This is the new implementation of Dual Energy, following Bryan 2013:

The pressure is computed using the next condition:

\[p=\left\{\begin{array}{ll}{\rho(\gamma-1)\left(E-\mathbf{v}^{2} / 2\right),} & {\left(E-\mathbf{v}^{2} / 2\right) / E>\eta_{1}} \\ {\rho(\gamma-1) e,} & {\left(E-\mathbf{v}^{2} / 2\right) / E<\eta_{1}}\end{array}\right.\]

The Internal Energy is synchronized using only the next condition:

\[e=\left\{\begin{array}{ll}{\left(E-\mathbf{v}^{2} / 2\right),} & {\rho\left(E-\mathbf{v}^{2} / 2\right) / \max \left(\rho_{j-1} E_{j-1}, \rho_{j} E_{j}, \rho_{j+1} E_{j+1}\right)>\eta_{2}} \\ {e,} & {\rho\left(E-\mathbf{v}^{2} / 2\right) / \max \left(\rho_{j-1} E_{j-1}, \rho_{j} E_{j}, \rho_{j+1} E_{j+1}\right)<\eta_{2}}\end{array}\right.\]

Comparison: VL and SIMPLE Integrators

Both simulations are using the next Dual Energy parameters: \(\eta_1 = 0.001\) \(\eta_2=0.03\)

Row 1: SIMPLE Integrator

Row 2: VL Integrator

Let’s forget about VL integrator.

Changing \(\eta_2\):

Phase Diagram

Power Spectrum

Cell Difference

Here is the L1 Distance defined for a field \(x\) as:

\[D_{L1} = \frac{1}{N} \sum \frac{ | x_{i}^{cholla} - x_{i}^{enzo} | }{ x_{i}^{enzo} }\]

NOTE: The scale for each field is different.

Projections

Dual Energy parameters used for Cholla: \(\eta_1 = 0.001\) \(\eta_2=0.03\)

Now the projected distance is 25 Mpc/h and the difference ranges from [-1, 1].

Zeldovich Pancake Revised

Now only for \(\eta_2=0.03\)