双曲型守恒律的一种三阶半离散中心迎风格式

对一维双曲型守恒律,给出了一种具有较小数值耗散的三阶半离散中心迎风格式.该格式以Liu和Tadmor提出的三阶无振荡重构为基础,同时考虑了波传播的单侧局部速度.时间离散用保持强稳定性的三阶Runge-Kutta方法.由于不需用Riemann解算器,避免了特征分解过程,保持了中心格式简单的优点.数值算例验证本方法可进一步减小数值耗散,提高分辨率.

A Third Order Semi-discrete Central-upwind Scheme for Hyperbolic Conservation Laws

For hyperbolic conservation laws,a third-order semi-discrete central-upwind scheme with less numerical dissipation is presented.The scheme is based on a third-order non-oscillatory reconstruction proposed by Liu and Tadmor.The local speed of wave propagation is also considered.An optimal third-order strong stability preserving(SSP) Runge-Kutta method is used for time integration.The resulting scheme is free of Riemann solvers and hence no characteristic decomposition is involved,so that it enjoys the advantages of central schemes.The present scheme is tested on a variety of numerical experiments in one dimension.To illustrate the improvement of the method,the results are compared with that of the original third-order semi-discrete central-upwind scheme. The numercial results demonstrate that the presented method reduce the numerical dissipation of the semi-discrete central-upwind scheme further and improve resolution of contact waves.