Refining the diffusive compressible Euler model

Abstract

We revisit the molecular arguments underpinning the diffusive compressible Euler model (proposed in Svärd (2018)), and conclude that a heat diffusive term is not accounted for in the energy equation of the original model. The new heat diffusive term complements the diffusion of the conserved variables already present in the model. By studying a diffusive and conductive heat transfer problem, we quantify the new term in the updated 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 system is compatible with the weak well-posedness that has previously been established for the original system.