基于带限制器的RKDG法的可压缩流数值模拟

Numerical simulation of the compressible fluid problem based on RKDG method with a limiter

采用带简单加权基本无振荡(WENO)限制器的Runge-Kutta间断有限元(RKDG)方法在笛卡尔网格上进行可压缩流数值模拟,同时结合ST(symmetry technique)方法和FGCM(Forrer’s ghost cell method)模拟计算具有复杂几何外形物体的可压缩流问题.该方法能保持计算格式的高精度且易于实现,可以计算具有复杂拓扑结构的物体绕流问题且对网格质量的要求较低.3个典型数值算例验证了该方法的有效性.

In this paper, the Runge-Kutta discontinuous Galerkin （RKDG） method with a simple weighted essentially non-oscillatory （WENO） limiter is applied to simulate the compressible fluid on Cartesian grids. Combined with ST （symmetry technique） and FGCM （Forrer＇s ghost cell method）, the above method is applied to compute the compressible fluid problem with complex geometrical shape object in the computing field. This method can keep high order of accuracy, is easier to implement, calculate flow around the object with complex topology shape and is low requirement for the high quality of the grid. Three classic numerical tests are provided to verify the viability of these methods.