Solution of pressure poisson equation in particle method using algebraic multigrid method

Abstract

In this paper, we present application of the algebraic multigrid method to a pressure Poisson equation that arises in the fluid flow simulation of the particle method. The solution method is based on the plain aggregation algebraic multigrid (PA-AMG), in which the double pairwise aggregation is employed for grid coarsening and K-cycle is adopted for multigrid cycle. The PA-AMG method is used as a preconditioner for BiCGSTAB method. The method is applied to fundamental test problems to examine the performance for solution of linear systems generated by discretizing a Poisson equation based on the MPS method. The numerical results showed that the present method is successful in coarsening grid with constant coarsening ratio and can solve Poisson equations faster than non-preconditioned BiCGSTAB method especially for large problems.