Now the Advected Internal Energy $ge_{advected}$ is set equal to the internal energy computed from the total energy $ge_{total}$ when $ge_{total}$ is used to compute the pressure.

Column 1: ENZO

Column 2: Phase diagram for All Gas ( top ) and Neutral Hydrogen ( bottom ). Temperature is internally computed by Grackle on run time.

Column 3: Phase diagram for the fraction of the gas that uses the Total Internal Energy to compute pressure.

Column 4: Phase diagram for the fraction of the gas that uses the Adavected Internal Energy to compute pressure.

Column 5: Phase diagram showing the temperature computed from the Total Internal Energy for ALL the gas.

Column 6: Phase diagram showing the temperature computed from the Advected Internal Energy for ALL the gas.

First 2 rows: CHOLLA computing pressure from total internal energy or advacted internal enegy using $\eta_1=0.001$ and $\eta_2 =0.1$ ( same as Bryan 2014 )

Last 2 rows: CHOLLA computing pressure from total internal energy or advacted internal enegy using $\eta_1=0.02$ and $\eta_2 =0.1$

Here is the phase diagram for $\eta_1=0.001$ without syncing the advacted internal energy with the total internal energy, only the cooling step updates the advected internal energy

Same as the previous diagrams but using the change in Kinetic Energy as the gravitational term on the Total Energy