TY - JOUR

T1 - A new continuum model for general relativistic viscous heat-conducting media

AU - Romenski, E.

AU - Peshkov, I.

AU - Dumbser, M.

AU - Fambri, F.

N1 - Funding Information: Data accessibility. This article has no additional data. Authors’ contributions. The theoretical part of the paper was developed by E.R. and I.P. with constant discussions and valuable support from F.F. and M.D. F.F. and M.D. developed and implemented the numerical scheme and carried out the numerical tests. I.P. drafted the manuscript. All authors read and approved the manuscript. Competing interests. The authors declare that they have no competing interests. Funding. This research has been supported by the European Union’s Horizon 2020 Research and Innovation Programme under the project ExaHyPE, grant no. 671698 (call FET-HPC-1-2014). M.D. also acknowledges funding from the Italian Ministry of Education, University and Research (MIUR) via the Departments of Excellence Initiative 2018–2022 attributed to DICAM of the University of Trento (grant no. L. 232/2016). M.D. has also received support from the University of Trento in the frame of the Strategic Initiative Modeling and Simulation. I.P. greatly acknowledges a financial support by Agence Nationale de la Recherche (FR) (grant no. ANR-11-LABX-0040-CIMI) within the program ANR-11-IDEX-0002-02. Theoretical results obtained by E.R. in §§2 and 3 were partially supported by the Russian Science Foundation (project 19-77-20004). Publisher Copyright: © 2020 The Author(s) Published by the Royal Society. All rights reserved. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/5/1

Y1 - 2020/5/1

N2 - 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'.

AB - 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'.

KW - causal dissipation

KW - hyperbolicity

KW - non-equilibrium thermodynamics

KW - 1ST-ORDER HYPERBOLIC FORMULATION

KW - ORDER ADER SCHEMES

KW - THERMODYNAMICS

KW - MECHANICS

KW - SYSTEMS

KW - MAGNETOHYDRODYNAMICS

KW - CAUSALITY

KW - FORMALISM

KW - FLUIDS

UR - http://www.scopus.com/inward/record.url?scp=85082634794&partnerID=8YFLogxK

U2 - 10.1098/rsta.2019.0175

DO - 10.1098/rsta.2019.0175

M3 - Article

C2 - 32223401

AN - SCOPUS:85082634794

VL - 378

JO - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

SN - 0962-8428

IS - 2170

M1 - 20190175

ER -