325–359) for the analysis of this scheme and its performance on square meshes is compared with that of the quasi‐stabilized FEM (Comput. Meth. Appl. Mech. Engrg 1995; 128:325–359). In particular, we show that the relative phase error of the numerical solution and the local truncation error of this scheme for plane wave solutions diminish at the rate O((ξℓ)4), where ξ, ℓ represent the wavenumber and the mesh size, respectively. An expression for the parameter α is given that minimizes the maximum relative phase error in a sense that will be explained in Section 4.5. Convergence studies of the error in the L2 norm, the H1 semi‐norm and the l∞ Euclidean norm are done and the pollution effect is found to be small. Copyright © 2010 John Wiley & Sons, Ltd.
Abstract
We propose a fourth‐order compact scheme on structured meshes for the Helmholtz equation given by R(φ):=f(x)+Δφ+ξ2φ=0. The scheme consists of taking [...]
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A high-resolution Petrov-Galerkin method for the 1D convection-diffusion-reaction problem
P. Nadukandi, E. Oñate, J. García-Espinosa

Int. J. Numer. Meth. Engng. (2010). Vol. 199, pp. 525–546

Abstract
We present the design of a high-resolution Petrov–Galerkin (HRPG) method using linear finite elements for the problem defined by the residual R (phi):= partial phi /partial t + u partial phi /partial x - k partial^2 phi /partial x^2 +s phi -f where k; s > o = 0. The structure of the method in 1D is identical to the consistent approximate upwind Petrov– Galerkin (CAU/PG) method [A.C. Galeão, E.G. Dutra do Carmo, A consistent approximate upwind Petrov– Galerkin method for the convection-dominated problems, Comput. Methods Appl. Mech. Engrg. 68 (1988) 83–95] except for the definitions of the stabilization parameters. Such a structure may also be attained via the finite-calculus (FIC) procedure [E. Oñate, Derivation of stabilized equations for numerical solution of advective–diffusive transport and fluid flow problems, Comput. Methods Appl. Mech. Engrg. 151 (1998) 233–265; E. Oñate, J. Miquel, G. Hauke, Stabilized formulation for the advection–diffusion– absorption equation using finite-calculus and linear finite elements, Comput. Methods Appl. Mech. Engrg. 195 (2006) 3926–3946] by an appropriate definition of the characteristic length. The prefix ‘high-resolution’ is used here in the sense popularized by Harten, i.e. second order accuracy for smooth/regular regimes and good shock-capturing in nonregular regimes. The design procedure embarks on the problem of circumventing the Gibbs phenomenon observed in L2-projections. Next we study the conditions on the stabilization parameters to circumvent the global oscillations due to the convective term. A conjuncture of the two results is made to deal with the problem at hand that is usually plagued by Gibbs, global and dispersive oscillations in the numerical solution. It is shown that the method indeed reproduces stabilized high-resolution numerical solutions for a wide range of values of u; k; s and f . Finally, some remarks are made on the extension of the HRPG method to multidimensions.
Abstract
We present the design of a high-resolution Petrov–Galerkin (HRPG) method using linear finite elements for the problem defined by the residual R (phi):= partial phi [...]
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A family of residual‐based stabilized finite element methods for Stokes flows
E. Oñate, P. Nadukandi, S. Idelsohn, J. García-Espinosa, C. Felippa

Int. J. Numer. Meth. Fluids (2011). Vol. 65 (1-3), pp. 106-134

Abstract
We present a collection of stabilized finite element (FE) methods derived via first‐ and second‐order finite calculus (FIC) procedures. It is shown that several well known existing stabilized FE methods such as the penalty technique, the Galerkin Least Square (GLS) method, the Pressure Gradient Projection (PGP) method and the orthogonal sub‐scales (OSS) method are recovered from the general residual‐based FIC stabilized form. A new family of stabilized Pressure Laplacian Stabilization (PLS) FE methods with consistent nonlinear forms of the stabilization parameters are derived. The distinct feature of the family of PLS methods is that they are residual‐based, i.e. the stabilization terms depend on the discrete residuals of the momentum and/or the incompressibility equations. The advantages and disadvantages of the different stabilization techniques are discussed and several examples of application are presented.
Abstract
We present a collection of stabilized finite element (FE) methods derived via first‐ and second‐order finite calculus (FIC) procedures. It is shown that several well known [...]
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A Petrov–Galerkin formulation for the alpha interpolation of FEM and FDM stencils: Applications to the Helmholtz equation
P. Nadukandi, E. Oñate, J. García-Espinosa

Int. J. Numer. Meth. Engng. (2012). Vol. 89 (11), pp. 1367-1391

Abstract
A new Petrov–Galerkin (PG) method involving two parameters, namely α1 and α2, is presented, which yields the following schemes on rectangular meshes: (i) a compact stencil obtained by the linear interpolation of the Galerkin FEM and the classical central finite difference method (FDM), should the parameters be equal, that is, α1 = α2 = α; and (ii) the nonstandard compact stencil presented in (Int. J. Numer. Meth. Engng 2011; 86:18–46) for the Helmholtz equation if the parameters are distinct, that is, α1 ≠ α2. The nonstandard compact stencil is obtained by taking the linear interpolation of the diffusive terms (specified by α1) and the mass terms (specified by α2) that appear in the stencils obtained by the standard Galerkin FEM and the classical central FDM, respectively. On square meshes, these two schemes were shown to provide solutions to the Helmholtz equation that have a dispersion accuracy of fourth and sixth order, respectively (Int. J. Numer. Meth. Engng 2011; 86:18–46). The objective of this paper is to study the performance of this PG method for the Helmholtz equation using nonuniform meshes and the treatment of natural boundary conditions.
Abstract
A new Petrov–Galerkin (PG) method involving two parameters, namely α1 and α2, is presented, which yields the following schemes on rectangular [...]
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FIC/FEM Formulation with Matrix Stabilizing Terms for Incompressible Flows at Low and High Reynolds Numbers
E. Oñate, A. Valls, J. García-Espinosa

Computational Mechanics (2006). Vol. 38 (4-5), pp. 440-455

Abstract
We present a general formulation for incompressible fluid flow analysis using the finite element method. The necessary stabilization for dealing with convective effects and the incompressibility condition are introduced via the Finite Calculus method using a matrix form of the stabilization parameters. This allows to model a wide range of fluid flow problems for low and high Reynolds numbers flows without introducing a turbulence model. Examples of application to the analysis of incompressible flows with moderate and large Reynolds numbers are presented.
Abstract
We present a general formulation for incompressible fluid flow analysis using the finite element method. The necessary stabilization for dealing with convective effects and [...]
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A high-resolution Petrov-Galerkin method for the convection-diffusion-reaction problem. Part II-A multidimensional extension
P. Nadukandi, E. Oñate, J. García-Espinosa

Comput. Methods Appl. Mech. Engrg., (2012). Vol. 213-216, pp. 327-352

Abstract
A multidimensional extension of the HRPG method using the lowest order block finite elements is presented. First, we design a nondimensional element number that quantifies the characteristic layers which are found only in higher dimensions. This is done by matching the width of the characteristic layers to the width of the parabolic layers found for a fictitious 1D reaction–diffusion problem. The nondimensional element number is then defined using this fictitious reaction coefficient, the diffusion coefficient and an appropriate element size. Next, we introduce anisotropic element length vectors li and the stabilization parameters αi, βi are calculated along these li. Except for the modification to include the new dimensionless number that quantifies the characteristic layers, the definitions of αi, βi are a direct extension of their counterparts in 1D. Using αi, βiand li, objective characteristic tensors associated with the HRPG method are defined. The numerical artifacts across the characteristic layers are manifested as the Gibbs phenomenon. Hence, we treat them just like the artifacts formed across the parabolic layers in the reaction-dominant case. Several 2D examples are presented that support the design objective—stabilization with high-resolution
Abstract
A multidimensional extension of the HRPG method using the lowest order block finite elements is presented. First, we design a nondimensional element number that quantifies [...]
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Lagrangian finite element model for the 3D simulation of glass forming processes
P. Ryzhakov, J. García-Espinosa, E. Oñate

Computers and Structures (2016). 117, 126-140 (preprint)

Abstract
We propose here a numerical model for a three-dimensional simulation of glass forming processes. Using the basic philosophy of the Particle Finite Element method (PFEM), we introduce several new features adapting the strategy to suit the problem of interest. A modified fractional step method for the solution of the flow equations is applied. This approach, on the one hand, inherits the computational efficiency of the original fractional step approach, and on the other hand shows better mass conservation features. These features are particularly attractive taking into account the importance of the correct prediction of the glass product's wall thickness. A smart mesh update strategy and a simple mechanical contact scheme are introduced. In order to account for temperature-dependent viscosity, the heat equation is coupled to the mechanical model. Viscosity is obtained from the temperature field via an empirical law. The model is validated and an example modeling the processes in the final blow mold of the bottle manufacturing process is proposed.
Abstract
We propose here a numerical model for a three-dimensional simulation of glass forming processes. Using the basic philosophy of the Particle Finite Element method (PFEM), we [...]
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Non-linear dynamic analysis of the response of moored floating structures
J. Gutiérrez Romero, J. García-Espinosa, B. Servan Camas, B. Zamora-Parra

Marine Structures (2016). Vol. 49 pp. 116-137 49, 116-137 (preprint)

Abstract
The complexity of the dynamic behaviour of offshore marine structures requires advanced simulations tools for the accurate assessment of the seakeeping behaviour of these devices. The aim of this work is to present a time-domain model for solving the dynamics of floating marine devices, subjected to non-linear environmental loads and paying special attention on the mooring dynamics. First, the formulation of the hydrodynamic approach for solving the wave-floater interaction is introduced. Second, the solver of the mooring dynamics, based on a non-linear Finite Element Method approach, is presented. Third, a procedure for coupling the hydrodynamic along with other external loads, with the floating structure and mooring dynamics is described. Fourth, some validation examples and comparisons among different mooring approaches are presented. Fifth, an analysis of the OC3 floating wind turbine concept is performed to study the influence of different mooring models, the effects of non-linear waves on the platform, and the tension in the mooring system. The dynamic mooring model along with the second-order wave model produce realistic simulations of the floating wind turbine performance.
Abstract
The complexity of the dynamic behaviour of offshore marine structures requires advanced simulations tools for the accurate assessment of the seakeeping behaviour of these [...]
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García-Espinosa, Julio 6764

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