非结构网格紧致高精度气体动理学格式

李启兵; 张潮

doi:10.7638/kqdlxxb-2020.0192

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非结构网格紧致高精度气体动理学格式

专栏——计算流体力学高精度格式及其应用 | 更新时间：2026-05-28

- 非结构网格紧致高精度气体动理学格式
- Compact high-order gas-kinetic scheme on unstructured meshes
- 空气动力学学报 2021年39卷第1期页码：191-200
- 作者机构：
  
  清华大学航天航空学院,北京,100084
- 作者简介：
  
  李启兵(1973-), 男, 四川大竹人, 副教授, 研究方向: 计算流体力学, 湍流和稀薄气体流动.E-mail: lqb@tsinghua.edu.cn
- 基金信息：
  
  国家自然科学基金（11672158，91852109）;国家重点基础研究发展计划（2014CB744100）
- DOI：10.7638/kqdlxxb-2020.0192
  中图分类号： V211.3
- 纸质出版：2021
- 稿件说明：
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李启兵, 张潮. 非结构网格紧致高精度气体动理学格式[J]. 空气动力学学报, 2021, 39(1): 191-200.

LI Qibing, ZHANG Chao. Compact high-order gas-kinetic scheme on unstructured meshes[J]. 2021, 39(1): 191-200.
李启兵, 张潮. 非结构网格紧致高精度气体动理学格式[J]. 空气动力学学报, 2021, 39(1): 191-200. DOI： 10.7638/kqdlxxb-2020.0192.

LI Qibing, ZHANG Chao. Compact high-order gas-kinetic scheme on unstructured meshes[J]. 2021, 39(1): 191-200. DOI： 10.7638/kqdlxxb-2020.0192.

摘要

简要介绍了非结构网格上基于内自由度高效紧致重构方法的几种高精度气体动理学格式（GKS），包括结合三阶GKS通量求解器与子单元有限体积法（SCFV）及通量重构方法（CPR）构造的两种单步时空三阶格式SCFV-GKS和CPR-GKS，以及结合二阶GKS通量和两步四阶方法构造的时空四阶CPR-GKS。进而在CPR-GKS中混合SCFV增强对流场间断的分辨能力，并拓展到三维六面体网格。通过几种典型数值算例，对比分析了这几种格式在可压缩流动问题中具有的高精度、高效率和良好的间断捕捉能力。GKS通量的多维时空演化特性与紧致重构方法的高效性为发展高精度格式提供了有力的支撑。

Abstract

Several high-order accurate gas-kinetic schemes (GKS) on unstructured meshes are briefly introduced

which are based on the efficient compact reconstruction using inner degree of freedom. They include two single-step schemes with third-order accuracy in space and time

developed with the combination of third-order GKS flux solver and the subcell finite volume scheme (SCFV) or the correction procedure via reconstruction (CPR) framework

respectively. The third one is the two-step forth-order CPR-GKS which is developed with the simple second-order GKS flux and two-step forth-order method. A hybrid of SCFV is then conducted to enhance the resolution of flow discontinuities and the three-dimensional scheme is further constructed on hexahedral meshes. Several typical flows are simulated for the comparative study of their high accuracy

high efficiency and good capability of discontinuity capturing in compressible flows. The multidimensional space and time evolution of GKS flux

as well as the high efficiency of compact reconstruction provide strong support for the development of high order schemes.

关键词

Keywords

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