A Straightforward hp -Adaptivity Strategy for Shock-Capturing with High-Order Discontinuous Galerkin Methods
A Straightforward hp -Adaptivity Strategy for Shock-Capturing with High-Order Discontinuous Galerkin Methods
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DOI：
10.1017/s2070073300002484
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发表时间：
2014-02
影响因子：
1.4
通讯作者：
Hongqiang Lu;Qiang Sun
中科院分区：
文献类型：
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作者：
Hongqiang Lu;Qiang Sun
本文采用高阶间断Galerkin（DG）方法求解二维Euler方程。基于人工粘性技术的激波捕捉方法被用来处理物理不连续性。数值试验表明，即使在非常粗糙的网格上，激波也可以被捕获在一个单元内。激波的厚度主要取决于局部网格尺寸和基函数的局部阶数。为了获得更好的冲击分辨率，一个简单的hp -自适应策略，这是基于高阶贡献计算的分层基础。数值结果表明，hp -自适应方法易于实现，且在较小的局部网格尺寸和较高的局部阶数下可以获得较好的激波分辨率。
In this paper, high-order Discontinuous Galerkin (DG) method is used to solve the two-dimensional Euler equations. A shock-capturing method based on the artificial viscosity technique is employed to handle physical discontinuities. Numerical tests show that the shocks can be captured within one element even on very coarse grids. The thickness of the shocks is dominated by the local mesh size and the local order of the basis functions. In order to obtain better shock resolution, a straightforward hp -adaptivity strategy is introduced, which is based on the high-order contribution calculated using hierarchical basis. Numerical results indicate that the hp -adaptivity method is easy to implement and better shock resolution can be obtained with smaller local mesh size and higher local order.