Parallel simulation of particulate flows

Abstract

Simulation of particles in fluids requires the solution of nonlinear Navier-Stokes equations for fluids coupled with Newton's equations for particle dynamics, in which the most time consuming part is the solution of nonsymmetric and indefinite sparse linear systems. In this paper, we present a comprehensive algorithm for the simulation of particulate flows in two dimensional domains. A backward Euler method is used for time evolution, and a variant of Newton's method is used to solve the nonlinear systems. The linear systems are solved efficiently by a novel multilevel algorithm that generates discrete divergence-free space for the incompressible fluid. Unlike incomplete factorization preconditioners, our technique has the desirable properties of robust and effective preconditioning along with efficient implementation on parallel computers. We present experiments on the SGI Origin2000 that demonstrate the parallel performance of our algorithm, and discuss various aspects of the simulation package and the associated software design.

This work is supported, in part, by the NSF through HPCC Grand Challenge grant ESC-95-27123. See http://www.aem.umn.edu/Solid-Liquid-Flows for more details.