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 secondorder 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:

 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):
 LAUR1723929
Journal ID: ISSN 00936413; TRN: US1703128
 Grant/Contract Number:
 AC5206NA25396
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Mechanics Research Communications
 Additional Journal Information:
 Journal Volume: 93; Journal ID: ISSN 00936413
 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. https://doi.org/10.1016/j.mechrescom.2017.10.006.
Margolin, L. G., & Hunter, A. Discrete Thermodynamics. United States. https://doi.org/10.1016/j.mechrescom.2017.10.006
Margolin, L. G., and Hunter, A. Wed .
"Discrete Thermodynamics". United States. https://doi.org/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 secondorder 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}
}
Web of Science