基于四阶半离散中心迎风格式的虚拟流方法的应用

Applications of the ghost fluid method based on the fourth-order semi-discrete central-upwind scheme

给出了求解多维无粘可压Euler方程组的四阶半离散中心迎风格式,该格式根据非线性波在网格单元边界上传播的局部速度来更准确地估计局部Riemann的宽度,避免了计算网格的交错,降低了格式的数值粘性。同时,考虑到LevelSet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,因此再将新的四阶半离散中心迎风格式与LevelSet方法以及虚拟流方法相结合,成功地处理了非反应激波和多介质流中爆轰间断的追踪问题。

A fourth-order semi-discrete central-upwind scheme for multidimensional inviscid compressible Euler equations is presented. Based on the local speeds of nonlinear wave propagation at grids' boundaries, the width of the local Riemann fans are calculated more accurately. Thus the scheme enjoys a much smaller numerical viscosity, and the staggering between two sets of grids is avoided. Since the location of the interface can be tracked by Level Set function implicitly and the boundary conditions are implicitly captured by the construction of a ghost fluid, the scheme is combined with the Level Set method and the ghost fluid method. In this way, the non-reacting shock problems and detonation discontinuities in multimaterial flows are tracked successfully.