Quick finite volume solver for incompressible Navier-Stokes equation by parallel Gram-Schmidt process based GMRES and HSS

Abstract

Purpose – The purpose of this paper is to develop Triple Finite Volume Method (tFVM), the author discretizes incompressible Navier-Stokes equation by tFVM, which leads to a special linear system of saddle point problem, and most computational efforts for solving the linear system are invested on the linear solver GMRES. Design/methodology/approach – In this paper, by recently developed preconditioner Hermitian/Skew-Hermitian Separation (HSS) and the parallel implementation of GMRES, the author develops a quick solver, HSS-pGMRES-tFVM, for fast solving incompressible Navier-Stokes equation. Findings – Computational results show that, the quick solver HSS-pGMRES-tFVM significantly increases the solution speed for saddle point problem from incompressible Navier-Stokes equation than the conventional solvers. Originality/value – Altogether, the contribution of this paper is that the author developed the quick solver, HSS-pGMRES-tFVM, for fast solving incompressible Navier-Stokes equation.