Fifth Mississippi State Conference on Differential Equations and Computational Simulations,
Electron. J. Diff. Eqns., Conf. 10, 2002, pp. 1-10.

Simulation of incompressible flows with heat and mass transfer using parallel finite element method

Jalal Abedi & Shahrouz Aliabadi

Abstract:
The stabilized finite element formulations based on the SUPG (Stream\-line-Upwind/Petrov-Galerkin) and PSPG (Pressure-Stabilization/Petrov-Galerkin) methods are developed and applied to solve buoyancy-driven incompressible flows with heat and mass transfer. The SUPG stabilization term allows us to solve flow problems at high speeds (advection dominant flows) and the PSPG term eliminates instabilities associated with the use of equal order interpolation functions for both pressure and velocity. The finite element formulations are implemented in parallel using MPI. In parallel computations, the finite element mesh is partitioned into contiguous subdomains using METIS, which are then assigned to individual processors. To ensure a balanced load, the number of elements assigned to each processor is approximately equal. To solve nonlinear systems in large-scale applications, we developed a matrix-free GMRES iterative solver. Here we totally eliminate a need to form any matrices, even at the element levels. To measure the accuracy of the method, we solve 2D and 3D example of natural convection flows at moderate to high Rayleigh numbers.

Published February 28, 2003.
Subject classifications: 65C20, 81T80.
Key words: Finite element method, parallel simulation, contaminant dispersion, free convection.

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Jalal Abedi
Department of Engineering
Clark Atlanta University
223 James P. Brawley Dr. S. W.
Atlanta, Georgia 30314, USA
e-mail: jabedi@cau.edu Phone 404-880-6938
Shahrouz Aliabadi
Department of Engineering
Clark Atlanta University
223 James P. Brawley Dr. S. W.
Atlanta, Georgia 30314, USA
e-mail: aliabadi@cau.edu

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