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  • Assessment of variational multiscale models for the large eddy simulation of tur- bulent incompressible flows

     Colomés Gené, Oriol; Badia Rodriguez, Santiago I.; Codina Rovira, Ramon; Principe Rubio, Ricardo Javier
    Computer methods in applied mechanics and engineering
    Vol. 285, p. 32-63
    DOI: 10.1016/j.cma.2014.10.041
    Date of publication: 2015-03
    Journal article

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    In this work we study the performance of some variational multiscale models (VMS) in the large eddy simulation (LES) of turbulent flows. We consider VMS models obtained by different subgrid scale approximations which include either static or dynamic subscales, linear or nonlinear multiscale splitting, and different choices of the subscale space. After a brief review of these models, we discuss some implementation aspects particularly relevant to the simulation of turbulent flows, namely the use of a skew symmetric form of the convective term and the computation of projections when orthogonal subscales are used. We analyze the energy conservation (and numerical dissipation) of the alternative VMS formulations, which is numerically evaluated. In the numerical study, we have considered three well known problems: the decay of homogeneous isotropic turbulence, the Taylor¿Green vortex problem and the turbulent flow in a channel. We compare the results obtained using different VMS models, paying special attention to the effect of using orthogonal subscale spaces. The VMS results are also compared against classical LES scheme based on filtering and the dynamic Smagorinsky closure. Altogether, our results show the tremendous potential of VMS for the numerical simulation of turbulence. Further, we study the sensitivity of VMS to the algorithmic constants and analyze the behavior in the small time step limit. We have also carried out a computational cost comparison of the different formulations. Out of these experiments, we can state that the numerical results obtained with the different VMS formulations (as far as they converge) are quite similar. However, some choices are prone to instabilities and the results obtained in terms of computational cost are certainly different. The dynamic orthogonal subscales model turns out to be best in terms of efficiency and robustness.

  • On a free open source extreme scale finite element software (FEXFEM)

     Martín Huertas, Alberto Francisco; Badia Rodriguez, Santiago I.; Principe Rubio, Ricardo Javier
    Competitive project

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  • A highly scalable asynchronous implementation of balancing domain decomposition by constraints

     Badia Rodriguez, Santiago I.; Martín Huertas, Alberto Francisco; Principe Rubio, Ricardo Javier
    Numerical Methods for High Performance Computers - International SPPEXA Workshop
    p. 14-16
    Presentation's date: 2014-12-03
    Presentation of work at congresses

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  • A highly scalable parallel implementation of balancing domain decomposition by constraints

     Principe Rubio, Ricardo Javier; Badia Rodriguez, Santiago I.; Martín Huertas, Alberto Francisco
    World Congress on Computational Mechanics
    p. 1-2
    Presentation's date: 2014-07-25
    Presentation of work at congresses

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

     Ávila, Matías; Codina Rovira, Ramon; Principe Rubio, Ricardo Javier
    Computers and fluids
    Vol. 99, p. 44-66
    DOI: 10.1016/j.compfluid.2014.04.003
    Date of publication: 2014-07
    Journal article

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    Objective: In this article we study the approximation to thermal turbulence from a strictly numerical point of view, without the use of any physical model. The main goal is to analyze the behavior of our numerical method in the large eddy simulation (LES) of thermally coupled turbulent flows at low Mach number.; Methods: Our numerical method is 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 as LES model) depends on the particular subscale 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.; Another important contribution of this work is the extension of the orthogonal subgrid scale method widely tested for incompressible flows to variable density flows, using a density-weighted L-2 product to define the orthogonality of the subscales and the finite element spaces.; Results: Referring to numerical testing, we present numerical results for a laminar testcase validation that shows the dissipative behavior of the different stabilized methods. Then, we present results of the numerical simulation of two turbulent flow problems, the turbulent channel flow with large temperature differences in the wall normal direction at Re-tau = 180, and the turbulent thermally driven cavity with aspect ratio 4. The behavior of the method is evaluated by comparison against results available in the literature obtained using LES and direct numerical simulation (DNS). They are explained based on a careful analysis of the dissipative structure of the method, showing the physical interpretation of the subgrid scale method presented.; conclusion: The material presented here is a clear indication of the potential of the method to model all kinds of turbulent thermally coupled flows. The formulation is the same in laminar and turbulent regimes. (C) 2014 Elsevier Ltd. All rights reserved.

  • Variational multiscale Large Eddy Simulation of turbulent incompressible flows

     Badia Rodriguez, Santiago I.; Codina Rovira, Ramon; Colomés Gené, Oriol; Principe Rubio, Ricardo Javier
    World Congress on Computational Mechanics
    Presentation's date: 2014-07
    Presentation of work at congresses

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  • A highly scalable asynchronous implementation of balancing domain decomposition by constraints

     Badia Rodriguez, Santiago I.; Martín Huertas, Alberto Francisco; Principe Rubio, Ricardo Javier
    Sparse Days
    Presentation's date: 2014-06
    Presentation of work at congresses

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  • A highly scalable parallel implementation of balancing domain decomposition by constraints

     Badia Rodriguez, Santiago I.; Martín Huertas, Alberto Francisco; Principe Rubio, Ricardo Javier
    SIAM journal on scientific computing
    Vol. 36, num. 2, p. C190-C218
    DOI: 10.1137/130931989
    Date of publication: 2014-01
    Journal article

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    In this work we propose a novel parallelization approach of two-level balancing domain decomposition by constraints preconditioning based on overlapping of fine-grid and coarse-grid duties in time. The global set of MPI tasks is split into those that have fine-grid duties and those that have coarse-grid duties, and the different computations and communications in the algorithm are then rescheduled and mapped in such a way that the maximum degree of overlapping is achieved while preserving data dependencies among them. In many ranges of interest, the extra cost associated to the coarse-grid problem can be fully masked by fine-grid related computations (which are embarrassingly parallel). Apart from discussing code implementation details, the paper also presents a comprehensive set of numerical experiments that includes weak scalability analyses with structured and unstructured meshes for the three-dimensional Poisson and linear elasticity problems on a pair of state-of-the-art multicore-based distributed-memory machines. This experimental study reveals remarkable weak scalability in the solution of problems with thousands of millions of unknowns on several tens of thousands of computational cores.

  • Anàlisis numèrica i computació científica

     Badia Rodriguez, Santiago I.; Principe Rubio, Ricardo Javier; Martín Huertas, Alberto Francisco; Espinoza Roman, Hector Gabriel; Castillo, Ernesto; Pont Ribas, Arnau; Hierro Fabregat, Alba; Bayona Roa, Camilo Andres; Villota Cadena, Angel Patricio; Codina Rovira, Ramon
    Competitive project

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  • Variational multiscale large eddy simulation of turbulent incompressible flows

     Colomés Gené, Oriol; Badia Rodriguez, Santiago I.; Codina Rovira, Ramon; Principe Rubio, Ricardo Javier
    Variational Multiscale and Stabilized Finite Elements
    Presentation's date: 2013-11
    Presentation of work at congresses

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  • Enhanced balancing Neumann-Neumann preconditioning in computational fluid and solid mechanics

     Badia Rodriguez, Santiago I.; Martín Huertas, Alberto Francisco; Principe Rubio, Ricardo Javier
    International journal for numerical methods in engineering
    Vol. 96, num. 4, p. 203-230
    DOI: 10.1002/nme.4541
    Date of publication: 2013-10
    Journal article

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    In this work, we propose an enhanced implementation of balancing Neumann¿Neumann (BNN) preconditioning together with a detailed numerical comparison against the balancing domain decomposition by constraints (BDDC) preconditioner. As model problems, we consider the Poisson and linear elasticity problems. On one hand, we propose a novel way to deal with singular matrices and pseudo-inverses appearing in local solvers. It is based on a kernel identification strategy that allows us to efficiently compute the action of the pseudo-inverse via local indefinite solvers. We further show how, identifying a minimum set of degrees of freedom to be fixed, an equivalent definite system can be solved instead, even in the elastic case. On the other hand, we propose a simple implementation of the algorithm that reduces the number of Dirichlet solvers to only one per iteration, leading to similar computational cost as additive methods. After these improvements of the BNN preconditioned conjugate gradient algorithm, we compare its performance against that of the BDDC preconditioners on a pair of large-scale distributed-memory platforms. The enhanced BNN method is a competitive preconditioner for three-dimensional Poisson and elasticity problems and outperforms the BDDC method in many cases.

  • Numerical Methods and Tools for Key Exascale Computing Challenges in Engineering and Applied Sciences (NUMEXAS)

     Badia Rodriguez, Santiago I.; Oñate Ibáñez de Navarra, Eugenio; Martín Huertas, Alberto Francisco; Principe Rubio, Ricardo Javier
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  • Implementation and scalability analysis of balancing domain decomposition methods

     Badia Rodriguez, Santiago I.; Martín Huertas, Alberto Francisco; Principe Rubio, Ricardo Javier
    Archives of computational methods in engineering
    Vol. 20, num. 3, p. 239-262
    DOI: 10.1007/s11831-013-9086-4
    Date of publication: 2013
    Journal article

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    n this paper we present a detailed description of a high-performance distributed-memory implementation of balancing domain decomposition preconditioning techniques. This coverage provides a pool of implementation hints and considerations that can be very useful for scientists that are willing to tackle large-scale distributed-memory machines using these methods. On the other hand, the paper includes a comprehensive performance and scalability study of the resulting codes when they are applied for the solution of the Poisson problem on a large-scale multicore-based distributed-memory machine with up to 4096 cores. Well-known theoretical results guarantee the optimality (algorithmic scalability) of these preconditioning techniques for weak scaling scenarios, as they are able to keep the condition number of the preconditioned operator bounded by a constant with fixed load per core and increasing number of cores. The experimental study presented in the paper complements this mathematical analysis and answers how far can these methods go in the number of cores and the scale of the problem to still be within reasonable ranges of efficiency on current distributed-memory machines. Besides, for those scenarios where poor scalability is expected, the study precisely identifies, quantifies and justifies which are the main sources of inefficiency.

  • Hybrid parallel solvers for the finite element approximation of PDEs

     Principe Rubio, Ricardo Javier; Badia Rodriguez, Santiago I.; Martín Huertas, Alberto Francisco
    World Congress on Computational Mechanics
    p. 1
    Presentation's date: 2012-07-11
    Presentation of work at congresses

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  • Análisis paramétrico de sistemas de ventilación natural en edificios (PARANAT).

     Martí Herrero, Jaime; Principe Rubio, Ricardo Javier; Danov, Stoyan; Ávila, Matias; Cipriano, Xavier; Carbonell, Jordi
    Competitive project

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  • Actes dels seminaris de recerca 1r, 2n i 3r, del Departament de Mecànica de Fluids - UPC

     De Las Heras Jimenez, Salvador Augusto; Carbo Bech, Alberto Antonio; Moreno Llagostera, Hipolit; Valle, L. J.; Poeata, I.; López, J.; Torres Camara, Ricardo; Barraco Serra, Marc; Fernandez Aguado, Enrique; Escaler Puigoriol, Francesc Xavier; Hutter, J.K.; Egusquiza Estevez, Eduardo; Farhat, Mohamed; Avellan, François; Esque de los Ojos, Daniel; Dalmau Andreu, Roger; Principe Rubio, Ricardo Javier; Roe Vellve, Nuria; Codina Rovira, Ramon; Badia Rodriguez, Santiago I.; Garcia Vilchez, Mercedes; Gamez Montero, Pedro Javier; Codina Macià, Esteban; Watton, John
    Date of publication: 2011-11-01
    Book

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

     Ávila, Matias; Principe Rubio, Ricardo Javier; Codina Rovira, Ramon
    Journal of computational physics
    Vol. 230, num. 22, p. 7988-8009
    DOI: 10.1016/j.jcp.2011.06.032
    Date of publication: 2011-09-10
    Journal article

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  • Dynamic nonlinear variational multiscale approximation of low Mach number flows

     Principe Rubio, Ricardo Javier; Ávila, Matias; Codina Rovira, Ramon
    US National Congress on Computational Mechanics
    Presentation's date: 2011-07-26
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  • Thermal coupling of fluid flow and structural response of a tunnel induced by fire

     Schrefler, Bernhard A.; Codina Rovira, Ramon; Pesavento, F.; Principe Rubio, Ricardo Javier
    International journal for numerical methods in engineering
    Vol. 87, num. 1-5, p. 361-385
    DOI: 10.1002/nme.3077
    Date of publication: 2011-07
    Journal article

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  • Dynamic nonlinear subgrid modelling in a finite element approximation of low Mach number flows

     Principe Rubio, Ricardo Javier; Ávila, Matias; Codina Rovira, Ramon
    16th International Conference on Finite Elements in Flow Problems
    Presentation's date: 2011-03-24
    Presentation of work at congresses

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  • Dissipative structure and long term behavior of a finite element approximation of incompressible flows with numerical subgrid scale modeling

     Codina Rovira, Ramon; Principe Rubio, Ricardo Javier; Badia Rodriguez, Santiago I.
    Date of publication: 2011
    Book chapter

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  • Spatial approximation of the radiation transport equation using a subgrid-scale finite element method

     Ávila, Matias; Codina Rovira, Ramon; Principe Rubio, Ricardo Javier
    Computer methods in applied mechanics and engineering
    Vol. 200, num. 5-8, p. 425-438
    DOI: 10.1016/j.cma.2010.11.003
    Date of publication: 2011-01
    Journal article

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    In this paper we present stabilized finite element methods to discretize in space the monochromatic radiation transport equation. These methods are based on the decomposition of the unknowns into resolvable and subgrid scales, with an approximation for the latter that yields a problem to be solved for the former. This approach allows us to design the algorithmic parameters on which the method depends, which we do here when the discrete ordinates method is used for the directional approximation. We concentrate on two stabilized methods, namely, the classical SUPG technique and the orthogonal subscale stabilization. A numerical analysis of the spatial approximation for both formulations is performed, which shows that they have a similar behavior: they are both stable and optimally convergent in the same mesh-dependent norm. A comparison with the behavior of the Galerkin method, for which a non-standard numerical analysis is done, is also presented.

  • Computational Methods for Fusion Technology (COMFUS)

     Martín Huertas, Alberto Francisco; Badia Rodriguez, Santiago I.; Principe Rubio, Ricardo Javier; Planas Badenas, Ramon; Otin, Ruben
    Competitive project

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  • Premi Extraordinari de doctorat 2010 corresponents al curs 2007/2008

     Principe Rubio, Ricardo Javier; Codina Rovira, Ramon
    Award or recognition

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  • Dynamic variational multiscale modeling of turbulent incompressible flows

     Principe Rubio, Ricardo Javier; Calo, Victor; Codina Rovira, Ramon; Hughes, Thomas
    World Congress on Computational Mechanics
    Presentation's date: 2010-07-20
    Presentation of work at congresses

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  • Backscatter in the finite element approximation of turbulent incompressible flows with numerical sub-grid scale modeling

     Codina Rovira, Ramon; Principe Rubio, Ricardo Javier
    World Congress on Computational Mechanics
    p. 1
    Presentation's date: 2010-07-20
    Presentation of work at congresses

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  • Variational multiscale modeling of turbulent processes in the ocean

     Tejada-Martinez, Andrés; Calo, Victor; Principe Rubio, Ricardo Javier; Bazilevs, Yuri
    World Congress on Computational Mechanics
    Presentation's date: 2010-07-20
    Presentation of work at congresses

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  • Finite element approximation of the convection-diffusion-reaction equation on distorted meshes using orthogonal subscales

     Principe Rubio, Ricardo Javier; Codina Rovira, Ramon
    International Conference on Boundary and Interior Layers
    Presentation's date: 2010-07
    Presentation of work at congresses

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  • International Journal of Numerical Methods for Heat and Fluid Flow.

     Principe Rubio, Ricardo Javier
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  • On the stabilization parameter in the subgrid scale approximation of scalar convection-diffusion-reaction equations on distorted meshes

     Principe Rubio, Ricardo Javier; Codina Rovira, Ramon
    Computer methods in applied mechanics and engineering
    Vol. 199, num. 21-22, p. 1386-1402
    DOI: 10.1016/j.cma.2009.08.011
    Date of publication: 2010-04
    Journal article

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    In this paper we revisit the definition of the stabilization parameter in the finite element approximation of the convection¿diffusion¿reaction equation. The starting point is the decomposition of the unknown into its finite element component and a subgrid scale that needs to be approximated. In order to incorporate the distortion of the mesh into this approximation, we transform the equation for the subgrid scale within each element to the shape-regular reference domain. The expression for the subgrid scale arises from an approximate Fourier analysis and the identification of the wave number direction where instabilities are most likely to occur. The final outcome is an expression for the stabilization parameter that accounts for anisotropy and the dominance of either convection or reaction terms in the equation.

    In this paper we revisit the definition of the stabilization parameter in the finite element approximation of the convection–diffusion–reaction equation. The starting point is the decomposition of the unknown into its finite element component and a subgrid scale that needs to be approximated. In order to incorporate the distortion of the mesh into this approximation, we transform the equation for the subgrid scale within each element to the shape-regular reference domain. The expression for the subgrid scale arises from an approximate Fourier analysis and the identification of the wave number direction where instabilities are most likely to occur. The final outcome is an expression for the stabilization parameter that accounts for anisotropy and the dominance of either convection or reaction terms in the equation.

  • Applied mathematics and computation

     Principe Rubio, Ricardo Javier
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  • The dissipative structure of variational multiscale methods for incompressible flows

     Principe Rubio, Ricardo Javier; Codina Rovira, Ramon; Henke, Florian
    Computer methods in applied mechanics and engineering
    Vol. 199, num. 13-16, p. 791-801
    DOI: 10.1016/j.cma.2008.09.007
    Date of publication: 2010-02
    Journal article

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    In this paper, we present a precise definition of the numerical dissipation for the orthogonal projection version of the variational multiscale method for incompressible flows. We show that, only if the space of subscales is taken orthogonal to the finite element space, this definition is physically reasonable as the coarse and fine scales are properly separated. Then we compare the diffusion introduced by the numerical discretization of the problem with the diffusion introduced by a large eddy simulation model. Results for the flow around a surface-mounted obstacle problem show that numerical dissipation is of the same order as the subgrid dissipation introduced by the Smagorinsky model. Finally, when transient subscales are considered, the model is able to predict backscatter, something that is only possible when dynamic LES closures are used. Numerical evidence supporting this point is also presented.

    In this paper, we present a precise definition of the numerical dissipation for the orthogonal projection version of the variational multiscale method for incompressible flows. We show that, only if the space of subscales is taken orthogonal to the finite element space, this definition is physically reasonable as the coarse and fine scales are properly separated. Then we compare the diffusion introduced by the numerical discretization of the problem with the diffusion introduced by a large eddy simulation model. Results for the flow around a surface-mounted obstacle problem show that numerical dissipation is of the same order as the subgrid dissipation introduced by the Smagorinsky model. Finally, when transient subscales are considered, the model is able to predict backscatter, something that is only possible when dynamic LES closures are used. Numerical evidence supporting this point is also presented.

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

     Codina Rovira, Ramon; Principe Rubio, Ricardo Javier; Ávila, Matias
    International journal of numerical methods for heat and fluid flow
    Vol. 20, num. 5, p. 492-516
    DOI: 10.1108/09615531011048213
    Date of publication: 2010
    Journal article

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    The purpose of this paper is to describe a variational multiscale finite element approximation for the incompressible Navier-Stokes equations using the Boussinesq approximation to model thermal coupling. The main feature of the formulation, in contrast to other stabilized methods, is that the subscales are considered as transient and orthogonal to the finite element space. These subscales are solution of a differential equation in time that needs to be integrated. Likewise, the effect of the subscales is kept, both in the nonlinear convective terms of the momentum and temperature equations and, if required, in the thermal coupling term of the momentum equation. This strategy allows the approaching of the problem of dealing with thermal turbulence from a strictly numerical point of view and discussion important issues, such as the relationship between the turbulent mechanical dissipation and the turbulent thermal dissipation.

  • Access to the full text
    Finite element dynamical sub-grid scale approximation of low mach number flow equations  Open access

     Ávila, Matias; Principe Rubio, Ricardo Javier; Codina Rovira, Ramon
    Argentinean Congress on Computacional Mechanics - South American Congress on Computacional Mechanics
    p. 7967-7983
    Presentation of work at congresses

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    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. 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 later, both systems have similar mathematical structure and their numerical approximation can suffer the same type of instabilities. We propose a stabilized finite element approximation based on the 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.

  • Solving finite element linear systems by a multilevel incomplete factorization algorithm

     Principe Rubio, Ricardo Javier; Baiges Aznar, Joan
    Argentinean Congress on Computacional Mechanics - South American Congress on Computacional Mechanics
    p. 7681
    Presentation of work at congresses

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  • Applied mathematical modelling

     Principe Rubio, Ricardo Javier
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  • Computers and fluids

     Principe Rubio, Ricardo Javier
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  • Long term dynamics in a finite element approximation of the incompressible Navier-Stokes equations with numerical subgrid scale modeling

     Codina Rovira, Ramon; Badia Rodriguez, Santiago I.; Principe Rubio, Ricardo Javier; Guasch, Oriol
    US National Congress on Computational Mechanics
    p. 1
    Presentation's date: 2009-07
    Presentation of work at congresses

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  • A numerical approximation of the thermal coupling of fluids and solids

     Principe Rubio, Ricardo Javier; Codina Rovira, Ramon
    International journal for numerical methods in fluids
    Vol. 59, num. 11, p. 1181-1201
    DOI: 10.1002/fld.1856
    Date of publication: 2009-04
    Journal article

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    In this article we analyze the problem of the thermal coupling of fluids and solids through a common interface. We state the global thermal problem in the whole domain, including the fluid part and the solid part. This global thermal problem presents discontinuous physical properties that depend on the solution of auxiliary problems on each part of the domain (a fluid flow problem and a solid state problem). We present a domain decomposition strategy to iteratively solve problems posed in both subdomains and discuss some implementation aspects of the algorithm. This domain decomposition framework is also used to revisit the use of wall function approaches used in this context.

  • Dissipative structure and long term behavior of a finite element approximation of incompressible flows with numerical subgrid scale modeling

     Codina Rovira, Ramon; Principe Rubio, Ricardo Javier; Badia Rodriguez, Santiago I.
    Multiscale Methods in Computational Mechanics
    p. 75-93
    Presentation's date: 2009-03
    Presentation of work at congresses

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  • Fusion Technology Programme (TECNO_FUS)

     Badia Rodriguez, Santiago I.; Sedano Miguel, Luis Angel; Otin, Ruben; Planas Badenas, Ramon; Principe Rubio, Ricardo Javier; Martín Huertas, Alberto Francisco
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  • Subscales on the element boundaries in the variational two-scale finite element method

     Codina Rovira, Ramon; Principe Rubio, Ricardo Javier; Baiges Aznar, Joan
    Computer methods in applied mechanics and engineering
    Vol. 198, num. 5-8, p. 838-852
    DOI: 10.1016/j.cma.2008.10.020
    Date of publication: 2009-01
    Journal article

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    In this paper, we introduce a way to approximate the subscales on the boundaries of the elements in a variational two-scale finite element approximation to flow problems. The key idea is that the subscales on the element boundaries must be such that the transmission conditions for the unknown, split as its finite element contribution and the subscale, hold. In particular, we consider the scalar convection¿diffusion¿reaction equation, the Stokes problem and Darcy¿s problem. For these problems the transmission conditions are the continuity of the unknown and its fluxes through element boundaries. The former is automatically achieved by introducing a single valued subscale on the boundaries (for the conforming approximations we consider), whereas the latter provides the effective condition for approximating these values. The final result is that the subscale on the interelement boundaries must be proportional to the jump of the flux of the finite element component and the average of the subscale calculated in the element interiors.

  • Mathematical models for thermally coupled low speed flows

     Principe Rubio, Ricardo Javier; Codina Rovira, Ramon
    Advances in Theoretical and Applied Mechanics
    Vol. 2, num. 2, p. 93-112
    Date of publication: 2009
    Journal article

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    In this paper we review and clarify some aspects of the asymptotic analysis of the compressible Navier Stokes equations in the low Mach number limit. In the absence of heat exchange (the isentropic regime) this limit is well understood and rigorous results are available. When heat exchange is considered different simplified models can be obtained, the most famous being the Boussinesq approximation. Here a unified formal justification of these models is presented, paying special attention to the relation between the low Mach number and the Boussinesq approximations. Precise conditions for their validity are given for classical problems in bounded domains

  • Journal of computational physics

     Principe Rubio, Ricardo Javier
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  • Finite element approximation of the modified Boussinesq equations using a stabilized formulation

     Codina Rovira, Ramon; Gonzalez Ondina, J. M.; Diaz Hernandez, G.; Principe Rubio, Ricardo Javier
    International journal for numerical methods in fluids
    Vol. 57, num. 9, p. 1249-1268
    DOI: 10.1002/fld.1718
    Date of publication: 2008-07
    Journal article

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    In this work, we present a finite element model to approximate the modified Boussinesq equations. The objective is to deal with the major problem associated with this system of equations, namely, the need to use stable velocity-depth interpolations, which can be overcome by the use of a stabilization technique. The one described in this paper is based on the splitting of the unknowns into their finite element component and the remainder, which we call the subgrid scale. We also discuss the treatment of high-order derivatives of the mathematical model and describe the time integration scheme.

  • Access to the full text
    On the approximation of the subgrid scale for systems of equations  Open access

     Principe Rubio, Ricardo Javier; Codina Rovira, Ramon
    World Congress on Computational Mechanics
    p. 218
    Presentation's date: 2008-07-01
    Presentation of work at congresses

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  • Energy budget in a sub-grid scale finite element model for turbulent incompressible flows

     Codina Rovira, Ramon; Principe Rubio, Ricardo Javier; Guasch, Oriol
    World Congress on Computational Mechanics
    p. 1-2
    Presentation's date: 2008-07-01
    Presentation of work at congresses

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  • Subgrid scale stabilized finite elements for low speed flows.  awarded activity

     Principe Rubio, Ricardo Javier
    Department of Strength of Materials and Structural Engineering, Universitat Politècnica de Catalunya
    Theses

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  • A variational subgrid scale model for transient incompressible flows

     Houzeaux, Guillaume; Principe Rubio, Ricardo Javier
    International journal of computational fluid dynamics
    Vol. 22, num. 3, p. 135-152
    DOI: 10.1080/10618560701816387
    Date of publication: 2008-03
    Journal article

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