Efficient Parallel Algorithms for Computational Fluid Dynamics 

Vivek Sarin

Department of Computer Sciences,
Purdue University,       
West Lafayette, IN 47907 
Email: sarin@cs.purdue.edu 
URL: http://www.cs.purdue.edu/homes/sarin 
Phone: (765)494-7816, FAX: (765)494-0739 

Abstract

This talk addresses a number of challenging issues in developing 
parallel algorithms for large scale scientific simulations.  We will 
present recent results from the simulation of particles in fluids, a 
problem of great interest to numerous industries, e.g., the 
petroleum industry.  As part of a Grand Challenge project, we have 
developed two state-of-the-art packages called Particle Movers based 
on distinct modeling approaches, and have implemented them on 
several parallel platforms.  The most time-consuming component of 
these simulations is the solution of nonsymmetric, indefinite, 
sparse linear systems at each time step.  This poses significant 
challenges in developing preconditioners for iterative solvers that 
are robust and effective in addition to being parallelizable.  We 
have developed a number of innovative techniques that include a 
novel multilevel algorithm to represent discrete divergence-free 
space for incompressible fluids and optimal matrix-free parallel 
preconditioners for enforcing the rigid-body motion of the 
particles.  Our approach combines robust and effective 
preconditioning with excellent parallel performance, and is more 
effective than other techniques for fluid problems.  Using our 
techniques, realistic three dimensional flows with thousands of 
particles have been simulated for the first time on high performance 
architectures such as the SGI Origin2000.  Ongoing work supported by 
a KDI award extends this work to various types of fluids.  Relevant 
publications and additional details are available at 

http://www.cs.purdue.edu/homes/sarin.