Runge-Kutta discontinuous Galerkin method using a new type of WENO limiters on unstructured meshes
Runge-Kutta discontinuous Galerkin method using a new type of WENO limiters on unstructured meshes
复制标题
在非结构化网格上使用新型 WENO 限制器的 Runge-Kutta 不连续 Galerkin 方法
DOI：
10.1016/j.jcp.2013.04.012
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发表时间：
2013-09
影响因子：
4.1
通讯作者：
Qiu, Jianxian
中科院分区：
文献类型：
--
作者：
Zhu, Jun;Zhong, Xinghui;Shu, Chi-Wang;Qiu, Jianxian
本文将基于加权本质无振荡(WENO)有限体积法的Runge-Kutta间断Galerkin(RKDG)方法的一种新型限制器推广到二维非结构三角网格。这种限制器的核心思想是利用问题单元及其相邻单元的DG解的全多项式，然后应用经典的WENO过程，基于光滑性指标和非线性权重来形成这些多项式的凸组合，并进行适当的调整以保证守恒性。这种新的限制器的主要优点是实现简单，特别是对于本文所考虑的非结构网格，因为它只需要来自近邻的信息，并且在很大程度上避免了使用复杂的网格几何信息。给出了可压缩气体动力学标量方程和欧拉系统的数值结果，说明了该方法的良好性能。
In this paper we generalize a new type of limiters based on the weighted essentially non-oscillatory (WENO) finite volume methodology for the Runge–Kutta discontinuous Galerkin (RKDG) methods solving nonlinear hyperbolic conservation laws, which were recently developed in [32] for structured meshes, to two-dimensional unstructured triangular meshes. The key idea of such limiters is to use the entire polynomials of the DG solutions from the troubled cell and its immediate neighboring cells, and then apply the classical WENO procedure to form a convex combination of these polynomials based on smoothness indicators and nonlinear weights, with suitable adjustments to guarantee conservation. The main advantage of this new limiter is its simplicity in implementation, especially for the unstructured meshes considered in this paper, as only information from immediate neighbors is needed and the usage of complicated geometric information of the meshes is largely avoided. Numerical results for both scalar equations and Euler systems of compressible gas dynamics are provided to illustrate the good performance of this procedure.
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影响因子：
4.1
作者：
Hu, CQ;Shu, CW
通讯作者：
Shu, CW
影响因子：
2
作者：
Bernardo Cockburn;S. Hou;Chi-Wang Shu
通讯作者：
Bernardo Cockburn;S. Hou;Chi-Wang Shu
DOI：
10.1016/j.jcp.2012.08.028
发表时间：
2013
期刊：
J. Comput. Phys.
影响因子：
--
作者：
Xinghui Zhong;Chi-Wang Shu
通讯作者：
Xinghui Zhong;Chi-Wang Shu
DOI：
10.1016/j.jcp.2006.06.043
发表时间：
2007-02
期刊：
J. Comput. Phys.
影响因子：
--
作者：
M. Dumbser;M. Käser
通讯作者：
M. Dumbser;M. Käser
影响因子：
4.1
作者：
HARTEN, A;ENGQUIST, B;CHAKRAVARTHY, SR
通讯作者：
CHAKRAVARTHY, SR