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Documents published in Scipedia

Concurrent finite element simulation of quadrupolar and dipolar flow noise in low Mach number aeroacoustics
O. Guasch, A. Pont, J. Baiges, R. Codina

Computers and Fluids (2016). Vol. 133, pp. 129-139

Abstract
The computation of flow-induced noise at low Mach numbers usually relies on a two-step hybrid methodolgy. In the first step, an incompressible fluid dynamics simulation (CFD) is performed and an acoustic source term is derived from it. The latter becomes the inhomogeneous term for an acoustic wave equation, which is solved in the second step, often resorting to boundary integral formulations. In the presence of rigid bodies, Curle’s acoustic analogy is probably the most extended approach. It has been shown that Curle’s boundary dipolar noise contribution does in fact correspond to the diffraction of the quadrupolar aerodynamic noise generated by the flow past the rigid body. In this work, advantage is taken from this fact to propose an alternative computational methodology to get the individual quadrupolar and dipolar contributions to the total acoustic pressure. For any linear acoustic wave operator, the unknown acoustic pressure can be split into its incident and diffracted components and be computed simultaneously to the incompressible flow field, in a single finite element computational run. This circumvents the problem found in Curle’s analogy of needing the total pressure at the body’s boundary, which includes the acoustic pressure fluctuations. The latter cannot be obtained from an incompressible CFD simulation. The proposed unified strategy could be beneficial for a large variety problems such as those involving noise generated from duct terminations, or those related with the simulation of fricatives in numerical voice production, among many others.
Abstract
The computation of flow-induced noise at low Mach numbers usually relies on a two-step hybrid methodolgy. In the first step, an incompressible fluid dynamics simulation (CFD) [...]
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A stabilized finite element method for the mixed wave equation in an ALE framework with application to diphthong production
O. Guasch, M. Arnela, R. Codina, H. Espinoza

Acta Acustica united with Acustica (2016). (preprint) Vol. 102, pp. 94-106

Abstract
Working with the wave equation in mixed rather than irreducible form allows one to directly account for both, the acoustic pressure field and the acoustic particle velocity field. Indeed, this becomes the natural option in many problems, such as those involving waves propagating in moving domains, because the equations can easily be set in an arbitrary Lagrangian-Eulerian (ALE) frame of reference. Yet, when attempting a standard Galerkin finite element solution (FEM) for them, it turns out that an inf-sup compatibility constraint has to be satisfied, which prevents from using equal interpolations for the approximated acoustic pressure and velocity fields. In this work it is proposed to resort to a subgrid scale stabilization strategy to circumvent this condition and thus facilitate code implementation. As a possible application, we address the generation of diphthongs in voice production.
Abstract
Working with the wave equation in mixed rather than irreducible form allows one to directly account for both, the acoustic pressure field and the acoustic particle velocity [...]
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Two-fluid flow problem for viscoelastic fluids using the level set method and pressure enriched shape functions
E. Castillo, J. Baiges, R. Codina

Journal of Non-Newtonian Fluid Mechanics (2015). Vol. 225, pp. 37-53

Abstract
The numerical simulation of complex flows has been a subject of intense research in the last years with important industrial applications in many fields. In this paper we present a finite element method to solve the two immiscible fluid flow problem using the level set method. When the interface between both fluids cuts an element, the discontinuity in the material properties leads to discontinuities in the gradients of the unknowns which cannot be captured using a standard finite element interpolation. The method presented in this work features a local enrichment for the pressure unknowns which allows one to capture pressure gradient discontinuities in fluids presenting different density values. The method is tested in two problems: the first example consists in a sloshing case that involves the interaction of a Giesekus and a Newtonian fluid. This example shows that the enriched pressure functions permit the exact resolution of the hydrostatic rest state. The second example is the classical jet buckling problem used to validate our method. To permit the use of equal interpolation between the variables, we use a variational multiscale formulation proposed recently by Castillo and Codina in Comput. Methods Appl. Mech. Engrg. 279 (2014) 579–605, that has shown very good stability properties, permitting also the resolution of the jet buckling flow problem in the the range of Weissenberg number 0 < We < 100, using the Oldroyd-B model without any sign of numerical instability. Additional ingredients of the work are the inclusion of a discontinuity capturing technique for the constitutive equation and some comparisons between a monolithic resolution and a fractional step approach to solve the viscoelastic fluid flow problem from the point of view of computational requirements
Abstract
The numerical simulation of complex flows has been a subject of intense research in the last years with important industrial applications in many fields. In this paper we [...]
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On some time marching schemes for the stabilized finite element approximation of the mixed wave equation
H. Espinoza, R. Codina, S. Badia

Comput. Methods Appl. Mech. Engrg., (2015). Vol. 296, pp. 295-326

Abstract
In this paper we analyze time marching schemes for the wave equation in mixed form. The problem is discretized in space using stabilized finite elements. On the one hand, stability and convergence analyses of the fully discrete numerical schemes are presented using different time integration schemes and appropriate functional settings. On the other hand, we use Fourier techniques (also known as von Neumann analysis) in order to analyze stability, dispersion and dissipation. Numerical convergence tests are presented for various time integration schemes, polynomial interpolations (for the spatial discretization), stabilization methods, and variational forms. To analyze the behavior of the different schemes considered, a 1D wave propagation problem is solved.
Abstract
In this paper we analyze time marching schemes for the wave equation in mixed form. The problem is discretized in space using stabilized finite elements. On the one hand, [...]
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A three‐field stabilized finite element method for fluid‐structure interaction: elastic solid and rigid body limit
E. Hachem, S. Feghali, T. Coupez, R. Codina

Comput. Methods Appl. Mech. Engrg., (2015). Vol. 104 (7), pp. 566-584

Abstract
We propose a full Eulerian framework for solving fluid‐structure interaction (FSI) problems based on a unified formulation in which the FSIs are modelled by introducing an extra stress in the momentum equation. The obtained three‐field velocity, pressure and stress system is solved using a stabilized finite element method. The key feature of this unified formulation is the ability to describe different kind of interactions between the fluid and the structure, which can be either elastic or a perfect rigid body, without the need of treating this last case via penalization. The level‐set method combined with a dynamic anisotropic mesh adaptation is used to track the fluid‐solid interface.
Abstract
We propose a full Eulerian framework for solving fluid‐structure interaction (FSI) problems based on a unified formulation in which the FSIs are modelled by introducing [...]
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Weak imposition of essential boundary conditions in the finite element approximation of elliptic problems with non‐matching meshes
R. Codina, J. Baiges

Int. J. Numer. Meth. Engng. (2015). Vol. 104 (7), pp. 624-654

Abstract
In this work, we propose a method to prescribe essential boundary conditions in the finite element approximation of elliptic problems when the boundary of the computational domain does not match with the element boundaries. The problems considered are the Poisson problem, the Stokes problem, and the Darcy problem, the latter both in the primal and in the dual formulation. The formulation proposed is of variational type. The key idea is to start with the variational form that defines the problem and treat the boundary condition as a constraint. The particular feature is that the Lagrange multiplier is not defined on the boundary where the essential condition needs to be prescribed but is taken as a certain trace of a field defined in the computational domain, either in all of it or just in a region surrounding the boundary. When approximated numerically, this may allow one to condense the DOFs of the new field and end up with a problem posed only in terms of the original unknowns. The nature of the field used to weakly impose boundary conditions depends on the problem being treated. For the Poisson problem, it is a flux; for the Stokes problem, a stress; for the Darcy problem in primal form, a velocity field; and for the Darcy problem in dual form, it is a potential.
Abstract
In this work, we propose a method to prescribe essential boundary conditions in the finite element approximation of elliptic problems when the boundary of the computational [...]
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Numerical modeling of chlorine concentration in water storage tank
R. Codina, C. Muñoz, J. Baiges, J. Principe

Int. J. Numer. Meth. Fluids (2015). Vol. 79 (2), pp. 84-107

Abstract
In this paper, we describe a numerical model to simulate the evolution in time of the hydrodynamics of water storage tanks, with particular emphasis on the time evolution of chlorine concentration. The mathematical model contains several ingredients particularly designed for this problem, namely, a boundary condition to model falling jets on free surfaces, an arbitrary Lagrangian–Eulerian formulation to account for the motion of the free surface because of demand and supply of water, and a coupling of the hydrodynamics with a convection–diffusion–reaction equation modeling the time evolution of chlorine. From the numerical point of view, the equations resulting from the mathematical model are approximated using a finite element formulation, with linear continuous interpolations on tetrahedra for all the unknowns. To make it possible, and also to be able to deal with convection‐dominated flows, a stabilized formulation is used. In order to capture the sharp gradients present in the chlorine concentration, particularly near the injection zone, a discontinuity capturing technique is employed.
Abstract
In this paper, we describe a numerical model to simulate the evolution in time of the hydrodynamics of water storage tanks, with particular emphasis on the time evolution [...]
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Analysis of an unconditionally convergent stabilized finite element formulation for incompressible magnetohydrodynamics
S. Badia, R. Codina, R. Planas

Archives of Comp. Meths. Engng. (2015). Vol. 22 (4), pp. 621-636

Abstract
In this work, we analyze a recently proposed stabilized finite element formulation for the approximation of the resistive magnetohydrodynamics equations. The novelty of this formulation with respect to existing ones is the fact that it always converges to the physical solution, even when it is singular. We have performed a detailed stability and convergence analysis of the formulation in a simplified setting. From the convergence analysis, we infer that a particular type of meshes with a macro-element structure is needed, which can be easily obtained after a straight modification of any original mesh.
Abstract
In this work, we analyze a recently proposed stabilized finite element formulation for the approximation of the resistive magnetohydrodynamics equations. The novelty of this [...]
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Finite element dynamical subgrid-scale model for low Mach number flows with radiative heat transfer
M. Ávila, R. Codina, J. Principe

Int. J. Numer. Meth. Heat and Fluid Flows (2015). (Preprint) Vol. 25 (6), pp. 1361-1384

Abstract
Purpose – The purpose of this paper is to present a finite element approximation of the low Mach number equations coupled with radiative equations to account for radiative heat transfer. For high-temperature flows this coupling can have strong effects on the temperature and velocity fields. Design/methodology/approach – The basic numerical formulation has been proposed in previous works. It is based on the variational multiscale (VMS) concept in which the unknowns of the problem are divided into resolved and subgrid parts which are modeled to consider their effect into the former. The aim of the present paper is to extend this modeling to the case in which the low Mach number equations are coupled with radiation, also introducing the concept of subgrid scales for the radiation equations. Findings – As in the non-radiative case, an important improvement in the accuracy of the numerical scheme is observed when the nonlinear effects of the subgrid scales are taken into account. Besides it is possible to show global conservation of thermal energy. Originality/value – The original contribution of the work is the proposal of keeping the VMS splitting into the nonlinear coupling between the low Mach number and the radiative transport equations, its numerical evaluation and the description of its properties.
Abstract
Purpose – The purpose of this paper is to present a finite element approximation of the low Mach number equations coupled with radiative equations to account for radiative [...]
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First, second and third order fractional step methods for the three-field viscoelastic flow problem
E. Castillo, R. Codina

Journal of Computational Physics (2015). Vol. 296, pp. 113-137

Abstract
In this paper, three different fractional step methods are designed for the three-field viscoelastic flow problem, whose variables are velocity, pressure and elastic stress. The starting point of our methods is the same as for classical pressure segregation algorithms used in the Newtonian incompressible Navier–Stokes problem. These methods can be understood as an inexact LU block factorization of the original system matrix of the fully discrete problem and are designed at the pure algebraic level. The final schemes allow one to solve the problem in a fully decoupled form, where each equation (for velocity, pressure and elastic stress) is solved separately. The first order scheme is obtained from a straightforward segregation of pressure and elastic stress in the momentum equation, whereas the key point for the second order scheme is a first order extrapolation of these variables. The third order fractional step method relies on Yosida's scheme. Referring to the spatial discretization, either the Galerkin method or a stabilized finite element formulation can be used. We describe the fractional step methods first assuming the former, and then we explain the modifications introduced by the stabilized formulation we employ and that has been proposed in a previous work. This discretization in space shows very good stability, permitting in particular the use of equal interpolation for all variables.
Abstract
In this paper, three different fractional step methods are designed for the three-field viscoelastic flow problem, whose variables are velocity, pressure and [...]
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Articles (Documents not available in Scipedia)

Assessment of variational multiscale models for the large eddy simulation of turbulent incompressible flows
O Colomés, S Badia, R Codina, J Principe

Computer Methods in Applied Mechanics and Engineering 285, 32-63, 2015
Mixed stabilized finite element methods in nonlinear solid mechanics. Part III: Compressible and incompressible plasticity
M Cervera, M Chiumenti, L Benedetti, R Codina

Computer Methods in Applied Mechanics and Engineering 285, 752-775, 2015
Large eddy simulation of low mach number flows using dynamic and orthogonal subgrid scales
M Avila, R Codina, J Principe

Computers & Fluids 99, 44-66, 2014
Stabilized stress–velocity–pressure finite element formulations of the Navier–Stokes problem for fluids with non-linear viscosity
E Castillo, R Codina

Computer Methods in Applied Mechanics and Engineering 279, 554-578, 2014
Variational multi-scale stabilized formulations for the stationary three-field incompressible viscoelastic flow problem
E Castillo, R Codina

Computer Methods in Applied Mechanics and Engineering 279, 579-605, 2014
Anisotropic adaptive meshing and monolithic Variational Multiscale method for fluid–structure interaction
E Hachem, S Feghali, R Codina, T Coupez

Computers & Structures 122, 88-100, 2013
On an unconditionally convergent stabilized finite element approximation of resistive magnetohydrodynamics
S Badia, R Codina, R Planas

Journal of Computational Physics 234, 399-416, 2013
Immersed stress method for fluid–structure interaction using anisotropic mesh adaptation
E Hachem, S Feghali, R Codina, T Coupez

International Journal for Numerical Methods in Engineering 94 (9), 805-825, 2013
Explicit reduced‐order models for the stabilized finite element approximation of the incompressible Navier–Stokes equations
J Baiges, R Codina, S Idelsohn

International Journal for Numerical Methods in Fluids 72 (12), 1219-1243, 2013
Statistical behavior of the orthogonal subgrid scale stabilization terms in the finite element large eddy simulation of turbulent flows
O Guasch, R Codina

Computer Methods in Applied Mechanics and Engineering 261, 154-166, 2013
Stokes, Maxwell and Darcy: A single finite element approximation for three model problems
S Badia, R Codina

Applied Numerical Mathematics 62 (4), 246-263, 2012
A nodal-based finite element approximation of the Maxwell problem suitable for singular solutions
S Badia, R Codina

SIAM Journal on Numerical Analysis 50 (2), 398-417, 2012
A symmetric method for weakly imposing Dirichlet boundary conditions in embedded finite element meshes
J Baiges, R Codina, F Henke, S Shahmiri, WA Wall

International Journal for Numerical Methods in Engineering 90 (5), 636-658, 2012
Approximation of the inductionless MHD problem using a stabilized finite element method
R Planas, S Badia, R Codina

Journal of Computational Physics 230 (8), 2977-2996, 2011
The Fixed‐Mesh ALE approach for the numerical simulation of floating solids
J Baiges, R Codina, H Coppola‐Owen

International Journal for Numerical Methods in Fluids 67 (8), 1004-1023, 2011
A finite element dynamical nonlinear subscale approximation for the low Mach number flow equations
M Avila, J Principe, R Codina

Journal of Computational Physics 230 (22), 7988-8009, 2011
Mesh objective modeling of cracks using continuous linear strain and displacement interpolations
M Cervera, M Chiumenti, R Codina

International Journal for Numerical Methods in Engineering 87 (10), 962-987, 2011
On the stabilization parameter in the subgrid scale approximation of scalar convection–diffusion–reaction equations on distorted meshes
J Principe, R Codina

Computer methods in applied mechanics and engineering 199 (21), 1386-1402, 2010
Long-term stability estimates and existence of a global attractor in a finite element approximation of the Navier–Stokes equations with numerical subgrid scale modeling
S Badia, R Codina, JV Gutiérrez-Santacreu

SIAM Journal on Numerical Analysis 48 (3), 1013-1037, 2010
Finite element approximation of turbulent thermally coupled incompressible flows with numerical sub-grid scale modelling
R Codina, J Principe, M Ávila

International Journal of Numerical Methods for Heat & Fluid Flow 20 (5), 492-516, 2010
The fixed‐mesh ALE approach applied to solid mechanics and fluid–structure interaction problems
J Baiges, R Codina

International journal for numerical methods in engineering 81 (12), 1529-1557, 2010
Stabilized continuous and discontinuous Galerkin techniques for Darcy flow
S Badia, R Codina

Computer Methods in Applied Mechanics and Engineering 199 (25), 1654-1667, 2010
The dissipative structure of variational multiscale methods for incompressible flows
J Principe, R Codina, F Henke

Computer Methods in Applied Mechanics and Engineering 199 (13), 791-801, 2010
Mixed stabilized finite element methods in nonlinear solid mechanics: Part ii: Strain localization
M Cervera, M Chiumenti, R Codina

Computer Methods in Applied Mechanics and Engineering 199 (37), 2571-2589, 2010
Mathematical models for thermally coupled low speed flows
J Principe, R Codina

Advances in Theoretical and Applied Mechanics 2 (2), 93-112, 2009
Subscales on the element boundaries in the variational two-scale finite element method
R Codina, J Principe, J Baiges

Computer Methods in Applied Mechanics and Engineering 198 (5), 838-852, 2009
Finite element approximation of the three-field formulation of the Stokes problem using arbitrary interpolations
R Codina

SIAM Journal on Numerical Analysis 47 (1), 699-718, 2009
Approximate imposition of boundary conditions in immersed boundary methods
R Codina, J Baiges

International Journal for Numerical Methods in Engineering 80 (11), 1379-1405, 2009
On a multiscale approach to the transient Stokes problem: Dynamic subscales and anisotropic space–time discretization
S Badia, R Codina

Applied Mathematics and Computation 207 (2), 415-433, 2009
The fixed-mesh ALE approach for the numerical approximation of flows in moving domains
R Codina, G Houzeaux, H Coppola-Owen, J Baiges

Journal of Computational Physics 228 (5), 1591-1611, 2009
Unified stabilized finite element formulations for the Stokes and the Darcy problems
S Badia, R Codina

SIAM journal on Numerical Analysis 47 (3), 1971-2000, 2009
A stabilized finite element approximation of low speed thermally coupled flows
J Principe, R Codina

International Journal of Numerical Methods for Heat & Fluid Flow 18 (7/8 ..., 2008
Finite element approximation of the modified Boussinesq equations using a stabilized formulation
R Codina, JM González‐Ondina, G Díaz‐Hernández, J Principe

International Journal for Numerical Methods in Fluids 57 (9), 1249-1268, 2008
Finite element approximation of the hyperbolic wave equation in mixed form
R Codina

Computer Methods in Applied Mechanics and Engineering 197 (13), 1305-1322, 2008
Analysis of a stabilized finite element approximation of the Oseen equations using orthogonal subscales
R Codina

Applied Numerical Mathematics 58 (3), 264-283, 2008
A finite element model for free surface flows on fixed meshes
AH Coppola‐Owen, R Codina

International Journal for Numerical Methods in Fluids 54 (10), 1151-1171, 2007
An algebraic subgrid scale finite element method for the convected Helmholtz equation in two dimensions with applications in aeroacoustics
O Guasch, R Codina

Computer Methods in Applied Mechanics and Engineering 196 (45), 4672-4689, 2007
Convergence analysis of the FEM approximation of the first order projection method for incompressible flows with and without the inf-sup condition
S Badia, R Codina

Numerische Mathematik 107 (4), 533-557, 2007
Algebraic pressure segregation methods for the incompressible Navier-Stokes equations
S Badia, R Codina

Archives of Computational Methods in Engineering 15 (3), 1-52, 2007
On some fluid–structure iterative algorithms using pressure segregation methods. Application to aeroelasticity
S Badia, R Codina

International Journal for Numerical Methods in Engineering 72 (1), 46-71, 2007
Dynamic subscales in the finite element approximation of thermally coupled incompressible flows
R Codina, J Principe

International journal for numerical methods in fluids 54 (6‐8), 707-730, 2007
A finite element method for the solution of rotary pumps
G Houzeaux, R Codina

Computers & Fluids 36 (4), 667-679, 2007
Time dependent subscales in the stabilized finite element approximation of incompressible flow problems
R Codina, J Principe, O Guasch, S Badia

Computer Methods in Applied Mechanics and Engineering 196 (21), 2413-2430, 2007
Numerical comparison of CBS and SGS as stabilization techniques for the incompressible Navier–Stokes equations
R Codina, H Coppola‐Owen, P Nithiarasu, CB Liu

International Journal for Numerical Methods in Engineering 66 (10), 1672-1689, 2006
On some pressure segregation methods of fractional-step type for the finite element approximation of incompressible flow problems
R Codina, S Badia

Computer Methods in Applied Mechanics and Engineering 195 (23), 2900-2918, 2006
Stabilized finite element approximation of the stationary magneto-hydrodynamics equations
R Codina, N Hernández-Silva

Computational Mechanics 38 (4-5), 344-355, 2006
Analysis of a stabilized finite element approximation of the transient convection-diffusion equation using an ALE framework
S Badia, R Codina

SIAM Journal on Numerical Analysis 44 (5), 2159-2197, 2006
The Characteristic‐Based Split (CBS) scheme—a unified approach to fluid dynamics
P Nithiarasu, R Codina, OC Zienkiewicz

International Journal for Numerical Methods in Engineering 66 (10), 1514-1546, 2006
Improving Eulerian two‐phase flow finite element approximation with discontinuous gradient pressure shape functions
AH Coppola‐Owen, R Codina

International journal for numerical methods in fluids 49 (12), 1287-1304, 2005
A finite element model for the simulation of lost foam casting
G Houzeaux, R Codina

International journal for numerical methods in fluids 46 (2), 203-226, 2004
A stabilized finite element predictor–corrector scheme for the incompressible Navier–Stokes equations using a nodal‐based implementation
R Codina, A Folch

International Journal for Numerical Methods in Fluids 44 (5), 483-503, 2004
Error estimates for an operator-splitting method for incompressible flows
J Blasco, R Codina

Applied Numerical Mathematics 51 (1), 1-17, 2004
Approximation of the incompressible Navier–Stokes equations using orthogonal subscale stabilization and pressure segregation on anisotropic finite element meshes
R Codina, O Soto

Computer Methods in Applied Mechanics and Engineering 193 (15), 1403-1419, 2004
An iteration-by-subdomain overlapping Dirichlet/Robin domain decomposition method for advection–diffusion problems
G Houzeaux, R Codina

Journal of Computational and Applied Mathematics 158 (2), 243-276, 2003
A Chimera method based on a Dirichlet/Neumann (Robin) coupling for the Navier–Stokes equations
G Houzeaux, R Codina

Computer Methods in Applied Mechanics and Engineering 192 (31), 3343-3377, 2003
A numerical model to track two‐fluid interfaces based on a stabilized finite element method and the level set technique
R Codina, O Soto

International Journal for Numerical Methods in Fluids 40 (1‐2), 293-301, 2002
CBS versus GLS stabilization of the incompressible Navier–Stokes equations and the role of the time step as stabilization parameter
R Codina, OC Zienkiewicz

International Journal for Numerical Methods in Biomedical Engineering 18 (2 ..., 2002
Analysis of a stabilized finite element approximation of the transient convection-diffusion-reaction equation using orthogonal subscales
R Codina, J Blasco

Computing and Visualization in Science 4 (3), 167-174, 2002
Stabilized finite element approximation of transient incompressible flows using orthogonal subscales
R Codina

Computer Methods in Applied Mechanics and Engineering 191 (39), 4295-4321, 2002
Transmission conditions with constraints in finite element domain decomposition methods for flow problems
G Houzeaux, R Codina

International Journal for Numerical Methods in Biomedical Engineering 17 (3 ..., 2001
Space and time error estimates for a first order, pressure stabilized finite element method for the incompressible Navier–Stokes equations
J Blasco, R Codina

Applied Numerical Mathematics 38 (4), 475-497, 2001
Implementation of a stabilized finite element formulation for the incompressible Navier–Stokes equations based on a pressure gradient projection
R Codina, J Blasco, GC Buscaglia, A Huerta

International Journal for Numerical Methods in Fluids 37 (4), 419-444, 2001
A stabilized finite element method for generalized stationary incompressible flows
R Codina

Computer Methods in Applied Mechanics and Engineering 190 (20), 2681-2706, 2001
Pressure stability in fractional step finite element methods for incompressible flows
R Codina

Journal of Computational Physics 170 (1), 112-140, 2001
A nodal‐based implementation of a stabilized finite element method for incompressible flow problems
R Codina

International Journal for numerical methods in fluids 33 (5), 737-766, 2000
Fourier analysis of an equal‐order incompressible flow solver stabilized by pressure gradient projection
GC Buscaglia, FG Basombrio, R Codina

International journal for numerical methods in fluids 34 (1), 65-92, 2000
Analysis of a pressure-stabilized finite element approximation of the stationary Navier-Stokes equations
R Codina, J Blasco

Numerische Mathematik 87 (1), 59-81, 2000
On stabilized finite element methods for linear systems of convection–diffusion-reaction equations
R Codina

Computer Methods in Applied Mechanics and Engineering 188 (1), 61-82, 2000
Stabilized finite element method for the transient Navier–Stokes equations based on a pressure gradient projection
R Codina, J Blasco

Computer Methods in Applied Mechanics and Engineering 182 (3), 277-300, 2000
Stabilization of incompressibility and convection through orthogonal sub-scales in finite element methods
R Codina

Computer methods in applied mechanics and engineering 190 (13), 1579-1599, 2000
Numerical solution of the incompressible Navier–Stokes equations with Coriolis forces based on the discretization of the total time derivative
R Codina

Journal of Computational Physics 148 (2), 467-496, 1999
Finite element implementation of two‐equation and algebraic stress turbulence models for steady incompressible flows
R Codina, O Soto

International journal for numerical methods in fluids 30 (3), 309-333, 1999
The characteristic‐based‐split procedure: an efficient and accurate algorithm for fluid problems
OC Zienkiewicz, P Nithiarasu, R Codina, M Vazquez, P Ortiz

International Journal for Numerical Methods in Fluids 31 (1), 359-392, 1999
A numerical model for temporal variations during explosive central vent eruptions
A Folch, J Martí, R Codina, M Vazquez

Journal of Geophysical Research: Solid Earth 103 (B9), 20883-20899, 1998
Shock capturing viscosities for the general fluid mechanics algorithm
P Nithiarasu, OC Zienkiewicz, BVK Sai, K Morgan, R Codina, M Vazquez

International Journal for Numerical Methods in Fluids 28 (9), 1325-1353, 1998
A fractional-step method for the incompressible Navier-Stokes equations related to a predictor-multicorrector algorithm
J Blasco Lorente, R Codina, A Huerta

International Journal for Numerical Methods in Fluids 28 (10), 1391-1419, 1998
A general algorithm for compressible and incompressible flows. Part III: The semi‐implicit form
R Codina, M Vázquez, OC Zienkiewicz

International Journal for Numerical Methods in Fluids 27 (1‐4), 13-32, 1998
Comparison of some finite element methods for solving the diffusion-convection-reaction equation
R Codina

Computer Methods in Applied Mechanics and Engineering 156 (1-4), 185-210, 1998
Finite element solution of the Stokes problem with dominating Coriolis force
R Codina, O Soto

Computer Methods in Applied Mechanics and Engineering 142 (3-4), 215-234, 1997
A finite element formulation for the Stokes problem allowing equal velocity-pressure interpolation
R Codina, J Blasco

Computer Methods in Applied Mechanics and Engineering 143 (3-4), 373-391, 1997
Block-iterative algorithms for nonlinear coupled problems.
M Cervera, R Codina

CIMNE, 1996
SPLIT, CHARACTERISTIC BASED SEMI‐IMPLICIT ALGORITHM FOR LAMINAR/TURBULENT INCOMPRESSIBLE FLOWS
OC Zienkiewicz, BVK Satya Sai, K Morgan, R Codina

International Journal for Numerical Methods in Fluids 23 (8), 787-809, 1996
On the computational efficiency and implementation of block-iterative algorithms for nonlinear coupled problems
M Cervera, R Codina, M Galindo

Engineering computations 13 (6), 4-30, 1996
A general algorithm for compressible and incompressible flow—Part II. Tests on the explicit form
OC Zienkiewicz, K Morgan, BVK Sai, R Codina, M Vasquez

International Journal for Numerical Methods in Fluids 20 (8‐9), 887-913, 1995
A general algorithm for compressible and incompressible flow—Part I. the split, characteristic‐based scheme
OC Zienkiewicz, R Codina

International Journal for Numerical Methods in Fluids 20 (8‐9), 869-885, 1995
Mould filling simulation using finite elements
R Codina, U Schäfer, E Oñate

International Journal of Numerical Methods for Heat & Fluid Flow 4 (4), 291-310, 1994
Stability analysis of the forward Euler scheme for the convection‐diffusion equation using the SUPG formulation in space
R Codina

International journal for numerical methods in engineering 36 (9), 1445-1464, 1993
An iterative penalty method for the finite element solution of the stationary Navier-Stokes equations
R Codina

Computer methods in applied mechanics and engineering 110 (3-4), 237-262, 1993
A finite element formulation for the numerical solution of the convection-diffusion equation
R Codina

Centro Internacional de Métodos Numéricos en Ingeniería, 1993
A discontinuity-capturing crosswind-dissipation for the finite element solution of the convection-diffusion equation
R Codina

Computer Methods in Applied Mechanics and Engineering 110 (3-4), 325-342, 1993
A finite element model for incompressible flow problems
R Codina

Universitat Politècnica de Catalunya, 1992
The intrinsic time for the streamline upwind/Petrov-Galerkin formulation using quadratic elements
R Codina, E Oñate, M Cervera

Computer Methods in Applied Mechanics and Engineering 94 (2), 239-262, 1992

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Articles (Documents not available in Scipedia)

Assessment of variational multiscale models for the large eddy simulation of turbulent incompressible flows

Mixed stabilized finite element methods in nonlinear solid mechanics. Part III: Compressible and incompressible plasticity

Large eddy simulation of low mach number flows using dynamic and orthogonal subgrid scales

Stabilized stress–velocity–pressure finite element formulations of the Navier–Stokes problem for fluids with non-linear viscosity

Variational multi-scale stabilized formulations for the stationary three-field incompressible viscoelastic flow problem

Anisotropic adaptive meshing and monolithic Variational Multiscale method for fluid–structure interaction

On an unconditionally convergent stabilized finite element approximation of resistive magnetohydrodynamics

Immersed stress method for fluid–structure interaction using anisotropic mesh adaptation

Explicit reduced‐order models for the stabilized finite element approximation of the incompressible Navier–Stokes equations

Statistical behavior of the orthogonal subgrid scale stabilization terms in the finite element large eddy simulation of turbulent flows

Stokes, Maxwell and Darcy: A single finite element approximation for three model problems

A nodal-based finite element approximation of the Maxwell problem suitable for singular solutions

A symmetric method for weakly imposing Dirichlet boundary conditions in embedded finite element meshes

Approximation of the inductionless MHD problem using a stabilized finite element method

The Fixed‐Mesh ALE approach for the numerical simulation of floating solids

A finite element dynamical nonlinear subscale approximation for the low Mach number flow equations

Mesh objective modeling of cracks using continuous linear strain and displacement interpolations

On the stabilization parameter in the subgrid scale approximation of scalar convection–diffusion–reaction equations on distorted meshes

Long-term stability estimates and existence of a global attractor in a finite element approximation of the Navier–Stokes equations with numerical subgrid scale modeling

Finite element approximation of turbulent thermally coupled incompressible flows with numerical sub-grid scale modelling

The fixed‐mesh ALE approach applied to solid mechanics and fluid–structure interaction problems

Stabilized continuous and discontinuous Galerkin techniques for Darcy flow

The dissipative structure of variational multiscale methods for incompressible flows

Mixed stabilized finite element methods in nonlinear solid mechanics: Part ii: Strain localization

Mathematical models for thermally coupled low speed flows

Subscales on the element boundaries in the variational two-scale finite element method

Finite element approximation of the three-field formulation of the Stokes problem using arbitrary interpolations

Approximate imposition of boundary conditions in immersed boundary methods

On a multiscale approach to the transient Stokes problem: Dynamic subscales and anisotropic space–time discretization

The fixed-mesh ALE approach for the numerical approximation of flows in moving domains

Unified stabilized finite element formulations for the Stokes and the Darcy problems

A stabilized finite element approximation of low speed thermally coupled flows

Finite element approximation of the modified Boussinesq equations using a stabilized formulation

Finite element approximation of the hyperbolic wave equation in mixed form

Analysis of a stabilized finite element approximation of the Oseen equations using orthogonal subscales

A finite element model for free surface flows on fixed meshes

An algebraic subgrid scale finite element method for the convected Helmholtz equation in two dimensions with applications in aeroacoustics

Convergence analysis of the FEM approximation of the first order projection method for incompressible flows with and without the inf-sup condition

Algebraic pressure segregation methods for the incompressible Navier-Stokes equations

On some fluid–structure iterative algorithms using pressure segregation methods. Application to aeroelasticity

Dynamic subscales in the finite element approximation of thermally coupled incompressible flows

A finite element method for the solution of rotary pumps

Time dependent subscales in the stabilized finite element approximation of incompressible flow problems

Numerical comparison of CBS and SGS as stabilization techniques for the incompressible Navier–Stokes equations

On some pressure segregation methods of fractional-step type for the finite element approximation of incompressible flow problems

Stabilized finite element approximation of the stationary magneto-hydrodynamics equations

Analysis of a stabilized finite element approximation of the transient convection-diffusion equation using an ALE framework

The Characteristic‐Based Split (CBS) scheme—a unified approach to fluid dynamics

Improving Eulerian two‐phase flow finite element approximation with discontinuous gradient pressure shape functions

A finite element model for the simulation of lost foam casting

A stabilized finite element predictor–corrector scheme for the incompressible Navier–Stokes equations using a nodal‐based implementation

Error estimates for an operator-splitting method for incompressible flows

Approximation of the incompressible Navier–Stokes equations using orthogonal subscale stabilization and pressure segregation on anisotropic finite element meshes

An iteration-by-subdomain overlapping Dirichlet/Robin domain decomposition method for advection–diffusion problems

A Chimera method based on a Dirichlet/Neumann (Robin) coupling for the Navier–Stokes equations

A numerical model to track two‐fluid interfaces based on a stabilized finite element method and the level set technique

CBS versus GLS stabilization of the incompressible Navier–Stokes equations and the role of the time step as stabilization parameter

Analysis of a stabilized finite element approximation of the transient convection-diffusion-reaction equation using orthogonal subscales

Stabilized finite element approximation of transient incompressible flows using orthogonal subscales

Transmission conditions with constraints in finite element domain decomposition methods for flow problems

Space and time error estimates for a first order, pressure stabilized finite element method for the incompressible Navier–Stokes equations

Implementation of a stabilized finite element formulation for the incompressible Navier–Stokes equations based on a pressure gradient projection

A stabilized finite element method for generalized stationary incompressible flows

Pressure stability in fractional step finite element methods for incompressible flows

A nodal‐based implementation of a stabilized finite element method for incompressible flow problems

Fourier analysis of an equal‐order incompressible flow solver stabilized by pressure gradient projection

Analysis of a pressure-stabilized finite element approximation of the stationary Navier-Stokes equations

On stabilized finite element methods for linear systems of convection–diffusion-reaction equations

Stabilized finite element method for the transient Navier–Stokes equations based on a pressure gradient projection

Stabilization of incompressibility and convection through orthogonal sub-scales in finite element methods

Numerical solution of the incompressible Navier–Stokes equations with Coriolis forces based on the discretization of the total time derivative

Finite element implementation of two‐equation and algebraic stress turbulence models for steady incompressible flows

The characteristic‐based‐split procedure: an efficient and accurate algorithm for fluid problems

A numerical model for temporal variations during explosive central vent eruptions

Shock capturing viscosities for the general fluid mechanics algorithm

A fractional-step method for the incompressible Navier-Stokes equations related to a predictor-multicorrector algorithm

A general algorithm for compressible and incompressible flows. Part III: The semi‐implicit form