双曲型守恒律方程的一个大时间步长二阶TVD差分格式

A Large Time-Step Second Order Accurate TVD Difference Scheme for Hyperbolic Conservation Laws

本文根据Harten,A.的大时间步长差分分格式构造思想,为双曲型守恒律方程弱解计算构造了一个2K+3点大时间步长二阶显式差分格式——LTS-LF格式,得到了其在CFL限制K下为总变差不增差分格式(TVD格式)。文章按照Roe的方法推广格式到方程组情形,并就Burger’s方程和Euler方程组黎曼问题进行数值试验,结果令人满意。

Based on the approach of Harten, A. a large time-step(2K + 3)-point explicit second-order accurate difference scheme(LTS-LF Scheme) is constructed in this paper for the computation of weak solutions of hyperbolic conservation laws. This highly nonlinear scheme is total-variation-diminishing under a CFL-res-triction of K (TVD scheme). By using Roe's linearization technique,we extend the new scheme to hyperbolic systems of conservation law. Finally, we conduct numerical experiments for the Riemann problems of Berger's equation and Euler Systems, the results are satisfactory.