WENO Schemes and Their Application as Limiters for RKDG Methods Based on Trigonometric Approximation Spaces
WENO Schemes and Their Application as Limiters for RKDG Methods Based on Trigonometric Approximation Spaces
复制标题
WENO方案及其作为基于三角逼近空间的RKDG方法限制器的应用
DOI：
10.1007/s10915-012-9649-9
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发表时间：
2013-06
影响因子：
2.5
通讯作者：
Qiu, Jianxian
中科院分区：
文献类型：
--
作者：
Zhu, Jun;Qiu, Jianxian
本文提出了一类有限体积三角加权本质无振荡（TWENO）格式，并将其作为三角多项式空间上Runge-Kutta间断Galerkin（RKDG）方法的限制器，用于求解双曲守恒律和高振荡问题.像往常一样，我们的目标是获得一个强大的和高阶的限制程序，这样的RKDG方法，同时实现均匀的高阶精度在光滑的区域和尖锐的，非振荡的冲击过渡。基于三角多项式空间的格式的主要优点是它们比基于代数多项式空间的格式能更好地模拟波动和高振荡的情况。我们提供数值结果在一个和两个维度来说明这些程序在这种情况下的行为。尽管我们没有利用三角多项式空间的最佳参数，但我们确实观察到基于此类空间的方案获得的数值结果优于或类似于基于代数多项式空间的方案。
In this paper, we present a class of finite volume trigonometric weighted essentially non-oscillatory (TWENO) schemes and use them as limiters for Runge-Kutta discontinuous Galerkin (RKDG) methods based on trigonometric polynomial spaces to solve hyperbolic conservation laws and highly oscillatory problems. As usual, the goal is to obtain a robust and high order limiting procedure for such a RKDG method to simultaneously achieve uniformly high order accuracy in smooth regions and sharp, non-oscillatory shock transitions. The major advantage of schemes which are based on trigonometric polynomial spaces is that they can simulate the wave-like and highly oscillatory cases better than the ones based on algebraic polynomial spaces. We provide numerical results in one and two dimensions to illustrate the behavior of these procedures in such cases. Even though we do not utilize optimal parameters for the trigonometric polynomial spaces, we do observe that the numerical results obtained by the schemes based on such spaces are better than or similar to those based on algebraic polynomial spaces.
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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：
10.1142/9789814354561_0013
发表时间：
1992
期刊：
--
影响因子：
--
作者：
C. Angelopoulos
通讯作者：
C. Angelopoulos
影响因子：
4.1
作者：
HARTEN, A;ENGQUIST, B;CHAKRAVARTHY, SR
通讯作者：
CHAKRAVARTHY, SR
影响因子：
4.1
作者：
Jiang, GS;Shu, CW
通讯作者：
Shu, CW
影响因子：
2
作者：
Bernardo Cockburn;Chi-Wang Shu
通讯作者：
Bernardo Cockburn;Chi-Wang Shu