Comparison of the symmetric hyperbolic thermodynamically compatible framework with Hamiltonian mechanics of binary mixtures

Comparison of the symmetric hyperbolic thermodynamically compatible framework with Hamiltonian mechanics of binary mixtures Full article

Journal

Continuum Mechanics and Thermodynamics
ISSN: 0935-1175 , E-ISSN: 1432-0959

Output data

Year: 2024, Volume: 36, Pages: 539–559 Pages count : 21 DOI: 10.1007/s00161-024-01281-9

Tags

Theory of mixtures · Hamiltonian mechanics · Symmetric hyperbolicity · Non-equilibrium thermodynamics · Reduction methods

Authors

Sýkora Martin ¹ , Pavelka Michal ¹ , Peshkov Ilya ² , Minakowski Piotr ³ , Klika Václav ⁴ , Romenski Evgeniy ⁵

Affiliations

1	Mathematical Institute, Faculty of Mathematics and Physics, Charles University
2	Department of Civil, Environmental and Mechanical Engineering, University of Trento
3	Institute of Analysis and Numerics, Otto-von-Guericke University Magdeburg
4	Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague
5	Sobolev Institute of Mathematics

Funding (1)

Министерство науки и высшего образования РФ
Mathematical Center in Akademgorodok

075-15-2019-1613, 075-15-2022-281

How to properly describe continuum thermodynamics of binary mixtures where each constituent has its own momentum? The Symmetric Hyperbolic Thermodynamically Consistent (SHTC) framework and Hamiltonian mechanics in the form of the General Equation for Non-Equilibrium Reversible-Irreversible Coupling (GENERIC) provide two answers, which are similar but not identical, and are compared in this article. They are compared both analytically and numerically on several levels of description, varying in the amount of detail. Namely, a reduction to a more common one-momentum setting is shown, where the effects of the second momentum translate into diffusive fluxes. Both SHTC and GENERIC can thus be interpreted as a method specifying diffusive flux in standard theory. The GENERIC equations, stemming from the Liouville equation, contain terms expressing self-advection of the relative velocity by itself, which lead to a vorticitydependent diffusion matrix after the reduction. The SHTC equations, on the other hand, do not contain such terms. We also discuss the possibility to formulate a theory of mixtures with two momenta and only one temperature that is compatible with the Liouville equation and possesses the Hamiltonian structure, including Jacobi identity.

Sýkora M. , Pavelka M. , Peshkov I. , Minakowski P. , Klika V. , Romenski E.
Comparison of the symmetric hyperbolic thermodynamically compatible framework with Hamiltonian mechanics of binary mixtures
Continuum Mechanics and Thermodynamics. 2024. V.36. P.539–559. DOI: 10.1007/s00161-024-01281-9 WOS Scopus РИНЦ OpenAlex

Submitted:	Jul 1, 2023
Accepted:	Jan 4, 2024
Published online:	Feb 21, 2024
Published print:	May 2, 2024

Web of science:	WOS:001168931900001
Scopus:	2-s2.0-85185271899
Elibrary:	66090716
OpenAlex:	W4392002098

DB	Citing
Web of science	1
OpenAlex	1
Scopus	1