TY - JOUR

T1 - Continuum mechanics and thermodynamics in the Hamilton and the Godunov-type formulations

AU - Peshkov, Ilya

AU - Pavelka, Michal

AU - Romenski, Evgeniy

AU - Grmela, Miroslav

N1 - Publisher Copyright: © 2018, Springer-Verlag GmbH Germany, part of Springer Nature.

PY - 2018/11/1

Y1 - 2018/11/1

N2 - Continuum mechanics with dislocations, with the Cattaneo-type heat conduction, with mass transfer, and with electromagnetic fields is put into the Hamiltonian form and into the form of the Godunov-type system of the first-order, symmetric hyperbolic partial differential equations (SHTC equations). The compatibility with thermodynamics of the time reversible part of the governing equations is mathematically expressed in the former formulation as degeneracy of the Hamiltonian structure and in the latter formulation as the existence of a companion conservation law. In both formulations the time irreversible part represents gradient dynamics. The Godunov-type formulation brings the mathematical rigor (the local well posedness of the Cauchy initial value problem) and the possibility to discretize while keeping the physical content of the governing equations (the Godunov finite volume discretization).

AB - Continuum mechanics with dislocations, with the Cattaneo-type heat conduction, with mass transfer, and with electromagnetic fields is put into the Hamiltonian form and into the form of the Godunov-type system of the first-order, symmetric hyperbolic partial differential equations (SHTC equations). The compatibility with thermodynamics of the time reversible part of the governing equations is mathematically expressed in the former formulation as degeneracy of the Hamiltonian structure and in the latter formulation as the existence of a companion conservation law. In both formulations the time irreversible part represents gradient dynamics. The Godunov-type formulation brings the mathematical rigor (the local well posedness of the Cauchy initial value problem) and the possibility to discretize while keeping the physical content of the governing equations (the Godunov finite volume discretization).

KW - Continuum thermodynamics

KW - GENERIC

KW - Godunov

KW - Hamiltonian

KW - Hyperbolic

KW - Non-equilibrium thermodynamics

KW - COMPLEX FLUIDS

KW - MOMENT EQUATIONS

KW - 1ST-ORDER HYPERBOLIC FORMULATION

KW - POISSON BRACKETS

KW - BRACKET FORMULATION

KW - ORDER ADER SCHEMES

KW - CONSERVATION EQUATIONS

KW - GENERAL FORMALISM

KW - SYSTEMS

KW - NONLINEAR MODEL

UR - http://www.scopus.com/inward/record.url?scp=85040777452&partnerID=8YFLogxK

U2 - 10.1007/s00161-018-0621-2

DO - 10.1007/s00161-018-0621-2

M3 - Article

AN - SCOPUS:85040777452

VL - 30

SP - 1343

EP - 1378

JO - Continuum Mechanics and Thermodynamics

JF - Continuum Mechanics and Thermodynamics

SN - 0935-1175

IS - 6

ER -