Continuum mechanics and thermodynamics in the Hamilton and the Godunovtype formulations
Abstract
Continuum mechanics with dislocations, with the Cattaneotype heat conduction, with mass transfer, and with electromagnetic fields is put into the Hamiltonian form and into the form of the Godunovtype system of the firstorder, 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 Godunovtype 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).
 Publication:

Continuum Mechanics and Thermodynamics
 Pub Date:
 November 2018
 DOI:
 10.1007/s0016101806212
 arXiv:
 arXiv:1710.00058
 Bibcode:
 2018CMT....30.1343P
 Keywords:

 Godunov;
 GENERIC;
 Hyperbolic;
 Hamiltonian;
 Continuum thermodynamics;
 Nonequilibrium thermodynamics;
 Physics  Classical Physics;
 Physics  Fluid Dynamics
 EPrint:
 doi:10.1007/s0016101806212