Scale matters.
Philosophical transactions. Series A, Mathematical, physical, and engineering sciences(2018)
摘要
The applicability of Navier-Stokes equations is limited to near-equilibrium flows in which the gradients of density, velocity and energy are small. Here I propose an extension of the Chapman-Enskog approximation in which the velocity probability distribution function (PDF) is averaged in the coordinate phase space as well as the velocity phase space. I derive a PDF that depends on the gradients and represents a first-order generalization of local thermodynamic equilibrium. I then integrate this PDF to derive a hydrodynamic model. I discuss the properties of that model and its relation to the discrete equations of computational fluid dynamics.This article is part of the theme issue 'Hilbert's sixth problem'.
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关键词
coarse-graining,finite scale,high Reynolds number
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