高阶精度非线性加权格式权函数研究综述

毛枚良; 白进维; 闵耀兵; 马燕凯; 江定武

doi:10.7638/kqdlxxb-2023.0187

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高阶精度非线性加权格式权函数研究综述

综述 | 更新时间：2026-05-28

- 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
- 空气动力学学报 2024年42卷第6期页码：1-14
- 作者机构：
  
  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
- 作者简介：
  
  毛枚良（1965—），男，湖南涟源人，博士，研究方向：计算流体力学. E-mail：mml219@163.com
  闵耀兵*，博士，研究方向：高阶精度数值算法及其应用. E-mail：minyb@126.com
- 基金信息：
  
  国家自然科学基金（11972362，11672321，11372342）
- DOI：10.7638/kqdlxxb-2023.0187
  中图分类号： V211.3
- 纸质出版：2024
- 稿件说明：
移动端阅览
毛枚良, 白进维, 闵耀兵, 等. 高阶精度非线性加权格式权函数研究综述[J]. 空气动力学学报, 2024, 42(6): 1−14.

MAO Meiliang, BAI Jinwei, MIN Yaobing, et al. Review on weighting functions of high-order nonlinear weighted methods[J]. 2024, 42(6): 1-14.
毛枚良, 白进维, 闵耀兵, 等. 高阶精度非线性加权格式权函数研究综述[J]. 空气动力学学报, 2024, 42(6): 1−14. DOI： 10.7638/kqdlxxb-2023.0187

MAO Meiliang, BAI Jinwei, MIN Yaobing, et al. Review on weighting functions of high-order nonlinear weighted methods[J]. 2024, 42(6): 1-14. DOI： 10.7638/kqdlxxb-2023.0187.

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

Keywords

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