高阶精度非线性加权格式权函数研究综述  

Review on weighting functions of high-order nonlinear weighted methods

作　　者：毛枚良[1] 白进维 闵耀兵[1,2] 马燕凯 江定武[1] MAO Meiliang;BAI Jinwei;MIN Yaobing;MA Yankai;JIANG Dingwu(China Aerodynamics Research and Development Center,Mianyang 621000,China;State Key Laboratory of Aerodynamics,Mianyang 621000,China)

机构地区：[1]中国空气动力研究与发展中心,绵阳621000 [2]空天飞行空气动力科学与技术全国重点实验室,绵阳621000

出　　处：《空气动力学学报》2024年第6期1-14,I0001,共15页Acta Aerodynamica Sinica

基　　金：国家自然科学基金(11972362,11672321,11372342)。

摘　　要：在简述用于捕捉间断的非线性格式发展历程的基础上,依托五阶精度WENO格式,介绍了非线性加权格式在候选模板集选取、光滑度指标计算方法及其与非线性权的函数关系等方面做出的努力。对于非等宽候选模板集的情况,给出了保证非线性加权格式精度的非线性权的量阶关系,强调了光滑度指标计算方法对格式精度和效率的重要性,提出了进一步开展多宽度模板集非线性加权格式研究的建议。After a brief introduction to the historical development of nonlinear schemes for capturing discontinuities,this paper delves into the research on selecting candidate stencils,calculating smoothness indicators and their relationships with nonlinear weighting functions.This review is centered on the fifth order WENO scheme,serving as a representative example of nonlinear weighted schemes.It highlights the crucial requirements for the leading term order of nonlinear weights to preserve the accuracy of these schemes,especially when dealing with candidate stencils of varying widths.This paper underscores the significance of smoothness indicator calculations in ensuring both the accuracy and efficiency of the scheme.Finally,it offers insights and suggestions for future research aimed at further enhancing nonlinear weighted schemes that utilize candidate stencils with non-uniform widths.

关 键 词：高阶精度非线性格式 非线性加权方法 极值点降阶问题 非等宽候选模板集 计算流体力学 

分 类 号：V211.3[航空宇航科学与技术—航空宇航推进理论与工程]