Parallel finite element simulations of incompressible viscous fluid flow by domain decomposition with Lagrange multipliers

  • Authors:

  • Christian A. Rivera;Mourad Heniche;Roland Glowinski;Philippe A. Tanguy

  • Affiliations:

  • Research Center for Industrial Flows Processes (URPEI), Department of Chemical Engineering, ícole Polytechnique Montreal, P.O. Box 6079, Station Centre-Ville, Montréal, QC, Canada H3C 3A ...;Research Center for Industrial Flows Processes (URPEI), Department of Chemical Engineering, ícole Polytechnique Montreal, P.O. Box 6079, Station Centre-Ville, Montréal, QC, Canada H3C 3A ...;Department of Mathematics, University of Houston, 651 PGH, Houston, TX 77204-3008, USA;Research Center for Industrial Flows Processes (URPEI), Department of Chemical Engineering, ícole Polytechnique Montreal, P.O. Box 6079, Station Centre-Ville, Montréal, QC, Canada H3C 3A ...

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2010

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Abstract

A parallel approach to solve three-dimensional viscous incompressible fluid flow problems using discontinuous pressure finite elements and a Lagrange multiplier technique is presented. The strategy is based on non-overlapping domain decomposition methods, and Lagrange multipliers are used to enforce continuity at the boundaries between subdomains. The novelty of the work is the coupled approach for solving the velocity-pressure-Lagrange multiplier algebraic system of the discrete Navier-Stokes equations by a distributed memory parallel ILU (0) preconditioned Krylov method. A penalty function on the interface constraints equations is introduced to avoid the failure of the ILU factorization algorithm. To ensure portability of the code, a message based memory distributed model with MPI is employed. The method has been tested over different benchmark cases such as the lid-driven cavity and pipe flow with unstructured tetrahedral grids. It is found that the partition algorithm and the order of the physical variables are central to parallelization performance. A speed-up in the range of 5-13 is obtained with 16 processors. Finally, the algorithm is tested over an industrial case using up to 128 processors. In considering the literature, the obtained speed-ups on distributed and shared memory computers are found very competitive.