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Title: Discrete Thermodynamics

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:
Report Number(s):
LA-UR-17-23929
Journal ID: ISSN 0093-6413; TRN: US1703128
Grant/Contract Number:
AC52-06NA25396
Type:
Accepted Manuscript
Journal Name:
Mechanics Research Communications
Additional Journal Information:
Journal Name: Mechanics Research Communications; Journal ID: ISSN 0093-6413
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; nonequilibrium thermodynamics; computational fluid dynamics
OSTI Identifier:
1406221

Margolin, L. G., and Hunter, A.. Discrete Thermodynamics. United States: N. p., 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.. 2017. "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 = ,
place = {United States},
year = {2017},
month = {10}
}