计算流体力学的时空观：模型的时空关联性及算法的时空耦合性

李杰权

doi:10.7638/kqdlxxb-2020.0162

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计算流体力学的时空观：模型的时空关联性及算法的时空耦合性

专栏——计算流体力学高精度格式及其应用 | 更新时间：2026-05-28

- 计算流体力学的时空观：模型的时空关联性及算法的时空耦合性
- A space-time outlook on CFD: Spatial-temporally correlated models and spatial-temporally coupled algorithms
- 空气动力学学报 2021年39卷第1期页码：92-110
- 作者机构：
  
  1. 北京应用物理与计算数学研究所计算物理重点实验室,北京,100088
  2. 北京大学应用物理与技术中心,北京,100871
- 作者简介：
  
  李杰权(1969-), 男, 安徽人, 研究员, 研究方向: 计算流体力学, 偏微分方程, 数值分析.E-mail: li_jiequan@iapcm.ac.cn
- 基金信息：
  
  国家自然科学基金（11771054，91852207，12072042）;国家重大项目（GJXM92579）;计算物理重点实验室基金
- DOI：10.7638/kqdlxxb-2020.0162
  中图分类号： V211.3
- 纸质出版：2021
- 稿件说明：
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李杰权. 计算流体力学的时空观：模型的时空关联性及算法的时空耦合性[J]. 空气动力学学报, 2021, 39(1): 92-110.

LI Jiequan. A space-time outlook on CFD: Spatial-temporally correlated models and spatial-temporally coupled algorithms[J]. 2021, 39(1): 92-110.
李杰权. 计算流体力学的时空观：模型的时空关联性及算法的时空耦合性[J]. 空气动力学学报, 2021, 39(1): 92-110. DOI： 10.7638/kqdlxxb-2020.0162.

LI Jiequan. A space-time outlook on CFD: Spatial-temporally correlated models and spatial-temporally coupled algorithms[J]. 2021, 39(1): 92-110. DOI： 10.7638/kqdlxxb-2020.0162.

摘要

流体力学中波的有限传播、粒子的碰撞、各种力之间相互作用，无不体现时空关联效应。本文从计算方法的视角探讨计算流体力学的时空观，即流体力学模型的时空关联性和计算方法的时空耦合性。从流体力学微团法建模出发，明确模型时空关联性的涵义，建立有限体积格式的基本原理，阐述算法时空耦合的必要性，实现流体力学基本控制方程物理建模与有限体积格式数学原理的统一。在实践中，给出时空耦合高精度数值方法设计思路，利用算例比较它与时空解耦方法的差别。期望通过时空观的建立，对未来计算流体力学的算法研究提供帮助。

Abstract

A space-time outlook on Computational Fluid Dynamics (CFD) is advocated: models in fluid mechanics often have the spatial-temporally correlated property

which should be inherited and preserved in the corresponding numerical algorithms. Starting from the fundamental formulas of fluid mechanics under continuum hypothesis

this paper defines the meaning of the spatial-temporal correlation of the models

establishes the fundamental principles of finite volume schemes

expounds the necessity of spatial-temporal coupling of algorithms

as well as realizes the physical and mathematical unification of basic governing equations of fluid mechanics and finite volume schemes. In practice

the design methodology of spatial-temporally coupled high-order numerical algorithms is presented

and the difference from spatial-temporally decoupled methods is compared. It is expected that this space-time outlook could guide the development of CFD algorithms in the near future.

关键词

Keywords

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