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

Ilya Peshkov, Michal Pavelka, Evgeniy Romenski, Miroslav Grmela

Research output: Contribution to journalArticlepeer-review

22 Citations (Scopus)

Abstract

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).

Original languageEnglish
Pages (from-to)1343-1378
Number of pages36
JournalContinuum Mechanics and Thermodynamics
Volume30
Issue number6
DOIs
Publication statusPublished - 1 Nov 2018

Keywords

  • Continuum thermodynamics
  • GENERIC
  • Godunov
  • Hamiltonian
  • Hyperbolic
  • Non-equilibrium thermodynamics
  • COMPLEX FLUIDS
  • MOMENT EQUATIONS
  • 1ST-ORDER HYPERBOLIC FORMULATION
  • POISSON BRACKETS
  • BRACKET FORMULATION
  • ORDER ADER SCHEMES
  • CONSERVATION EQUATIONS
  • GENERAL FORMALISM
  • SYSTEMS
  • NONLINEAR MODEL

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