WENO格式的一种新型光滑因子及其应用

刘旭亮; 武从海; 李虎; 范召林

doi:10.7638/kqdlxxb-2022.0013

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WENO格式的一种新型光滑因子及其应用

研究论文 | 更新时间：2026-05-28

- WENO格式的一种新型光滑因子及其应用
- A new type of smoothness indicator for weighted essentially non-oscillatory schemes and its application
- 空气动力学学报 2023年41卷第5期页码：20-34
- 作者机构：
  
  1. 空气动力学国家重点实验室,绵阳,621000
  2. 中国空气动力研究与发展中心,绵阳,621000
- 作者简介：
  
  刘旭亮（1986-），男，助理研究员，研究方向：计算流体力学. E-mail：xlliu@foxmail.com
- 基金信息：
  
  国家自然科学基金（11972360，11732016）;四川省科技计划项目（2018JZ0076）;国家数值风洞工程（ NNW）
- DOI：10.7638/kqdlxxb-2022.0013
  中图分类号： V211.3
- 纸质出版：2023
- 稿件说明：
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刘旭亮, 武从海, 李虎, 等. WENO格式的一种新型光滑因子及其应用[J]. 空气动力学学报, 2023, 41(5): 20−34.

LIU Xuliang, WU Conghai, LI Hu, et al. A new type of smoothness indicator for weighted essentially non-oscillatory schemes and its application[J]. 2023, 41(5): 20-34.
刘旭亮, 武从海, 李虎, 等. WENO格式的一种新型光滑因子及其应用[J]. 空气动力学学报, 2023, 41(5): 20−34. DOI： 10.7638/kqdlxxb-2022.0013

LIU Xuliang, WU Conghai, LI Hu, et al. A new type of smoothness indicator for weighted essentially non-oscillatory schemes and its application[J]. 2023, 41(5): 20-34. DOI： 10.7638/kqdlxxb-2022.0013.

摘要

光滑因子是构造WENO格式的关键，决定了WENO格式能否达到最优收敛精度以及在间断附近能否保持本质无振荡特性。针对广泛应用的五阶WENO格式，采用算子函数近似导数关系的方法，设计了一种新型光滑因子。在间断区域，与传统的光滑因子相比，新型光滑因子对间断的识别更准确。在光滑区域，新型光滑因子使得新型WENO格式的非线性权更接近线性权。理论分析和数值验证表明新型WENO格式即使在一阶临界点也能保持一致五阶精度。一维典型激波问题的数值结果表明，与现有WENO格式相比，新型WENO格式提高了短波的分辨率，降低了格式的耗散，同时能够准确识别间断。对于典型包含激波和剪切层的流动问题，新型WENO格式不仅能够准确地捕捉强激波，而且能够精细模拟剪切层和声波等流场结构。

Abstract

The smoothness indicator determines whether WENO (weighted essentially-non-oscillatory) schemes can achieve the optimal convergence accuracy and maintain the essentially non-oscillatory characteristics near discontinuities; consequently

it is the key to constructing WENO schemes. This paper proposes a new type of smoothness indicator for the widely used fifth-order WENO scheme by the operator function method. Compared to existing smoothness indicators

this new smoothness indicator has two advantages: firstly

it quantifies the smoothness of stencils and identifies discontinuities more accurately in discontinuous regions; secondly

the nonlinear weights are closer to the linear weights in smooth regions. The resulting WENO scheme maintains the optimal fifth-order accuracy at the first-order critical point and has lower dissipation

better shock-capturing capability

and higher resolution for short waves than those using existing smoothness indicators. It

therefore

captures strong shock waves and flow structures such as shear layers and sound waves more accurately

suggesting the great potential of this smoothness indicator in simulating complex flows.

关键词

Keywords

references

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