Refining the Eulerian flow model

TL;DR

This paper revisits the Eulerian flow model for compressible and diffusive flows, identifying a missing heat diffusion term, quantifying its impact, and demonstrating its significance in specific problems while confirming the model's robustness.

Contribution

It introduces a missing heat diffusive term into the Eulerian model and evaluates its effects across different flow scenarios.

Findings

The new diffusive term is significant in heat transfer problems.

The term has negligible impact on aerodynamic validation cases.

The updated model remains well-posed and compatible with previous theory.

Abstract

We revisit the molecular arguments underpinning the Eulerian model for compressible and diffusive flows, and conclude that a heat diffusive term appears to be missing in the original model. By studying a pure heat transfer problem, we quantify the new term in the updated Eulerian model and evaluate it in the context sound attenuation. Although the new diffusive term is important for certain problems, we also demonstrate that it has a negligible effect on the aerodynamic validation cases that the original model has already successfully passed. Furthermore, the updated Eulerian system is compatible with the weak well-posedness that has previously been established for the original Eulerian system.