Hindered settling computations using a parallel boundary element method

摘要

This paper presents a parallel implementation of the boundary element method (BEM) for multiple instruction multiple data (MIMD) computer architectures to determine the hindered settling function for a suspension of sedimenting rigid particles in Stokes flow. The hindered settling function is a measure of the average sedimentation velocity of the suspension. This function can be determined numerically by performing statistical analyses of several random realizations of a physical system characterized by a set of defining parameters. These defining parameters can include the volume fraction of the solid phase, shape factors, orientation characteristics, and others. The boundary element method is particularly well suited for studying such systems because of the simplification in the discretization associated with the method. However, as the number of solid particles to be modeled is increased so are the computational demands. Parallel computation offers the opportunity to model systems of greater complexity. We discuss a parallel boundary element formulation based on the torus-wrap mapping. In this approach, blocks of the coefficient matrix associated with the discretized boundary element equations are assigned to processors as opposed to more traditional parallel boundary element implementations where rows or columns are assigned to processors. The torus-wrap mapping can be shown to minimize the communication volume between processors during the LU factorization. Therefore, the present formulation scales well with increases in the number of processors.