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Documents published in Scipedia

Pseudoplastic fluid flows for different Prandtl numbers: steady and time-dependent solutions
A. Aguirre, E. Castillo, M. Cruchaga, R. Codina, J. Baiges

International Journal for Numerical Methods in Engineering (2019). Vol. 145, pp. 106022-1/106022-17

Abstract
In this work, a variational multiscale (VMS) finite element formulation is used to approximate numerically the natural convection in square cavity with differentially heated from sidewalls problem for Newtonian and power-law fluids. The problem is characterized for going through a Hopf bifurcation when reaching high enough Rayleigh numbers, which initiates the transition between steady and time dependent behavior, however, results found in the literature are only for air Prandtl number. The presented VMS formulation is validated using existing results, and is used to study highly convective cases, to determine the flow conditions at which it becomes time dependent, and to establish new benchmark solutions for non-Newtonian fluid flows for different Pr and power-law indexes n. The range of solutions were found in the range 0.6
Abstract
In this work, a variational multiscale (VMS) finite element formulation is used to approximate numerically the natural convection in square cavity with differentially heated [...]
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Approximation of the transport of pollutants with reaction terms in shallow waters using finite elements
A. Villota, R. Codina

Rev. int. métodos numér. cálc. diseño ing. (2021). Vol. 37, (1), 6

Abstract
In this article we present the approximation of the coupled model of the equations of motion of a fluid in shallow waters with the convection-diffusion-reaction (CDR) equation of pollutant transport. This approximation is carried out using high order finite elements and using stabilised variational sub-scale methods. We write the coupled system of equations, previously discretised in time and linearised, as a transient vector equation of CDR. The stabilised finite element methods used are the known ASGS and OSS sub-scale methods, the same ones that allow us to use the same interpolation for all unknowns, as well as to deal with dominant convection and reaction flows. We consider the possibility of non-linearity in both the convective and reaction terms. We will not consider the possible development of shocks in the solution. In order to examine the accuracy and robustness of the ASGS and OSS methods, we present four test cases: mesh convergence, transport of a pollutant in a square cavity, transport of a pollutant in the Gulf of Roses and at the river Guadalquivir mouth, and the predator-prey model, which can be written as a transient CDR vector equation with non-linearity in the reaction term.
Abstract
In this article we present the approximation of the coupled model of the equations of motion of a fluid in shallow waters with the convection-diffusion-reaction (CDR) equation [...]
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A finite element dynamical nonlinear subscale approximation for the low Mach number flow equations
M. Ávila, J. Principe, R. Codina

Journal of Computational Physics (2011). Vol. 230 (22), pp. 7988-8009

Abstract
In this work we propose a variational multiscale finite element approximation of thermally coupled low speed flows. The physical model is described by the low Mach number equations, which are obtained as a limit of the compressible Navier–Stokes equations in the small Mach number regime. In contrast to the commonly used Boussinesq approximation, this model permits to take volumetric deformation into account. Although the former is more general than the latter, both systems have similar mathematical structure and their numerical approximation can suffer from the same type of instabilities. We propose a stabilized finite element approximation based on the variational multiscale method, in which a decomposition of the approximating space into a coarse scale resolvable part and a fine scale subgrid part is performed. Modeling the subscale and taking its effect on the coarse scale problem into account results in a stable formulation. The quality of the final approximation (accuracy, efficiency) depends on the particular model. The distinctive features of our approach are to consider the subscales as transient and to keep the scale splitting in all the nonlinear terms. The first ingredient permits to obtain an improved time discretization scheme (higher accuracy, better stability, no restrictions on the time step size). The second ingredient permits to prove global conservation properties. It also allows us to approach the problem of dealing with thermal turbulence from a strictly numerical point of view. Numerical tests show that nonlinear and dynamic subscales give more accurate solutions than classical stabilized methods.
Abstract
In this work we propose a variational multiscale finite element approximation of thermally coupled low speed flows. The physical model is described by the low Mach number [...]
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Generació de malles estructurades a partir d'equacions el·líptiques
R. Codina

(1990). Research Report, Nº PI7

Abstract
En aquest treball es descriu un mètode de generació de malles estructurades d'elements finits basat en imposar que les línies coordenades satisfacin una equació el·líptica, analitzant l'efecte de diferents termes amb les incògnites sense derivar d'aquesta equció sobre la malla resultant. Les equacions que cal resoldre es descrititzen en diferències finites, adaptant-hi les tècniques anomenades d'upwind pròpies del mètode dels elements finits. Es presenta també una tècnica de resolució del sistema algebraic d'equacions resultant.
Abstract
En aquest treball es descriu un mètode de generació de malles estructurades d'elements finits basat en imposar que les línies coordenades satisfacin [...]
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A finite element reduced order model based on adaptive mesh refinement and artificial neural networks
J. Baiges, R. Codina, I. Castañar, E. Castillo

Comput. Methods Appl. Mech. Engrg., (2019). (prepint) pp. 1-14

Abstract
In this work a reduced order model based on adaptive finite element meshes and a correction term obtained by using an artificial neural network (FAN-ROM) is presented. The idea is to run a high-fidelity simulation by using an adaptively refined finite element mesh, and compare the results obtained with those of a coarse mesh finite element model. From this comparison, a correction forcing term can be computed for each training configuration. A model for the correction term is built by using an artificial neural network, and the final reduced order model is obtained by putting together the coarse mesh finite element model, plus the artificial neural network model for the correction forcing term. The methodology is applied to non-linear solid mechanics problems, transient quasi-incompressible flows, and a fluid-structure interaction problem. The results of the numerical examples show that the FAN-ROM is capable of improving the simulation results obtained in coarse finite element meshes at a reduced computational cost.
Abstract
In this work a reduced order model based on adaptive finite element meshes and a correction term obtained by using an artificial neural network (FAN-ROM) is presented. The [...]
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Variational multi-scale approximation of the one-dimensional forced Burguers' equation: the role of orthogonal sub-grid scales in turbulence modelling
C. Bayona, J. Baiges, R. Codina

Int. J. Numer. Meth. Fluids (2018). Vol. 86, pp. 313-328

Abstract
A numerical approximation for the one-dimensional Burgers equation is proposed by means of the orthogonal subgrid scales–variational multiscale (OSGS-VMS) method. We evaluate the role of the variational subscales in describing the Burgers “turbulence” phenomena. Particularly, we seek to clarify the interaction between the subscales and the resolved scales when the former are defined to be orthogonal to the finite-dimensional space. Direct numerical simulation is used to evaluate the resulting OSGS-VMS energy spectra. The comparison against a large eddy simulation model is presented for numerical discretizations in which the grid is not capable of solving the small scales. An accurate approximation to the phenomena of turbulence is obtained with the addition of the purely dissipative numerical terms given by the OSGS-VMS method without any modification of the continuous problem
Abstract
A numerical approximation for the one-dimensional Burgers equation is proposed by means of the orthogonal subgrid scales–variational multiscale (OSGS-VMS) method. We [...]
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Statistical behavior of the orthogonal subgrid scale stabilization terms in the finite element large eddy simulation of turbulent flows
O. Guasch, R. Codina

Comput. Methods Appl. Mech. Engrg., (2013). Vol. 261-262, pp. 145-166

Abstract
Abstract Numerical simulations have proved that Variational Multiscale Methods (VMM) perform well as pure numerical large eddy simulation (LES) models. In this paper we focus on the orthogonal subgrid scale (OSS) finite element method and make an analysis of the statistical behavior of its stabilization terms in the quasi static approximation. This is done by resorting to results from classical statistical fluid mechanics concerning two point velocity, pressure and combined correlation functions of various orders. Given a fine enough mesh with characteristic element size h in the inertial subrange of a turbulent flow, it is shown that the rate of transfer of subgrid kinetic energy provided by the OSS stabilization terms does not depend on h and that it equals the molecular physical dissipation rate (up to a dimensionless constant that only depends on the finite element shapes) for a proper redesign of the standard parameters of the formulation. This is a noteworthy fact taking into account that the subgrid stabilization terms do not arise from physical considerations, but from the mathematical necessity to allow equal interpolation for the pressure and velocity fields, as well as to control convection. Therefore, the obtained results contribute somehow to the line of reasoning supporting that pure numerical approaches (i.e., without introducing additional physical models) could probably suffice in the LES simulation of turbulent flows
Abstract
Abstract Numerical simulations have proved that Variational Multiscale Methods (VMM) perform well as pure numerical large eddy simulation (LES) models. In this paper we focus [...]
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A general algorithm for compressible and incompressible flow—Part II. tests on the explicit form
O. Zienkiewicz, K. Morgan, B. Sai, R. Codina, M. Vasquez

Int. J. Numer. Meth. Fluids (1995). Vol. 20 (8-9), pp. 887-913

Abstract
The algorithm introduced in Part I of this paper is applied in its explicit form to a variety of problems in order to demonstrate its wide range of applicability and excellent performance. Examples range from nearly incompressible, viscous, flows through transonic applications to high speed flows with shocks. In most examples linear triangular elements are used in the finite element approximation, but some use of quadratic approximation, again in triangles, indicates satisfactory performance even in the case of severe shocks.
Abstract
The algorithm introduced in Part I of this paper is applied in its explicit form to a variety of problems in order to demonstrate its wide range of applicability and excellent [...]
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Chebyshev spectral collocation method approximations of the Stokes eigenvalue problem based on penalty techniques
Ö. Türk, R. Codina

Applied Numerical Mathematics (2019). (preprint) Vol. 145, pp. 188-200

Abstract
Numerical solution strategies for the Stokes eigenvalue problem based on the use of penalty formulations are investigated in this study. It is shown that the penalty method approach can successfully be adapted for the eigenproblem to rectify the associated problems such as the existence of zero diagonal entries in the resulting algebraic system. Two different schemes, namely, the standard penalisation with a small penalty parameter, and the iterative penalisation that enables relatively large parameters, are implemented. The employment of the latter leads to a so-called inhomogeneous generalised eigenvalue problem which requires a special attention. A feasible solution strategy is presented which is adapted from a procedure based on Newton's method proposed for the corresponding standard (inhomogeneous) eigenvalue problems. Concerning the spatial discretisation, among other possible options, the Chebyshev spectral collocation method based on expanding the unknown fields in tensor product of Chebyshev polynomials is employed. It is shown that the method constitutes a novel way of efficiently examining the approximate eigensolutions of the Stokes operator with the use of Chebyshev spectral collocation method directly, without a decoupling of velocity and pressure.
Abstract
Numerical solution strategies for the Stokes eigenvalue problem based on the use of penalty formulations are investigated in this study. It is shown that the penalty method [...]
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Logarithmic conformation reformulation in viscoelastic flow problems approximated by a VMS-type stabilized finite element formulation
L. Moreno García, R. Codina, J. Baiges, E. Castillo

Comput. Methods Appl. Mech. Engrg., (2019). Vol. 354, pp. 706-731

Abstract
The log-conformation reformulation, originally proposed by Fattal and Kupferman (2004), allows computing incompressible viscoelastic problems with high Weissenberg numbers which are impossible to solve with the typical three-field formulation. By following this approach, in this work we develop a new stabilized finite element formulation based on the logarithmic reformulation using the Variational Multiscale (VMS) method as stabilization technique, together with a modified log-conformation formulation. Our approach follows the term-by-term stabilization proposed by Castillo and Codina (2014) for the standard formulation, which is more effective when there are stress singularities. The formulation can be used when the relaxation parameter is set to zero, and permits a direct steady numerical resolution. The formulation is validated in the classical benchmark flow past a cylinder and in the well-known planar contraction 4:1, achieving very accurate, stable and mesh independent results for highly elastic fluids.
Abstract
The log-conformation reformulation, originally proposed by Fattal and Kupferman (2004), allows computing incompressible viscoelastic problems with high Weissenberg numbers [...]
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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