Preconditioned iterative methods and finite difference schemes for convection–diffusion

摘要

We conduct experimental study on numerical solution of the two dimensional convection–diffusion equation discretized by three finite difference schemes: the traditional central difference scheme, the standard upwind scheme and the fourth-order compact scheme. We study the computed accuracy achievable by each scheme, the algebraic properties of the coefficient matrices arising from different schemes and the performance of the Gauss–Seidel iterative method, the preconditioned GMRES iterative method, and the multigrid method, for solving linear systems arising from these schemes.