A variational principle for two-fluid models

TL;DR

This paper introduces a variational principle for two-fluid models, deriving equations of motion and conditions for shock waves, and proves that internal energy convexity ensures hyperbolicity of the linearized system.

Contribution

It presents a novel variational formulation for two-fluid mixtures, linking thermodynamics and dynamics, and establishes conditions for hyperbolicity based on internal energy convexity.

Findings

Derived equations of motion and Rankine-Hugoniot conditions

Proved hyperbolicity is guaranteed by internal energy convexity

Established a variational principle connecting thermodynamics and fluid dynamics

Abstract

A variational principle for two-fluid mixtures is proposed. The Lagrangian is constructed as the difference between the kinetic energy of the mixture and a thermodynamic potential conjugated to the internal energy with respect to the relative velocity of phases. The equations of motion and a set of Rankine-Hugoniot conditions are obtained. It is proved also that the convexity of the internal energy guarantees the hyperbolicity of the one-dimensional equations of motion linearized at rest.