非线性双曲型守恒律的两步二阶TVD差分格式

A two-step second-order TVD scheme for nonlinear hyperbolic conservation laws

通过 Mac Cormack格式和 Warming- Beam的结合 ,构造了一种非常简单的两步二阶 TVD差分格式。该差分格式更适合于使用分量形式差分计算而无须对欧拉方程组进行特征解耦。通过对流体力学方程组的大量数值试验 ,并与二阶 ENO格式进行了比较 ,充分显示了该格式高精度。

TVD schemes are a kind of high resolution shock capturing schemes. However when applied to systems of conservation laws, the conventional TVD schemes are often built upon the complicated field by field decompositions. In this paper, we propose a two step component wise TVD scheme for nonlinear hyperbolic conservation laws, which is obtained by combining the schemes of Mac Cormack and Warming Beam. This two step scheme takes the predictor of the first order upwinding and employs a corrector of component wise TVD limiting. It does not necessitate the conventional characteristic decomposition. For the approximations to Euler systems of conservation laws, the new scheme is found to be two times faster in computation than the usual TVD schemes based on field by field decomposition limiting. Moreover, it runs even a bit faster and presents higher resolution than the same order component wise ENO schemes. A lot of numerical results show adequately the superiorities of the new scheme.