An improved (9,5) higher order compact scheme for the transient two-dimensional convection–diffusion equation

Abstract

In the present study, we propose an implicit, unconditionally stable high order compact (HOC) finite difference scheme for the unsteady two-dimensional (2-D) convection–diffusion equations. The scheme is second-order accurate in time and fourth-order accurate in space. The stencil requires nine points at the nth and five points at the (n+ 1)th time level and is therefore termed a (9,5) HOC scheme. It efficiently captures both transient and steady solutions of linear and nonlinear convection–diffusion equations with Dirichlet as well as Neumann boundary conditions. It is applied to a linear Gaussian pulse problem, a linear 2-D Schrodinger equation and the lid driven square cavity flow governed by the 2-D incompressible Navier–Stokes (N–S) equations. The results are presented and are compared with established numerical results. Excellent comparison is obtained in all the cases. Copyright © 2005 John Wiley & Sons, Ltd.