A generic framework for the derivation of conservation terms with source terms through stationary action principle and irreversible thermodynamics.

Résumé de l'exposé

In this presentation, we will discuss the modelling of conservation laws with dissipative effects. Several strategies for the derivation of such models have recently been developed [1,2,3]. Here a generic framework is presented. It consists in two steps: first, the reversible part of the model is obtained through Stationary Action Principle and second, dissipation is added following irreversible thermodynamics. The methodology is applied to two cases: the derivation of a multi-fluid model including relative velocity and turbulent agitation and the derivation of a hyperbolic approximation of the Euler-Fourier model that has recently been proposed [3]. For the second case, we also propose a comparison of the model with kinetic theory.

[1] Lhuillier D., Internal variables and the non-equilibrium thermodynamics of colloidal suspensions. Journal of Non-Newtonian Fluid Mechanics, 2001

[2] Peshkov I., Pavelka M., Romenski E., Grmela M., Continuum Mechanics and Thermodynamics in the Hamilton and the Godunov-type Formulations. Continuum Mechanics and Thermodynamics. 2018

[3] Dhaouadi F., Garvilyuk S., An Eulerian hyperbolic model for heat transfer derived via Hamilton’s principle: analytical and numerical study. Proc. R. Soc. A. 2024

Ajouter l'événement à l'agenda (ics)