Nonlocal Heat Transport Due to Steep Temperature Gradients

By comparison with fully kinetic Fokker-Planck calculations, a nonlocal macroscopic formula has been derived for the thermal heat flux. This formula leads in a physically relevant way to the saturation and the delocalization of the heat flux. Its introduction in a fluid code is straightforward and gives to some extent results comparable with classical flux-limited transport calculations with $f=0.1$. However, it also describes a significant level of preheating.