限制器
间断伽辽金法
数学
龙格-库塔方法
限制
应用数学
有界函数
伽辽金法
数学优化
数学分析
数值分析
计算机科学
有限元法
电信
物理
机械工程
热力学
工程类
作者
Jianxian Qiu,Chi‐Wang Shu
摘要
In [SIAM J. Sci. Comput., 26 (2005), pp. 907--929], we initiated the study of using WENO (weighted essentially nonoscillatory) methodology as limiters for the RKDG (Runge--Kutta discontinuous Galerkin) methods. The idea is to first identify "troubled cells," namely, those cells where limiting might be needed, then to abandon all moments in those cells except the cell averages and reconstruct those moments from the information of neighboring cells using a WENO methodology. This technique works quite well in our one- and two-dimensional test problems [SIAM J. Sci. Comput., 26 (2005), pp. 907--929] and in the follow-up work where more compact Hermite WENO methodology is used in the troubled cells. In these works we used the classical minmod-type TVB (total variation bounded) limiters to identify the troubled cells; that is, whenever the minmod limiter attempts to change the slope, the cell is declared to be a troubled cell. This troubled-cell indicator has a TVB parameter M to tune and may identify more cells than necessary as troubled cells when M is not chosen adequately, making the method costlier than necessary. In this paper we systematically investigate and compare a few different limiter strategies as troubled-cell indicators with an objective of obtaining the most efficient and reliable troubled-cell indicators to save computational cost.
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