初始间断诱导非物理波动及其消减算法

刘君; 韩芳; 孙逸轩; 刘瑜

doi:10.7638/kqdlxxb-2023.0203

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初始间断诱导非物理波动及其消减算法

研究论文 | 更新时间：2026-07-27

- 初始间断诱导非物理波动及其消减算法
- Initial discontinuity induced non-physical fluctuation and its elimination algorithm
- 空气动力学学报 2024年42卷第11期页码：18-32
- 作者机构：
  
  1. 大连理工大学航天航空学院,大连,116024
  2. 北京宇航系统工程研究所,北京,100076
  3. 宁波大学机械工程与力学学院,宁波,315211
- 作者简介：
  
  刘君*（1965—），男，内蒙古人，教授，研究方向：空气动力学. E-mail：liujun65@dlut.edu.cn
- 基金信息：
  
  国家自然科学基金（U21B2054）
- DOI：10.7638/kqdlxxb-2023.0203
  中图分类号： V211.3;O354.5
- 纸质出版：2024
- 稿件说明：
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刘君, 韩芳, 孙逸轩, 等. 初始间断诱导非物理波动及其消减算法[J]. 空气动力学学报, 2024, 42(11): 18−32.

LIU Jun, HAN Fang, SUN Yixuan, et al. Initial discontinuity induced non-physical fluctuation and its elimination algorithm[J]. 2024, 42(11): 18-32.
刘君, 韩芳, 孙逸轩, 等. 初始间断诱导非物理波动及其消减算法[J]. 空气动力学学报, 2024, 42(11): 18−32. DOI： 10.7638/kqdlxxb-2023.0203

LIU Jun, HAN Fang, SUN Yixuan, et al. Initial discontinuity induced non-physical fluctuation and its elimination algorithm[J]. 2024, 42(11): 18-32. DOI： 10.7638/kqdlxxb-2023.0203.

摘要

使用激波捕捉法求解以数学间断作为初始条件的无黏可压缩流场时，间断结构会逐渐演变为包含多个网格节点的数值过渡区，在此过程中会产生两个平行于间断且规则分布的非物理波动。使用捕捉法计算激波流场时，流场参数应满足修正方程，但作为初始条件进行计算的初始激波满足Euler方程，两者之间的矛盾是产生初始激波诱导非物理波动的原因。鉴于激波等间断是由特征型Euler方程定义的，从该方程出发构造了一种基于特征值迎风特性的通量计算格式（upwind flux scheme based on characteristics

UFSC），并采用若干种常规守恒型通量分裂格式作为参考。数值计算结果表明，UFSC可以消除Steger-Warming、Van Leer等矢通量分裂格式的初始接触间断诱导非物理波动，还可以减小初始激波诱导扰动的幅值。在光滑流场区域，UFSC和矢通量分裂格式的计算结果相近，但是在强激波附近会出现较大的压力尖峰。为克服这一缺陷，进一步构造了在激波区域和其他区域分别采用Steger-Warming格式和UFSC格式计算的混合通量计算格式UFSC+S，可以有效抑制初始激波诱导误差，提高计算精度。

Abstract

When the shock capturing method is used to solve inviscid compressible flow with a mathematical discontinuity as the initial condition

the discontinuity will gradually evolve into a numerical transition region across several grid points

and non-physical fluctuations in two directions parallel to the discontinuity can be induced in this process. The initial shock

which is calculated as the initial condition

satisfies the Euler equation

while the flow field parameters should satisfy the modified equations

such conflict might be the reason for the initial shock-induced non-physical fluctuations. As the discontinuities such as shock waves are defined by the characteristic lines of the Euler equation

an upwind flux scheme based on characteristics (UFSC) is proposed in the present study. Using several conventional conservation flux schemes as a reference

the UFSC can eliminate the non-physical fluctuations induced by the Steger-Warming and Van Leer schemes at the initial contact discontinuities

and can reduce the amplitude of the initial shock-induced disturbances. For the flow field in smooth regions

the computational results from the UFSC and conserved flux scheme are similar

but larger pressure peaks appear near the strong shock. To overcome this defect

a hybrid scheme UFSC+S is constructed

which uses the Steger-Warming for calculation in the shock region and the UFSC in other regions.

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references

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