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.