Using the new Dual Energy Scheme From Teyssier 2015, for PPMC + HLLC + SIMPLE:

The Total Internal energy is used where $\Delta v \approx 0$ and the delay in the formation of the shock is still there.

Comparing to the Evolution when not Using Dual Energy:

Using The Gravitational Work to update the Total Energy and Teyssier scheme:

Using The both Dual Energy Conditions ( Enzo and Teyssier):