Scale matters
Abstract
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:
-
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Publication Date:
- Research Org.:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)
- OSTI Identifier:
- 1440438
- Report Number(s):
- LA-UR-17-28788
Journal ID: ISSN 1364-503X
- Grant/Contract Number:
- AC52-06NA25396
- Resource 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
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; kinetic theory Navier-Stokes
Citation Formats
Margolin, L. G. Scale matters. United States: N. p., 2018.
Web. doi:10.1098/rsta.2017.0235.
Margolin, L. G. Scale matters. United States. https://doi.org/10.1098/rsta.2017.0235
Margolin, L. G. Mon .
"Scale matters". United States. https://doi.org/10.1098/rsta.2017.0235. https://www.osti.gov/servlets/purl/1440438.
@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 = {Mon Mar 19 00:00:00 EDT 2018},
month = {Mon Mar 19 00:00:00 EDT 2018}
}
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