Castro
Castro copied to clipboard
allow for a 2 temperature formulation for hydro
The WarpX folks want to have a separate temperature for electrons and ions (heavies), and a source term that represents the equilibriation via collisions. It seems like we can do this by tapping into the aux passives.
We will define the total energy always as:
$$\rho E = \rho e_e + \rho e_h + \frac{1}{2} |U|^2$$
and that is the conserved energy the is needed to get shocks correct. We still still have the Castro internal energy / dual energy formulation that will keep track of
$$\rho e = \rho e_e + \rho e_h$$
but now we will have an aux state of $\rho e_h$. This will satisfy via Castro
$$\frac{\partial (\rho e_h)}{\partial t} + \nabla \cdot (\rho U e_h) = S$$
where the $$S$$ part will rely on PR #2678 . I think there is additional work needed there to use the source in the interface state prediction.
But the energy should follow:
$$\frac{\partial (\rho e_h)}{\partial t} + \nabla \cdot (\rho U e_h) + p_h \nabla \cdot U = S$$