A FOUR-STEP TIME SPLITTING SCHEME FOR CONVECTION-DIFFUSION EQUATION

Abstract

In this article we develop a four-step time splitting scheme for solving the two-dimensional convection-diffusion equation by using a fourth-order-accurate Pade approximation. The resulting temporal scheme includes two explicit equations and two coupled implicit equations. For constructing an equal-order scheme for the explicit equations, we approximate the second derivative terms using the fourth-order-accurate centered scheme. In the approximation of the first-derivative term, it is essential that the fourth-order-accurate scheme takes solutions at the upwind side into favorable consideration. For constructing an efficient scheme for the implicit equations, we apply the alternating direction implicit scheme of Peaceman and Rachford. For the sake of accuracy, in each sweep we apply a three-point, nodally exact, one-dimensional convection-diffusion-reaction (CDR) scheme. As is standard practice, we validate the proposed method by solving several problems that are amenable to exact solutions. Results with good rate of convergence are obtained for the investigated one- and two-dimensional problems.

Acknowledgments

The support provided by the National Science Council under grant NSC 90-2811-E-002-008 is gratefully acknowledged.