限制器
平滑度
数学
间断伽辽金法
基函数
水准点(测量)
伽辽金法
应用数学
磁通限制器
投影(关系代数)
正交(天文学)
功能(生物学)
数学分析
算法
计算机科学
有限元法
地理
工程类
物理
电气工程
热力学
生物
进化生物学
电信
大地测量学
作者
Wanai Li,Qian Wang,Yu-Xin Ren
标识
DOI:10.1016/j.jcp.2020.109246
摘要
This paper presents an accuracy-preserving p-weighted limiter for discontinuous Galerkin methods on one-dimensional and two-dimensional triangular grids. The p-weighted limiter is the extension of the second-order WENO limiter by Li et al. (2018) [22] to high-order accuracy, with the following important improvements of the limiting procedure. First, the candidate polynomials of the p-weighted limiter are the p-hierarchical orthogonal polynomials of the current cell, and the linear polynomials constructed by minimizing the projection error on the face-neighboring cells. Second, the p-weighted procedure introduces a new smoothness indicator which has less numerical dissipation comparing with the classical WENO one. The smoothness indicator is efficiently computed through a quadrature-free approach that takes advantage of the orthogonal property of the basis functions. Third, the small positive number ϵ, which is introduced in the weights to avoid dividing by zero, is set as a function of the smoothness indicator to preserve accuracy near smooth extremas. Numerous benchmark problems are solved to test the p1, p3 and p5 discontinuous Galerkin schemes using the p-weighted limiter. Numerical results demonstrate that the p-weighted limiter is capable of capturing strong shocks while preserving accuracy in smooth regions.
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