基于简单WENO-间断Galerkin的Euler方程自适应计算

Adaptive simple WENO limiter-discontinuous Galerkin method for Euler equations

为了得到Euler方程的高精度、高分辨率数值解,介绍了间断Galerkin方法、三角形单元上简单WENO限制器的基本原理以及基于自适应网格加密的激波捕捉方法。将简单WENO限制器-间断Galerkin方法应用到曲边四边形单元上,通过单元边界上高斯积分点的坐标来搜索相邻单元从而得到相邻单元的单元编号,实现了基于"问题单元"的局部网格加密自适应计算。对若干典型问题进行编程计算,结果表明,简单WENO限制器可以应用到曲边四边形单元上,且可适用于局部网格加密时具有"悬挂节点"的非结构网格上的激波捕捉。

To achieve high precision and high resolution numerical result of Euler equations,the basic principle of discontinuous Galerkin method,the simple WENO limiter on triangular meshes and shock capturing method based on adaptive mesh refinement were introduced. The simple WENO limiter-discontinuous Galerkin method was applied to the curved quadrilateral element,and the adjacent elements of every element with the same coordinates of the Gauss integral points on the boundaries were found. The adaptive computation based on ＂trouble element＂refinement was accomplished. Several benchmark test cases were computed. The numerical results show that the simple WENO limiter is appropriate for the curvilinear boundary quadrilateral element and for the shock capturing based on unstructured grids with hanging nodes.