On the Solution of Incompressible Fluid Flow Equations: a Comparative Study

Abstract

This paper studies and contrasts the performances of three iterative methods for computing the solution of large sparse linear systems arising in the numerical computations of incompressible Navier-Stokes equations. The emphasis is on the traditional Gauss-Seidel (GS) and Point Successive Over-relaxation (PSOR) algorithms as well as Krylov projection techniques such as Generalized Minimal Residual (GMRES). The performances of these three solvers for the second-order ï¬nite difference algebraic equations are comparatively studied by their application to solve a benchmark problem in Computational Fluid Dynamics (CFD). It is found that as the mesh size increases, GMRES gives the fastest convergence rate in terms of cpu time and number of iterations.

Keywords: viscous flows, Navier-Stokes equations, linear system, iterative, GMRES