  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.
