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.

Citation

Zhao, D. (2015), "Quick finite volume solver for incompressible Navier-Stokes equation by parallel Gram-Schmidt process based GMRES and HSS", Engineering Computations, Vol. 32 No. 5, pp. 1460-1476. https://doi.org/10.1108/EC-02-2014-0032