A spacetime outlook on CFD: Spacetime correlated models and spacetime coupled algorithms

TL;DR

This paper advocates a spacetime perspective in CFD, emphasizing the importance of preserving spacetime correlations in models and algorithms, and introduces a unified, coupled high-order numerical approach.

Contribution

It introduces the concept of spacetime correlation in fluid models and develops a unified, coupled high-order numerical scheme that preserves these correlations.

Findings

Spacetime correlation property is fundamental in fluid models.

Spacetime coupling algorithms outperform decoupling methods.

The methodology applies mainly to continuous medium and compressible flows.

Abstract

A spacetime outlook on Computational Fluid Dynamics is advocated: models in fluid mechanics often have the spacetime correlation property, which should be inherited and preserved in the corresponding numerical algorithms. Starting from the fundamental formulation of fluid mechanics under continuum hypothesis, this paper defines the meaning of spacetime correlation of the models, establishes the fundamental principle of finite volume schemes, expounds the necessity of spacetime 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 spacetime coupling high order numerical algorithms is presented, and the difference from spacetime decoupling method is compared. It should be pointed out that most of the contents in this paper are suitable for computational fluid dynamics under the assumption of continuous medium, and some are only suitable for compressible flow.