A simple weighted essentially nonoscillatory limiter for Runge-Kutta discontinuous Galerkin methods
A simple weighted essentially nonoscillatory limiter for Runge-Kutta discontinuous Galerkin methods
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DOI：
10.1016/j.jcp.2012.08.028
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
Xinghui Zhong;Chi-Wang Shu
中科院分区：
文献类型：
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作者：
Xinghui Zhong;Chi-Wang Shu
在本文中，我们研究了一个简单的限制器使用加权本质无振荡（韦诺）方法的Runge-Kutta间断Galerkin（RKDG）方法求解守恒律，其目标是获得一个强大的和高阶的限制程序，同时实现一致的高阶精度和尖锐的，无振荡的冲击过渡。该限制器的想法是重建整个多项式，而不是重建经典韦诺重建中的点值或矩。也就是说，目标细胞上的重建多项式是该细胞及其相邻细胞上的多项式的凸组合，并且凸组合的非线性权重遵循经典韦诺过程。这种限制器的主要优点是实现简单，特别是对于多维网格。在一个和两个维度的数值结果来说明这个过程的行为。
In this paper, we investigate a simple limiter using weighted essentially non-oscillatory (WENO) methodology for the Runge–Kutta discontinuous Galerkin (RKDG) methods solving conservation laws, with the goal of obtaining a robust and high order limiting procedure to simultaneously achieve uniform high order accuracy and sharp, non-oscillatory shock transitions. The idea of this limiter is to reconstruct the entire polynomial, instead of reconstructing point values or moments in the classical WENO reconstructions. That is, the reconstruction polynomial on the target cell is a convex combination of polynomials on this cell and its neighboring cells and the nonlinear weights of the convex combination follow the classical WENO procedure. The main advantage of this limiter is its simplicity in implementation, especially for multi-dimensional meshes. Numerical results in one and two dimensions are provided to illustrate the behavior of this procedure.