基于映射的模板光滑探测子的三阶WENO格式  

A 3rd-Order WENO Scheme for Stencil Smoothness Indicators Based on Mapping

作　　者：王亚辉 郭城 杜玉龙 WANG Yahui;GUO Cheng;DU Yulong(School of Mathematics and Statistics,Zhengzhou Normal University,Zhengzhou 450044,P.R.China;School of Science,Jiangsu Ocean University,Lianyungang,Jiangsu 222005,P.R.China)

机构地区：[1]郑州师范学院数学与统计学院,郑州450044 [2]江苏海洋大学理学院,江苏连云港222005

出　　处：《应用数学和力学》2025年第3期394-411,共18页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(12071470);河南省高等学校重点科研项目(22B110020);河南省自然科学基金(252300420394)。

摘　　要：加权本质无振荡(weighted essentially non-oscillatory,WENO)格式能否具有低耗散特性及高分辨率特性,关键在于光滑探测子的构造.该文针对三阶WENO格式的光滑探测子进行修正,通过最光滑的探测子,构造出了一个关于子模板光滑探测子的映射函数.在该函数作用下,减小了欠光滑模板的光滑探测子,进而增大了欠光滑模板的非线性权重.这明显地降低了格式的数值耗散,提高了格式的分辨率.一系列数值测试表明,基于映射的模板光滑探测子的三阶WENO格式比传统的三阶WENO-JS3和WENO-Z3格式具有更高的分辨率.The key to whether the WENO scheme can achieve optimal convergence accuracy and maintain essential no-oscillation characteristics near discontinuities lies in the construction of smoothness indicators.The smoothness indicator of the 3rd-order WENO scheme was modified through the construction of a mapping function to correct the smoothness indicators on each candidate stencil with the smoothest indicator.Under the influence of this mapping function,the smoothness indicator of the under-smooth stencil was reduced,thereby the nonlinear weight of the under-smooth stencil was increased.Then the numerical dissipation of the scheme was significantly lowered and its resolution was improved.A series of numerical examples demonstrate that,the new 3rd-order WENO scheme for smoothness indicators based on mapping has higher resolution than the classical WENO-JS3 and WENO-Z3 schemes.

关 键 词：双曲守恒律 WENO 映射 光滑探测子 非线性权 

分 类 号：O357.41[理学—流体力学]