论文标题
用于高阶冲击拟合的扩展不连续的盖尔金方法
An Extended Discontinuous Galerkin Method for High-Order Shock-Fitting
论文作者
论文摘要
我们使用高阶扩展不连续的Galerkin（XDG）方法提出了子电池精确的减震技术，其中将背景网格的计算单元切成冲击位置的两个切口。我们的技术利用了尖锐的界面描述，其中冲击阵线是通过级别函数的零ISO-CONTOUR隐式定义的。通过使用细胞本地指示剂，采用一种新型的隐式伪时间步进程序来纠正切割背景细胞内的冲击锋的位置，因为冲击波的位置和形状是普通的多维情况的先验性的。这种迭代校正是否终止了电击锋会汇聚到确切的位置。对于一维固定的正常冲击波的测试案例，证明了该过程。此外，由于可以使用简单的笛卡尔背景网格，因此底层尖锐的界面方法大大降低了网格处理的复杂性。
We present a sub-cell accurate shock-fitting technique using a high-order extended discontinuous Galerkin (XDG) method, where a computational cell of the background grid is cut into two cut-cells at the shock position. Our technique makes use of a sharp interface description where the shock front is implicitly defined by means of the zero iso-contour of a level-set function. A novel implicit pseudo-time-stepping procedure is employed to correct the position of the shock front inside the cut background cell by using cell-local indicators, since the position and shape of shock waves are not known a priori for the general, multi-dimensional case. This iterative correction terminates if the shock front has converged to the exact position. The procedure is demonstrated for the test case of a one-dimensional stationary normal shock wave. Furthermore, the underlying sharp interface approach drastically reduces the complexity of the grid handling, since a simple Cartesian background grid can be employed.
