Here is the Comparison against Ramses:

DM Only Comparison:

Initially this was the power spectrum comparison:

Surprisingly RAMSES has ~30% more power then Cholla on small scales. For reference, Cholla has ~25% more power than Enzo on similar scales.

On the Ramses paper they say: Using the potential, the acceleration is computed on the mesh using the 5-points finite difference approximation of the gradient.

I changed the way the gravitational field is computed from the potential, originally I was using 3 point finite differences for the derivatives for the gradient :

\[\frac{\partial \phi_{i,j,k}}{\partial x} = \frac{1}{2 \Delta x} \left( \phi_{i+1,j,k} - \phi_{i-1,j,k} \right)\]

I changed for the 5 point finite differences:

\[\frac{\partial \phi_{i,j,k}}{\partial x} = \frac{1}{12 \Delta x} \left( -\phi_{i+2,j,k} + 8\phi_{i+1,j,k} - 8\phi_{i-1,j,k} + \phi_{i-2,j,k} \right)\]

Now the results are much better:

Differences are <~1%.

Hydro Comparison:

I still have the temperature issue in Ramses: