基于推广的Fu-Shu坏单元指示子的h自适应RKDG方法

An h-adaptive RKDG method based on generalized Fu-Shu troubled-cell indicator

为提高使用坏单元指示子生成的h自适应网格质量,在求解双曲守恒律方程的Runge-Kutta间断Galerkin方法中引入推广的Fu-Shu指示子,实现在自适应网格中间断区域使用密网格、连续区域使用粗网格的效果,从而节约计算成本,提高间断处的数值模拟效果.对二维Euler方程组的数值试验验证了本文方法的有效性,与常用的KXRCF坏单元指示子的比较展示了推广的Fu-Shu指示子的优势.

In order to improve the quality of the h-adaptive meshes generated by troubled-cell indicators,this paper introduces the generalized Fu-Shu troubled-cell indicator to the Runge-Kutta discontinuous Galerkin method for solving hyperbolic conservation laws.In such adaptive meshes,fine meshes are used at the discontinuities and coarse meshes elsewhere so that the computational cost is saved and the solution quality near the discontinuities is improved.The numerical experiments on the two-dimensional Euler equations verify the effectiveness of the proposed method.They also show the advantage of the generalized Fu-Shu troubled-cell indicator compared with the commonly used KXRCF troubled-cell indicator.