求解无粘可压Euler方程组的虚拟流方法

首先将三阶Godunov型半离散中心迎风格式推广到四阶,之后再将该新的四阶半离散中心迎风格式与Level Set方法以及虚拟流方法结合起来,成功地处理了非反应激波问题和多介质流中的爆轰间断问题。由于Level Set函数能隐式地追踪到界面的位置,而虚拟流的构造能隐式地捕捉到界面的边界条件,故而本文的方法可以很自然地推广到多维情况。

The ghost fluid method for inviscid compressible Euler equations

At first,the third-order Godunov-type semi-discrete central-upwind schemes were extended to fourth-order schemes.Then the new fourth-order semi-discrete central-upwind schemes were combined with the Level Set method and the ghost fluid method.By this way,the non-reacting shocks problems and detonation discontinuities in multimaterial flows are tracked successfully.Since the location of the interface is tracked by Level Set function implicitly and the boundary conditions are implicitly captured by the construction of a ghost fluid,the overall scheme becomes easy to implement in multidimension.