%0 Journal Article
%A Margolin, L. G.
%T Scale matters
%D 2018
%R 10.1098/rsta.2017.0235
%J Philosophical Transactions of the Royal Society A: Mathematical,
Physical and Engineering Sciences
%V 376
%N 2118
%X 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’.
%U http://rsta.royalsocietypublishing.org/content/roypta/376/2118/20170235.full.pdf