非结构网格通量重构算法下三种紧致WENO限制器对比研究

石京昶; 严红

doi:10.7638/kqdlxxb-2021.0383

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非结构网格通量重构算法下三种紧致WENO限制器对比研究

研究论文 | 更新时间：2026-05-28

- 非结构网格通量重构算法下三种紧致WENO限制器对比研究
- Comparison of three WENO limiters in flux reconstruction framework using unstructured grid
- 空气动力学学报 2023年41卷第5期页码：1-11
- 作者机构：
  
  1. 西北工业大学长三角研究院，太仓,215400
  2. 陕西省航空发动机内流动力学重点实验室,西安,710072
- 作者简介：
  
  石京昶（1992-），男，博士研究生，研究方向：超声速流动、计算流体力学.Email：shijingchang@nwpu.edu.cn
  严红*（1969-），女，博士，教授，研究方向：超声速流动、计算流体力学. Email：yanhong@nwpu.edu.cn
- 基金信息：
  
  国家数值风洞工程（ NNW）
- DOI：10.7638/kqdlxxb-2021.0383
  中图分类号： V211.3
- 纸质出版：2023
- 稿件说明：
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石京昶, 严红. 非结构网格通量重构算法下三种紧致WENO限制器对比研究[J]. 空气动力学学报, 2023, 41(5): 1−11.

SHI Jingchang, YAN Hong. Comparison of three WENO limiters in flux reconstruction framework using unstructured grid[J]. 2023, 41(5): 1-11.
石京昶, 严红. 非结构网格通量重构算法下三种紧致WENO限制器对比研究[J]. 空气动力学学报, 2023, 41(5): 1−11. DOI： 10.7638/kqdlxxb-2021.0383

SHI Jingchang, YAN Hong. Comparison of three WENO limiters in flux reconstruction framework using unstructured grid[J]. 2023, 41(5): 1-11. DOI： 10.7638/kqdlxxb-2021.0383.

摘要

在通量重构算法框架下对比研究了3种最新提出的用于间断伽辽金算法的紧致型WENO（weighted essentially non-oscillatory）限制器，即简单WENO限制器、

阶加权WENO限制器和多精度WENO限制器。这3种WENO限制器能够较高精度地模拟流场并捕捉激波，其紧致性在于问题网格单元中的重构只涉及问题网格单元及其相邻网格单元。同时，使用保精度的保正限制器用以避免可能出现的非物理的密度和压力负值。最后，采用非结构四边形网格在双马赫反射、激波与涡相互作用、激波反射、黏性弓形激波和激波与层流边界层相互作用等多个二维算例中，对这3种WENO限制器进行分析比较。结果显示：多精度WENO限制器与

阶加权WENO限制器能够高精度模拟流场并捕捉激波，同时一定程度抑制通量重构方法本身在激波附近的数值伪振荡；

阶加权WENO限制器与多精度WENO限制器相比，其稳态收敛性相对更好；简单WENO限制器则性能较差。根据以上研究，提出亟须发展能够使高阶WENO限制器在稳态问题中收敛的间断探测器。

Abstract

Three recently proposed compact WENO limiters

including the simple WENO limiter

-weighted WENO limiter and the multi-resolution WENO limiter

are studied in the flux reconstruction framework. The WENO limiter is able to simulate the flow with a relatively high resolution and capture the shock wave. They are compact since the reconstruction expands only the trouble cell and its neighbors. The positivity-preserving limiter is applied to avoid negative density/pressure near the shock. Based on unstructured quadrilateral

cells

the three WENO limiters in the flux reconstruction framework are compared in multiple cases including the double Mach reflection

strong shock/vortex interaction

shock reflection

viscous bow shock and shock/laminar boundary layer interaction. The results show that

both the multi-resolution WENO limiter and the

-weighted WENO limiter are able to simulate the flow field with a relatively high resolution and capture the shock wave. The spurious oscillations near the shock due to the intrinsic numerical instability of the flux reconstruction method are suppressed by the multi-resolution WENO and the p-weighted WENO limiter. Compared to the multi-resolution WENO limiter

the

-weighted WENO limiter shows a better convergence property. The simple WENO limiter leads to the worst result among the three WENO limiters. The results also show that the WENO limiters call for a better shock sensor to achieve convergence.

关键词

Keywords

references

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