间断探测器在间断Galerkin方法中的应用

摘要

在二维非结构网格上,对高阶间断Galerkin方法求解定常二维欧拉方程进行数值研究.为了很好地抑制解在流场间断附近处产生的伪振荡,采用了间断探测器和限制器相结合的方法,并分别对Krivodonova间断探测器和基于激波物理特征的激波探测器进行了比较和研究.数值结果表明:如果流场中只存在激波时,两者探测效果相似,且后者更适合应用于求解激波问题.如果流场更加复杂,即存在多种间断时,前者依然可以比较准确地用来探测间断单元,能够很好抑制流场间断附近处产生的伪振荡,而后者失效.%A high- order accurate discontinuous Galerkin finite element method is presented to solve the steady Euler equations based on two dimensional unstructured grids. In order to suppress numerical oscillations, the technique of shock detector and slope limiter are introduced. Krivodonova shock detector and physics- based shock detector are studied and compared in this paper. The numerical results show that the effect of the two detectors is similar when the only discontinuity is the shock, the later is even better. However,when the flow is complex with many kinds of discontinuities,the former can still detect the discontinuous cells accurately and suppress the pseudo oscillations well, while the later is disabled.