A HIGHER ORDER COMPACT SCHEME FOR THE NONLINEAR ADVECTION DIFFUSION PROCESSES

Abstract

This paper presents a highly accurate finite difference based scheme through the Pade approximation in analyzing the behaviour of the nonlinear advection-diffusion processes governed by the unsteady Burgers equation. It has then been proved that the present method is unconditionally stable based on the von Neumann stability analysis. The proposed approach has been shown to be capable of solving the model equation effectively. Two challenging examples have been taken to illustrate the physical behaviour of the model in detail. The computed results have been seen to be highly accurate and be oscillation free even if advection dominated cases are considered.