一种结合Roe格式的高精度半拉氏方法  

A ROE-RELATED SEMI-LAGRANGIAN METHOD

作　　者：齐进[1] 田保林[1,2] 王双虎[1,2,3] 

机构地区：[1]北京应用物理与计算数学研究所,北京100094 [2]计算物理国防重点实验室,北京100088 [3]北京大学应用物理与技术研究中心,北京100871

出　　处：《力学学报》2011年第4期660-666,672+671,共7页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金(10931004;10802010;10972043;10901021);国家重点基础研究发展计划(2005CB321700);计算物理国防科技重点实验室基金(9140C690101110C69);中国物理研究院科学技术发展基金(2007A09006)资助项目~~

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模拟效果,可用于可压缩复杂流动问题的计算.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.

关 键 词：Roe格式 半拉氏方法 ENO 有限体积方法 特征不变量 

分 类 号：O354.5[理学—流体力学]