A Comparison of the Performance of Limiters for Runge-Kutta Discontinuous Galerkin Methods

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	A Comparison of the Performance of Limiters for Runge-Kutta Discontinuous Galerkin Methods
	Zhu, Hongqiang ; Cheng, Yue ; Qiu, Jianxian ; Qiu JX(邱建贤)
刊名	http://dx.doi.org/10.4208/aamm.2012.m22
	2013
关键词	FINITE-ELEMENT-METHOD HYPERBOLIC CONSERVATION-LAWS SHOCK-CAPTURING SCHEMES EFFICIENT IMPLEMENTATION SYSTEMS
英文摘要	NSFC grant [10931004, 11126287, 11201242]; NJUPT grant [NY211029]; ISTCP of China grant [2010DFR00700]; Discontinuities usually appear in solutions of nonlinear conservation laws even though the initial condition is smooth, which leads to great difficulty in computing these solutions numerically. The Runge-Kutta discontinuous Galerkin (RKDG) methods are efficient methods for solving nonlinear conservation laws, which are high-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 oscillations near such discontinuities. Many such limiters have been used in the literature 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 reconstruction 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 computational cost.
语种	英语
出版者	GLOBAL SCIENCE PRESS
内容类型	期刊论文
源URL	[http://dspace.xmu.edu.cn/handle/2288/91272]
专题	数学科学－已发表论文
推荐引用方式 GB/T 7714	Zhu, Hongqiang,Cheng, Yue,Qiu, Jianxian,et al. A Comparison of the Performance of Limiters for Runge-Kutta Discontinuous Galerkin Methods[J]. http://dx.doi.org/10.4208/aamm.2012.m22,2013.
APA	Zhu, Hongqiang,Cheng, Yue,Qiu, Jianxian,&邱建贤.(2013).A Comparison of the Performance of Limiters for Runge-Kutta Discontinuous Galerkin Methods.http://dx.doi.org/10.4208/aamm.2012.m22.
MLA	Zhu, Hongqiang,et al."A Comparison of the Performance of Limiters for Runge-Kutta Discontinuous Galerkin Methods".http://dx.doi.org/10.4208/aamm.2012.m22 (2013).