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    Adaptive finite element simulation of incompressible flows by hybrid continuous-discontinuous Galerkin formulations  Open access

     Badia Rodriguez, Santiago I.; Baiges Aznar, Joan
    SIAM journal on scientific computing
    Vol. 35, num. 1, p. A491-A516
    DOI: 10.1137/120880732
    Date of publication: 2013-02
    Journal article

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    In this work we design hybrid continuous-discontinuous finite element spaces that permit discontinuities on nonmatching element interfaces of nonconforming meshes. Then we develop an equal-order stabilized finite element formulation for incompressible flows over these hybrid spaces, which combines the element interior stabilization of SUPG-type continuous Galerkin formulations and the jump stabilization of discontinuous Galerkin formulations. Optimal stability and convergence results are obtained. For the adaptive setting, we use a standard error estimator and marking strategy. Numerical experiments show the optimal accuracy of the hybrid algorithm for both uniformly and adaptively refined nonconforming meshes. The outcome of this work is a finite element formulation that can naturally be used on nonconforming meshes, as discontinuous Galerkin formulations, while keeping the much lower CPU cost of continuous Galerkin formulations.

    In this work we design hybrid continuous-discontinuous finite element spaces that permit discontinuities on non-matching element interfaces of non-conforming meshes. Then, we develop an equal-order stabilized finite element formulation for incompressible flows over these hybrid spaces, which combines the element interior stabilization of SUPGtype continuous Galerkin formulations and the jump stabilization of discontinuous Galerkin formulations. Optimal stability and convergence results are obtained. For the adaptive setting, we use an standard error estimator and marking strategy. Numerical experiments show the optimal accuracy of the hybrid algorithm both for uniformly and adaptively refined non-conforming meshes. The outcome of this work is a finite element formulation that can naturally be used on nonconforming meshes, as discontinuous Galerkin formulations, while keeping the much lower CPU cost of continuous Galerkin formulations.

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

     Baiges Aznar, Joan; Codina Rovira, Ramon; Henke, Florian; Shahmiri, S.; Wall, W. A.
    International journal for numerical methods in engineering
    Vol. 90, num. 5, p. 636-658
    DOI: 10.1002/nme.3339
    Date of publication: 2012-05-04
    Journal article

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  • The fixed-Mesh ALE method applied to multiphysics problems using stabilized formulations  Open access  awarded activity

     Baiges Aznar, Joan
    Universitat Politècnica de Catalunya
    Theses

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    The finite element method is a tool very often employed to deal with the numerical simulation of multiphysics problems.Many times each of these problems can be attached to a subdomain in space which evolves in time. Fixed grid methods appear in order to avoid the drawbacks of remeshing in ALE (Arbitrary Lagrangian-Eulerian) methods when the domain undergoes very large deformations. Instead of having one mesh attached to each of the subdomains, one has a single mesh which covers the whole computational domain. Equations arising from the finite element analysis are solved in an Eulerian manner in this background mesh. In this work we present our particular approach to fixed mesh methods, which we call FM-ALE (Fixed-Mesh ALE). Our main concern is to properly account for the advection of information as the domain boundary evolves. To achieve this, we use an arbitrary Lagrangian-Eulerian framework, the distinctive feature being that at each time step results are projected onto a fixed, background mesh, that is where the problem is actually solved.We analyze several possibilities to prescribe boundary conditions in the context of immersed boundary methods. When dealing with certain physical problems, and depending on the finite element space used, the standard Galerkin finite element method fails and leads to unstable solutions. The variational multiscale method is often used to deal with this instability. We introduce a way to approximate the subgrid scales on the boundaries of the elements in a variational twoscale 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. We then use the subscales on the element boundaries to improve transmition conditions between subdomains by introducing the subgrid scales between the interfaces in homogeneous domain interaction problems and at the interface between the fluid and the solid in fluid-structure interaction problems. The benefits in each case are respectively a stronger enforcement of the stress continuity in homogeneous domain decomposition problems and a considerable improvement of the behaviour of the iterative algorithm to couple the fluid and the solid in fluid-structure interaction problems. We develop FELAP, a linear systems of equations solver package for problems arising from finite element analysis. The main features of the package are its capability to work with symmetric and unsymmetric systems of equations, direct and iterative solvers and various renumbering techniques. Performance is enhanced by considering the finite element mesh graph instead of the matrix graph, which allows to perform highly efficient block computations.

  • Finite element approximation of transmission conditions in fluids and solids introducing boundary subgrid scales

     Codina Rovira, Ramon; Baiges Aznar, Joan
    International journal for numerical methods in engineering
    Vol. 87, num. 1-5, p. 386-411
    DOI: 10.1002/nme.3111
    Date of publication: 2011-02-02
    Journal article

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

     Baiges Aznar, Joan; Codina Rovira, Ramon; Coppola Owen, Angel H.
    International journal for numerical methods in fluids
    Vol. 67, num. 8, p. 1004-1023
    DOI: 10.1002/fld.2403
    Date of publication: 2011-11-20
    Journal article

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  • Fixed mesh methods in computational mechanics

     Codina Rovira, Ramon; Baiges Aznar, Joan
    Date of publication: 2010
    Book chapter

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    A numerical strategy to compute optical parameters in turbulent flow: application to telescopes  Open access

     Codina Rovira, Ramon; Baiges Aznar, Joan; Pérez Sánchez, Daniel; Collados, Manuel
    Computers and fluids
    Vol. 39, num. 1, p. 87-98
    DOI: 10.1016/j.compfluid.2009.07.005
    Date of publication: 2010-01
    Journal article

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    We present a numerical formulation to compute optical parameters in a turbulent air flow. The basic numerical formulation is a large eddy simulation (LES) of the incompressible Navier–Stokes equations, which are approximated using a finite element method. From the time evolution of the flow parameters we describe how to compute statistics of the flow variables and, from them, the parameters that determine the quality of the visibility. The methodology is applied to estimate the optical quality around telescope enclosures.

    Postprint (author’s final draft)

  • 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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  • GRUP DE RESISTÈNCIA DE MATERIALS I ESTRUCTURES A L'ENGINYERIA

     Hernandez Ortega, Joaquin Alberto; Davalos Chargoy, Cesar Emilio; Baiges Aznar, Joan; Chiumenti, Michele; Cante Teran, Juan Carlos; Bugeda Castelltort, Gabriel; Barbat Barbat, Horia Alejandro; Codina Rovira, Ramon; Cervera Ruiz, Miguel; Suarez Arroyo, Benjamin; Miquel Canet, Juan; Weyler Perez, Rafael; González Lopez, Jose Manuel; Badia Rodriguez, Santiago I.; Agelet de Saracibar Bosch, Carlos; Oller Martinez, Sergio Horacio; Pelà, Luca; Oliver Olivella, Fco. Javier
    Competitive project

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  • Approximate imposition of boundary conditions in immersed boundary methods

     Codina Rovira, Ramon; Baiges Aznar, Joan
    International journal for numerical methods in engineering
    Vol. 80, num. 11, p. 1379-1405
    DOI: 10.1002/nme.2662
    Date of publication: 2009-06
    Journal article

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  • The fixed-mesh ALE approach applied to solid mechanics and fluid-structure interaction problems

     Baiges Aznar, Joan; Codina Rovira, Ramon
    International journal for numerical methods in engineering
    Vol. 81, num. 12, p. 1529-1557
    DOI: 10.1002/nme.2740
    Date of publication: 2009-09-09
    Journal article

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

     Codina Rovira, Ramon; Houzeaux, G; Coppola Owen, Angel H.; Baiges Aznar, Joan
    Journal of computational physics
    Vol. 228, num. 5, p. 1591-1611
    DOI: 10.1016/j.jcp.2008.11.004
    Date of publication: 2009-03
    Journal article

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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: doi:10.1016/j.cma.2008.10.020
    Date of publication: 2009-01
    Journal article

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  • Premis CELSA 2007

     Baiges Aznar, Joan
    Award or recognition

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