Fourth-order optimal iterative schemes for convection-diffusion equation

Abstract

Successive overrelaxation schemes along with their scope are presented for the one-dimensional convection-diffusion equation with a small diffusion coefficient. Optimum relaxation parameters are derived analytically for these schemes developed by approximating the derivatives in the equation using the compact fourth-order differences. The solutions are compared with the widely used central difference solutions and are found to be both oscillation-free and convergent for ail ceil Reynolds numbers. Numeri- cal experiments carried out on the schemes supplement the analytical results.

Keywords:

• Central-difference
• convection-diffusion equation
• cyclic reduction
• fourth-order
• difference
• Jacobi method
• successive overrelaxation
• upwind difference

C.R. CATEGORIES:

• G.1.3