一种结合Roe格式的高精度半拉氏方法

摘要

针对守恒形式的欧拉方程组,构造了一种结合Roe格式的守恒型有限体积形式的半拉氏方法.通过发展一种基于Roe特征速度的拉氏质点回溯方法,由此来计算半点的流量并作为边界通量的近似,使得这种半拉氏方法在时空离散上达到二阶精度,并且保证了守恒性.其中回溯点处物理量采用本质无振荡格式（ENO）方法进行插值重构得到,不需要增加人工黏性且避免了有限体积多矩半拉氏方法中限制器选择的问题,又能够达到时空的高阶精度.方法简便,易于实现,兼具拉氏方法和欧拉方法的优点.一维和二维数值算例表明,此方法对激波和接触间断都取得了满意的%An algorithm for 1D and 2D Euler equations was proposed by combining the Roe scheme and the semi-Lagrangian method based on characteristic theory.The finite volume method（FVM）is cast in a flux form and thus guarantees the numerical conservation.We calculated the flux at the cell boundary by using its value at the boundary＇s center,which could make the algorithm second-order accuracy in time.The semi-Lagrangian method with characteristic theory was implemented to trace the fluid particles.The characteristic velocities were modified based on Roe average to locate the departure points.The interpolation by ENO reconstruction made the algorithm free of limiters.The high order algorithm is simple and convenient to implement.The numerical results showed that it was competitive comparing with other schemes.