Numerical Mathematics: Theory, Methods and Applications
Numerical Mathematics: Theory, Methods and Applications
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DOI：
10.4208/nmtma
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
Jianming Liu;J. Qiu;M. Goman;Xinkai Li;Meilin Liu
中科院分区：
文献类型：
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作者：
Jianming Liu;J. Qiu;M. Goman;Xinkai Li;Meilin Liu
为了克服保正性限制器技术不能保持密度或压力为正的缺点，提出了一种保正性限制器技术与h-自适应Runge-Kutta间断Galerkin（RKDG）方法相结合的方法.该方法可用于模拟大马赫数、强激波/障碍物干扰和激波绕射的流动。本文还介绍了适用于任意复杂几何形状的笛卡尔网格-鬼胞浸入边界法。该方法直接利用DG有限元空间的单元解多项式作为插值公式。通过大量的复杂体非定常可压缩流的实验验证了该方法的有效性。数值结果表明，所提出的方法的鲁棒性和通用性。AMS科目分类：65 M50; 65 M60; 76 L05
In order to suppress the failure of preserving positivity of density or pressure, a positivity-preserving limiter technique coupled with h-adaptive Runge-Kutta discontinuous Galerkin (RKDG) method is developed in this paper. Such a method is implemented to simulate flows with the large Mach number, strong shock/obstacle interactions and shock diffractions. The Cartesian grid with ghost cell immersed boundary method for arbitrarily complex geometries is also presented. This approach directly uses the cell solution polynomial of DG finite element space as the interpolation formula. The method is validated by the well documented test examples involving unsteady compressible flows through complex bodies over a large Mach numbers. The numerical results demonstrate the robustness and the versatility of the proposed approach. AMS subject classifications: 65M50; 65M60; 76L05