一类加权型MUSCL格式的构造  

The construction of a family of weighted MUSCL scheme

作　　者：韩爽 唐树江[1] 李明军[1] Han Shuang;Tang Shujiang;Li Mingjun(School of Mathematics and Computational Science,Xiangtan University,411105,Xiangtan,China)

机构地区：[1]湘潭大学数学与计算科学学院,湘潭411105

出　　处：《应用力学学报》2021年第4期1703-1709,共7页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(11971411);湖南省重点项目(18A067)。

摘　　要：通过引入两个非线性权函数与Yee型对称限制器相结合,构造了一类加权Yee型限制器。将此类加权型限制器应用到高精度MUSCL格式中,从而得到一类加权型MUSCL格式。数值误差分析发现,相比于Yee型对称限制器,加权Yee型限制器具有更低的数值耗散,且误差更小,收敛速度更快。通过求解三类Riemann问题的数值解进一步发现,加权Yee型限制器具有更高的分辨率和更好的数值稳定性。In this paper, a new kind of weighted-Yee limiter is obtained by utilizing two nonlinear weight functions and combining with Yee symmetrical limiters. By applying this kind of weighted limiter to high-precision MUSCL scheme, a kind of weighted MUSCL scheme is put forwarded. Compared with Yee symmetrical limiters, numerical error shows that the weighted-Yee limiter has lower numerical dissipation, smaller error and faster convergent speed. Furthermore, the numerical solution of three kind of Riemann problems demonstrate the weighted-Yee limiter has higher resolution and better numerical stability.

关 键 词：非线性权函数 Yee型对称限制器 加权型限制器 MUSCL格式 低耗散 

分 类 号：O242[理学—计算数学]