A new type of approximate Riemann solver with adaptive anti-diffusion and its application

LIU Xuliang; FAN Zhaolin; ZHANG Shuhai; LI Hu; LUO Yong; SUN Xiaofeng

doi:10.7638/kqdlxxb-2022.0009

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A new type of approximate Riemann solver with adaptive anti-diffusion and its application

更新时间：2026-05-28

- A new type of approximate Riemann solver with adaptive anti-diffusion and its application
- Vol. 41, Issue 4, Pages: 52-63(2023)
- 作者机构：
  
  1. 中国空气动力研究与发展中心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
  3. 北京航空航天大学能源与动力工程学院,北京,100191
- 作者简介：
- 基金信息：
- DOI：10.7638/kqdlxxb-2022.0009
  CLC： O241.8
- Published：2023
- 稿件说明：
移动端阅览
刘旭亮, 范召林, 张树海, 等. 一类新型自适应反扩散近似Riemann求解器及其应用[J]. 空气动力学学报, 2023, 41(4): 52−63.

LIU Xuliang, FAN Zhaolin, ZHANG Shuhai, et al. A new type of approximate Riemann solver with adaptive anti-diffusion and its application[J]. 2023, 41(4): 52-63.
刘旭亮, 范召林, 张树海, 等. 一类新型自适应反扩散近似Riemann求解器及其应用[J]. 空气动力学学报, 2023, 41(4): 52−63. DOI： 10.7638/kqdlxxb-2022.0009

LIU Xuliang, FAN Zhaolin, ZHANG Shuhai, et al. A new type of approximate Riemann solver with adaptive anti-diffusion and its application[J]. 2023, 41(4): 52-63. DOI： 10.7638/kqdlxxb-2022.0009.

摘要

对于包含激波、剪切层等复杂结构的流动问题，为了精确模拟剪切层等精细结构，且保证激波计算的稳定性，必须采用低耗散且强鲁棒的数值通量方法。传统的HLL近似Riemann求解器的耗散性较大，Roe、HLLEM和HLLC等近似Riemann求解器在计算某些含有强激波的物理问题时会出现非物理解，容易导致不稳定。针对这一问题，本文在Riemann求解器中通过合理设计反扩散矩阵，发展了一类具有自适应反扩散的新型Riemann求解器，并将其应用到高阶加权紧致格式，实现了高阶精度求解。通过典型数值算例验证了新型方法的计算精度和稳定性，结果表明本文提出的新型自适应反扩散Riemann求解器克服了传统Riemann求解器的缺陷，既能准确识别剪切层等精细结构，又能保证激波解的稳定性。

Abstract

Constructing numerical fluxes using Riemann solvers is one of the most important steps for solving hyperbolic systems of conservation laws. However

it is still of great challenge for existing Riemann solvers to simulate high-speed flows with shock waves. The Riemann solver based on the HLL approximation has a high dissipation

while those based on the Roe

HLLEM

and HLLC approximation may result in non-physical solutions and numerical instability when simulating complex flows with strong shock waves. Because of this

a new type of Riemann solver with adaptive anti-diffusion is developed by a dedicated design of the anti-diffusion matrix. Due to its low dissipation

the proposed Riemann solver yields high-accuracy solutions when applied to high-order weighted compact finite difference schemes. The standard numerical experiments verify computational accuracy and stability for the new method

which show that the new Riemann solver overcomes the shortcomings of the traditional approximate Riemann solver. The new Riemann solver can accurately identify the fine structures such as shear layers

and maintain the numerical stability for the computation of shock wave.

关键词

Keywords

references

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