An adaptive high-resolution hybrid scheme using central flux scheme and WENO scheme

TIAN Qi; GUO Yuan; LIANG Xian; LI Xinliang

doi:10.7638/kqdlxxb-2017.0050

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An adaptive high-resolution hybrid scheme using central flux scheme and WENO scheme

更新时间：2026-05-28

- An adaptive high-resolution hybrid scheme using central flux scheme and WENO scheme
- Vol. 37, Issue 4, Pages: 541-545, 577(2019)
- 作者机构：
  
  1. 北方民族大学数学与信息科学学院,银川,750021
  2. 中国科学院大学工程科学学院,北京,100049
  3. 中国科学院力学研究所高温气体动力学国家重点实验室,北京,100190
- 作者简介：
- 基金信息：
- DOI：10.7638/kqdlxxb-2017.0050
  CLC： V211.3
- Published：2019
- 稿件说明：
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田奇, 郭元, 梁贤, 李新亮. 自适应的高精度中心-WENO混合格式[J]. 空气动力学学报, 2019, 37(4): 541-545, 577.

TIAN Qi, GUO Yuan, LIANG Xian, et al. An adaptive high-resolution hybrid scheme using central flux scheme and WENO scheme[J]. 2019, 37(4): 541-545, 577.
田奇, 郭元, 梁贤, 李新亮. 自适应的高精度中心-WENO混合格式[J]. 空气动力学学报, 2019, 37(4): 541-545, 577. DOI： 10.7638/kqdlxxb-2017.0050.

TIAN Qi, GUO Yuan, LIANG Xian, et al. An adaptive high-resolution hybrid scheme using central flux scheme and WENO scheme[J]. 2019, 37(4): 541-545, 577. DOI： 10.7638/kqdlxxb-2017.0050.

摘要

为对可压缩流动进行高精度高分辨率的数值模拟，基于模板的光滑度量函数，构造了新型的加权因子，在此基础上将7阶精度的WENO格式与8阶中心格式进行加权组合，构造了一种自适应低耗散的中心-WENO混合格式（H-WENO7-CD8），并采用Fourier方法对离散格式数学特性进行了理论分析。该自适应的高精度中心-WENO混合格式相比于七阶的WENO格式具有更小的耗散误差。通过对激波-密度干扰问题、Rayleigh-Taylor不稳定性问题和双Mach反射问题的数值模拟，并与WENO-JS格式的计算结果对比，结果表明：该格式结合了WENO格式和中心格式的特点，能更好地捕捉激波，对物理脉动也具有较高的分辨率，适合于复杂流体流动的数值模拟。

Abstract

Aiming at high accuracy and high resolution computation for numerical simulation of compressible fluid flows

based on the smoothness measurement of the flux function of the stencil

the new kind of weighted factor is constructed. On the basis

the hybrid scheme (H-WENO7-CD8) combines the characteristics of WENO scheme and central flux scheme

and it improves the resolution of the scheme and the ability to capture the shock wave. The Fourier method is adopted to analysis the mathematical characteristics of the discrete scheme. The adaptive hybrid scheme has low dissipation. By the numerical simulation tests of the Shu-Osher shock-density interference problem

the two-dimensional Rayleigh-Taylor instability problem

and double Mach reflection

compared with the numerical tests of the WENO-JS scheme

the present hybrid scheme can capture the shock wave better

and it has higher resolution for shock waves and small-scale waves with a low computation cost. Therefore

the present scheme lays an algorithm foundation for high resolution numerical simulation of compressible fluid flows such as the shock wave-turbulent layer interaction problem or Richtmyer-Meshkov instability problem.

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references

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