A Comparison of the Performance of Limiters for Runge-Kutta Discontinuous Galerkin Methods
A Comparison of the Performance of Limiters for Runge-Kutta Discontinuous Galerkin Methods
复制标题
龙格-库塔间断伽辽金方法限制器的性能比较
DOI：
10.4208/aamm.2012.m22
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发表时间：
2013-06
影响因子：
1.4
通讯作者：
Qiu, Jianxian
中科院分区：
文献类型：
--
作者：
Zhu, Hongqiang;Cheng, Yue;Qiu, Jianxian
非线性守恒律的解即使初始条件是光滑的，也常常出现不连续现象，这给数值计算带来了很大的困难。龙格-库塔不连续伽辽金（RKDG）方法是求解非线性守恒律的有效方法，具有高阶精度和高度并行性，可方便地用于处理复杂几何和边界条件。求解强不连续非线性守恒律的RKDG方法的一个重要组成部分是非线性限制器，它用于检测不连续点和控制不连续点附近的杂散振荡。许多这样的限制已经在RKDG方法的文献中使用。限制器包含两个部分，首先识别“麻烦单元”，即那些可能需要限制程序的单元，然后用保持原始单元平均（守恒）的重构多项式代替这些麻烦单元中的解多项式。[j]。第一版。， 26(2005)，第995-1013.)集中讨论的第一部分的限制。本文以第二部分为重点，对几种不同的重建策略进行了系统的研究和比较，以期获得最有效、最可靠的重建策略。这项工作有助于选择合适的限制器，从而可以解决更明显的不连续性，得到更好的数值解，节省计算成本。AMS学科分类：65M60、65M99、35L65
Discontinuities usually appear in solutions of nonlinear conservation laws even though the initial condition is smooth, which leads to great difficulty in com- puting these solutions numerically. The Runge-Kutta discontinuous Galerkin (RKDG) methods areefficient methods for solving nonlinear conservation laws, whicharehigh- order accurate and highly parallelizable, and can be easily used to handle complicated geometries and boundary conditions. An important component of RKDG methods for solving nonlinear conservation laws with strong discontinuities in the solution is a nonlinear limiter, which is applied to detect discontinuities and control spurious os- cillations near such discontinuities. Many such limiters have been used in the litera- ture on RKDG methods. A limiter contains two parts, first to identify the "troubled cells", namely, those cells which might need the limiting procedure, then to replace the solution polynomials in those troubled cells by reconstructed polynomials which maintain the original cell averages (conservation). (SIAM J. Sci. Comput., 26 (2005), pp. 995-1013.) focused on discussing the first part of limiters. In this paper, focused on the second part, we will systematically investigate and compare a few different re- construction strategies with an objective of obtaining the most efficient and reliable reconstruction strategy. This work can help with the choosing of right limiters so one can resolve sharper discontinuities, get better numerical solutions and save the com- putational cost. AMS subject classifications: 65M60, 65M99, 35L65
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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
使用不同指标的自适应龙格-库塔不连续伽辽金方法：一维情况
影响因子：
4.1
作者：
Zhu, Hongqiang;Qiu, Jianxian
通讯作者：
Qiu, Jianxian
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
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