A fictitious domain method with distributed
Lagrange multipliers for the numerical simulation
of particulate flow and its parallel implementation

T.-W. Pana, V. Sarinb, R. Glowinskia, A. Samehb and J. Periauxc
aDepartment of Mathematics, University of Houston, Houston, TX 77204, USA
bDepartment of Computer Science, Purdue University, West Lafayette, IN 47907, USA
cDassault Aviation, 92214 Saint-Cloud, France

Abstract

The numerical simulation of particulate flow, a mixtures of incompressible viscous fluids and hundreds of rigid particles, is computational expensive and parallelism often appears as the only way towards large scale of simulations even we have a fast Navier-Stokes solver. The method we advocate here combines distributed Lagrange multipliers based fictitious domain methods, which allows the use of fixed structured finite element grids on a simple shape auxiliary domain containing the actual one for the fluid flow computations, with time discretizations by operator splitting a la Marchuk-Yanenko to decouple the various computational dificulties associated to the simulation. This method offers an alternative to the ALE methods investigated in [H.H. Hu 1996], [B. Maury and R. Glowinski, 1997], and [O. Pironneau, J. Liou and T. Tezduyar, 1992] and can be easily parallelized due to the use of uniform structured grids and no need to generate mesh at each time step right after finding the new position of rigid particles. Numerical results of particulate flow obtained on a SGI Origin 2000 are presented.


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Last updated October 16, 2000