Non-hyperbolicity of the inviscid Cattaneo-Christov system for compressible fluid flow in several space dimensions

TL;DR

This paper analyzes the inviscid Cattaneo-Christov system for compressible fluid flow, demonstrating that it is not hyperbolic due to the Lie-Oldroyd derivative, impacting the mathematical understanding of heat flux modeling.

Contribution

It proves the non-hyperbolicity of the inviscid Cattaneo-Christov system in multiple dimensions, revealing limitations in the mathematical structure of this heat flux model.

Findings

The system is not hyperbolic due to the Lie-Oldroyd derivative.

The analysis applies to both two and three space dimensions.

Implications for modeling heat flux in compressible fluids.

Abstract

We consider the coupling between the equations of motion of a compressible fluid in two and three space dimensions with Christov's equation for the heat flux. Christov's equation is a frame indifferent formulation of the classical model of Cattaneo that allows for the heat flux to be eliminated to obtain a single hyperbolic equation for the temperature. The obtained system is written in quasilinear form for the state variables density, velocity, temperature and heat flux. It is then shown that this system is not of hyperbolic type as consequence of the presence of the Lie-Oldroyd upper convected material derivative involved in Christov's formulation.