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allow for a 2 temperature formulation for hydro

Open zingale opened this issue 6 months ago • 5 comments

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:

$$\frac{\partial (\rho e_h)}{\partial t} + \nabla \cdot (\rho U e_h) + p_h \nabla \cdot U = S$$

zingale avatar Dec 12 '23 19:12 zingale