The diffusive compressible Euler model in moving reference frames

TL;DR

This paper investigates the diffusive compressible Euler (dcE) model for viscous, heat-conducting fluids, revealing its non-symmetric stress tensor leads to frame-dependent dissipation, contrasting with classical models.

Contribution

It analyzes the consequences of the non-symmetric stress tensor in the dcE model, highlighting its lack of objectivity under moving reference frames.

Findings

The dcE model's stress tensor is non-symmetric.

The viscous dissipation in dcE is frame-dependent.

The model's quantities are not objective under Euclidean transformations.

Abstract

We continue to investigate the diffusive compressible Euler (dcE) model for viscous and heat conducting compressible fluid flow, which has been proposed by M. Sv\"ard as an alternative to the Navier-Stokes-Fourier (NSF) equations. The non-convective contribution to the momentum flux tensor in the dcE model is, with inverted sign, the analog of the viscous stress tensor in the NSF formulation. Unlike the latter quantity, the former tensor is non-symmetric, and here we examine some of the consequences of this property. In particular, we demonstrate that the dcE model's analog viscous stress tensor, and its resulting analog viscous dissipation term, are not objective -- that is to say, these quantities, under general time-dependent Euclidean transformations, feature moving reference frame dependence.