Now every row along the X axis has the exact same evolution and there are no cross fluxes. The issue was that originally for the $p \nabla \cdot \mathbf{v}$ term on the advected internal energy energy the value of $\nabla \cdot \mathbf{v}$ was computed on th same kernel were the conserved variables were updated, this means that there was a synchronization error because it was using values of the neighbors velocities to compute $\nabla \cdot \mathbf{v}$ and at the same time those velocities were being updated.

The solution was to add the $p \nabla \cdot \mathbf{v}$ term to the internal energy in a separate kernel before the Update_Conserved kernel.

## Zeldovich Pancake

Now every row has the same values ( all overlap in the same line ) but the density still drops in the boundaries of the shock.

## Cosmological Simulation

After fixing the bug, this are the results for the cosmological simulations using different values for $eta_2$:

### Projections

$/eta_2 = 0.030$

$/eta_2 = 0.035$

$/eta_2 = 0.040$

$/eta_2 = 0.045$

$/eta_2 = 0.050$

Difference