An Eulerian hyperbolic model for heat transfer derived via Hamilton’s principle: analytical and numerical study

I present a new model for heat transfer in compressible fluid flows. The model is derived from Hamilton’s principle of stationary action in Eulerian coordinates, in a setting where the entropy conservation is recovered as an Euler–Lagrange equation. The governing system is shown to be hyperbolic under  natural physical assumptions. It is asymptotically consistent with the Euler equations for compressible heat conducting fluids and with  the Clausius–Duhem inequality. The last important property is usually failed for almost all relaxation models found in the litterature. 

This is a joint work with Firas Dhaouadi (Trento University, Italy).