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

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...

A space-time outlook on CFD: Spatial-temporally correlated models and spatial-temporally coupled algorithms

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.