求解对流扩散方程的低耗散中心迎风格式

A Low Dissipation Central-upwind Scheme for Convection-diffusion Equations

以四阶CWENO重构为基础,通过将对流项采用低耗散中心迎风格式离散,扩散项采用四阶中心差分格式离散,对得到的半离散格式采用四阶龙格库塔方法在时间方向上推进,得到一种求解对流扩散方程的高阶有限差分格式.数值结果验证了该格式的四阶精度和基本无振荡特性.

A fourth order finite difference scheme is proposed for solving convection-diffusion equations. The convection term is discretized by a low dissipation central-upwind scheme and the diffusion term is discretized by a fourth order central difference scheme. After that, a fourth order Runge-Kutta method is employed to advance in time. Numerical results verify the desired accuracy and almost non-oscillation of our scheme.