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Title: Discrete Thermodynamics

Abstract

Here, we consider the dependence of velocity probability distribution functions on the finite size of a thermodynamic system. We are motivated by applications to computational fluid dynamics, hence discrete thermodynamics. We then begin by describing a coarsening process that represents geometric renormalization. Then, based only on the requirements of conservation, we demonstrate that the pervasive assumption of local thermodynamic equilibrium is not form invariant. We develop a perturbative correction that restores form invariance to second-order in a small parameter associated with macroscopic gradients. Finally, we interpret the corrections in terms of unresolved kinetic energy and discuss the implications of our results both in theory and as applied to numerical simulation.

Authors:
ORCiD logo [1]; ORCiD logo [1]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1406221
Report Number(s):
[LA-UR-17-23929]
[Journal ID: ISSN 0093-6413; TRN: US1703128]
Grant/Contract Number:  
[AC52-06NA25396]
Resource Type:
Accepted Manuscript
Journal Name:
Mechanics Research Communications
Additional Journal Information:
[ Journal Volume: 93]; Journal ID: ISSN 0093-6413
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; nonequilibrium thermodynamics; computational fluid dynamics

Citation Formats

Margolin, L. G., and Hunter, A. Discrete Thermodynamics. United States: N. p., 2017. Web. doi:10.1016/j.mechrescom.2017.10.006.
Margolin, L. G., & Hunter, A. Discrete Thermodynamics. United States. doi:10.1016/j.mechrescom.2017.10.006.
Margolin, L. G., and Hunter, A. Wed . "Discrete Thermodynamics". United States. doi:10.1016/j.mechrescom.2017.10.006. https://www.osti.gov/servlets/purl/1406221.
@article{osti_1406221,
title = {Discrete Thermodynamics},
author = {Margolin, L. G. and Hunter, A.},
abstractNote = {Here, we consider the dependence of velocity probability distribution functions on the finite size of a thermodynamic system. We are motivated by applications to computational fluid dynamics, hence discrete thermodynamics. We then begin by describing a coarsening process that represents geometric renormalization. Then, based only on the requirements of conservation, we demonstrate that the pervasive assumption of local thermodynamic equilibrium is not form invariant. We develop a perturbative correction that restores form invariance to second-order in a small parameter associated with macroscopic gradients. Finally, we interpret the corrections in terms of unresolved kinetic energy and discuss the implications of our results both in theory and as applied to numerical simulation.},
doi = {10.1016/j.mechrescom.2017.10.006},
journal = {Mechanics Research Communications},
number = ,
volume = [93],
place = {United States},
year = {2017},
month = {10}
}

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Cited by: 2 works
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Figures / Tables:

Figure 1 Figure 1: The coarsening process consists of merging two cells with possibly different values of state variables density, velocity and internal energy into a single larger cell. Values of the state variables in the larger cell are constrained by conservation, but not completely determined by conservation.

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