PT - JOURNAL ARTICLE
AU - Margolin, L. G.
TI - Scale matters
DP - 2018 Apr 28
TA - Philosophical Transactions of the Royal Society A: Mathematical,
Physical and Engineering Sciences
VI - 376
IP - 2118
4099 - http://rsta.royalsocietypublishing.org/content/376/2118/20170235.short
4100 - http://rsta.royalsocietypublishing.org/content/376/2118/20170235.full
SO - Philos Transact A Math Phys Eng Sci2018 Apr 28; 376
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’.