Combined Compact Difference Scheme for Solving Unsteady Convection-Diffusion Equations

Abstract

By using a fifth-order upwind discrete scheme for the convection term, a fourth-order central difference scheme for the diffusion term, we construct a boundary scheme that matches the interior point and obtain a stable combination semi-discrete compact scheme which is discretized by the third-order Runge-Kutta method in the time direction. Compared with the other fourth-order scheme, the error of the proposed method is small and the accuracy is high.