The lack of formulation of macroscopic equations for irreversible dynamics of viscous heat-conducting media compatible with the causality principle of Einstein's special relativity and the Euler-Lagrange structure of general relativity is a long-lasting problem. In this paper, we propose a possible solution to this problem in the framework of SHTC equations. The approach does not rely on postulates of equilibrium irreversible thermodynamics but treats irreversible processes from the non-equilibrium point of view. Thus, each transfer process is characterized by a characteristic velocity of perturbation propagation in the non-equilibrium state, as well as by an intrinsic time/length scale of the dissipative dynamics. The resulting system of governing equations is formulated as a first-order system of hyperbolic equations with relaxation-type irreversible terms. Via a formal asymptotic analysis, we demonstrate that classical transport coefficients such as viscosity, heat conductivity, etc., are recovered in leading terms of our theory as effective transport coefficients. Some numerical examples are presented in order to demonstrate the viability of the approach. This article is part of the theme issue 'Fundamental aspects of nonequilibrium thermodynamics'.

A new continuum model for general relativistic viscous heat-conducting media / Romenski, E.; Peshkov, I.; Dumbser, M.; Fambri, F.. - In: PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY OF LONDON SERIES A: MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES. - ISSN 1364-503X. - 378:2170(2020), p. 20190175. [10.1098/rsta.2019.0175]

A new continuum model for general relativistic viscous heat-conducting media

Romenski E.;Peshkov I.;Dumbser M.;Fambri F.
2020-01-01

Abstract

The lack of formulation of macroscopic equations for irreversible dynamics of viscous heat-conducting media compatible with the causality principle of Einstein's special relativity and the Euler-Lagrange structure of general relativity is a long-lasting problem. In this paper, we propose a possible solution to this problem in the framework of SHTC equations. The approach does not rely on postulates of equilibrium irreversible thermodynamics but treats irreversible processes from the non-equilibrium point of view. Thus, each transfer process is characterized by a characteristic velocity of perturbation propagation in the non-equilibrium state, as well as by an intrinsic time/length scale of the dissipative dynamics. The resulting system of governing equations is formulated as a first-order system of hyperbolic equations with relaxation-type irreversible terms. Via a formal asymptotic analysis, we demonstrate that classical transport coefficients such as viscosity, heat conductivity, etc., are recovered in leading terms of our theory as effective transport coefficients. Some numerical examples are presented in order to demonstrate the viability of the approach. This article is part of the theme issue 'Fundamental aspects of nonequilibrium thermodynamics'.
2020
2170
Romenski, E.; Peshkov, I.; Dumbser, M.; Fambri, F.
A new continuum model for general relativistic viscous heat-conducting media / Romenski, E.; Peshkov, I.; Dumbser, M.; Fambri, F.. - In: PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY OF LONDON SERIES A: MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES. - ISSN 1364-503X. - 378:2170(2020), p. 20190175. [10.1098/rsta.2019.0175]
File in questo prodotto:
File Dimensione Formato  
PTRSA_paper.pdf

accesso aperto

Descrizione: A new continuum model for general relativistic viscous heat-conducting media
Tipologia: Post-print referato (Refereed author’s manuscript)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 539.12 kB
Formato Adobe PDF
539.12 kB Adobe PDF Visualizza/Apri
rsta.2019.0175.pdf

Solo gestori archivio

Tipologia: Versione editoriale (Publisher’s layout)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 453.29 kB
Formato Adobe PDF
453.29 kB Adobe PDF   Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/264522
Citazioni
  • ???jsp.display-item.citation.pmc??? 1
  • Scopus 19
  • ???jsp.display-item.citation.isi??? 18
social impact