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Title: Scale matters

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. Finally, I discuss the properties of that model and its relation to the discrete equations of computational fluid dynamics.
Authors:
ORCiD logo [1]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Report Number(s):
LA-UR-17-28788
Journal ID: ISSN 1364-503X
Grant/Contract Number:
AC52-06NA25396
Type:
Accepted Manuscript
Journal Name:
Philosophical Transactions of the Royal Society. A, Mathematical, Physical and Engineering Sciences
Additional Journal Information:
Journal Volume: 376; Journal Issue: 2118; Journal ID: ISSN 1364-503X
Publisher:
The Royal Society Publishing
Research Org:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org:
USDOE National Nuclear Security Administration (NNSA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; kinetic theory Navier-Stokes
OSTI Identifier:
1440438

Margolin, L. G.. Scale matters. United States: N. p., Web. doi:10.1098/rsta.2017.0235.
Margolin, L. G.. Scale matters. United States. doi:10.1098/rsta.2017.0235.
Margolin, L. G.. 2018. "Scale matters". United States. doi:10.1098/rsta.2017.0235.
@article{osti_1440438,
title = {Scale matters},
author = {Margolin, L. G.},
abstractNote = {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. Finally, I discuss the properties of that model and its relation to the discrete equations of computational fluid dynamics.},
doi = {10.1098/rsta.2017.0235},
journal = {Philosophical Transactions of the Royal Society. A, Mathematical, Physical and Engineering Sciences},
number = 2118,
volume = 376,
place = {United States},
year = {2018},
month = {3}
}