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

作　　者：Hongqiang Zhu Yue Cheng Jianxian Qiu 

机构地区：[1]School of Natural Science,Nanjing University of Posts and Telecommunications,Nanjing,Jiangsu 210023,China [2]Department of Mathematics,Nanjing University,Nanjing,Jiangsu 210093,China [3]School of Mathematical Sciences,Xiamen University,Xiamen,Fujian 361005,China [4]Baidu,Inc.Baidu Campus,No.10,Shangdi 10th Street,Haidian District,Beijing 100085,China

出　　处：《Advances in Applied Mathematics and Mechanics》2013年第3期365-390,共26页应用数学与力学进展（英文）

基　　金：The research was partially supported by NSFC grant 10931004,11126287,11201242,NJUPT grant NY211029 and ISTCP of China grant No.2010DFR00700.The authors would like to thank the referees for the helpful suggestions.

摘　　要：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 efficientmethods for solving nonlinear conservation laws,which are highorder 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.

关 键 词：LIMITER discontinuous Galerkin method hyperbolic conservation laws 

分 类 号：O17[理学—数学]