Hyperbolic systems of quasilinear equations in compressible fluid dynamics with an objective Cattaneo-type extension for the heat flux

TL;DR

This paper investigates the mathematical structure of coupled fluid dynamics and heat transfer equations, identifying conditions under which the system remains hyperbolic, ensuring well-posedness and physical plausibility.

Contribution

It introduces a formulation of the heat flux extension that preserves hyperbolicity in compressible fluid models with Cattaneo-type heat conduction.

Findings

Identifies conditions for hyperbolicity in the coupled system

Determines formulations compatible with well-posedness

Provides insights into heat flux modeling in fluid dynamics

Abstract

We consider the coupling between the equations of motion of an inviscid compressible fluid in space with an objective Cattaneo-type extension for the heat flux. These equations are written in quasilinear form and we determine which of the given formulations for the heat flux allows for the hyperbolicity of the system. This feature is necessary for a physically acceptable sense of well-posedness for the Cauchy problem of such system of equations.