RT Journal Article
SR Electronic
T1 Scale matters
JF Philosophical Transactions of the Royal Society A: Mathematical,
Physical and Engineering Sciences
JO Philos Transact A Math Phys Eng Sci
FD The Royal Society
DO 10.1098/rsta.2017.0235
VO 376
IS 2118
A1 Margolin, L. G.
YR 2018
UL http://rsta.royalsocietypublishing.org/content/376/2118/20170235.abstract
AB 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’.