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

作　　者：李杰权 LI Jiequan(Laboratory of Computational Physics,Institute of Applied Physics and Computational Mathematics,Beijing 100088,China;Center for Applied Physics and Technology,Peking University,Beijing 100871,China)

机构地区：[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

出　　处：《空气动力学学报》2021年第1期92-110,共19页Acta Aerodynamica Sinica

基　　金：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。

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。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：计算流体力学 时空关联模型 时空耦合算法 积分平衡律 有限体积方法 时间区间通量 广义黎曼问题解法器 

分 类 号：V211.3[航空宇航科学与技术—航空宇航推进理论与工程]