Refining the Eulerian flow model

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.