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
毛枚良 1白进维 1闵耀兵 2马燕凯 2江定武1
作者信息
- 1. 中国空气动力研究与发展中心,绵阳 621000
- 2. 中国空气动力研究与发展中心,绵阳 621000;空天飞行空气动力科学与技术全国重点实验室,绵阳 621000
- 折叠
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.
Abstract
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Key words
high-order nonlinear scheme/nonlinear weighted method/order degradation problem at critical points/non-uniform width candidate stencil/CFD引用本文复制引用
基金项目
国家自然科学基金(11972362)
国家自然科学基金(11672321)
国家自然科学基金(11372342)
出版年
2024
国家科技期刊平台
NSTL
万方数据