基于混合模板改进的五阶WENO格式在求解双曲守恒律方程中的应用  

APPLICATION OF THE IMPROVED FIFTH ORDER WENO SCHEMES BASED ON A HYBRID TEMPLATE IN SOLVING HYPERBOLIC CONSERVATION EQUATION

作　　者：高志辉 张学莹 GAO Zhi-hui;ZHANG Xue-ying(School of Mathematics,Hohai University,Nanjing 211100,China)

机构地区：[1]河海大学数学学院,江苏南京211100

出　　处：《数学杂志》2024年第5期441-452,共12页Journal of Mathematics

基　　金：河海大学2023年新工科、新农科、新文科研究与改革实践项目资助(B2301914);河海大学2023年研究生“课程思政”示范课程建设项目资助(421203160).

摘　　要：本文在WENO-MZQ3格式的基础上,将其模板推广到五阶WENO,即在经典五阶WENO格式的三个三点模板的基础上引入五点模板,并引入新的改进的全局光滑因子,对其进行加权处理得到新的五阶WENO格式.理论分析表明新的五阶WENO格式在光滑区域比五阶WENO-JS格式具有更高阶的计算精度,通过一系列一维和二维数值算例也验证了新的五阶WENO格式具有更高的精度和分辨率.In this paper,we extend the template of WENO-MZQ3 scheme to fth-order WENO schemes.This means that we introduce a ve-point template based on the three three-point templates of the conventional fth-order WENO scheme.We introduce a new improved global smoothness indicator and apply weighted treatment to obtain a new fth-order WENO scheme.Theoretical analysis demonstrate that the new fth-order WENO scheme achieves higher computational accuracy in smooth regions compared to the fth-order WENO-JS scheme.A series of one-dimensional and two-dimensional numerical examples validate the higher accuracy and resolution of the new fth-order WENO scheme.

关 键 词：WENO格式 五点模板 全局光滑因子 

分 类 号：O241.82[理学—计算数学]