eulerTwoTemp

Defines the equations of inviscid compressible hydrodynamics with separate electron and heavy particle energies:

\[\notag \begin{align} \frac{\partial \rho}{\partial t} + \nabla\cdot\left[ \rho\,\mathbf{u} \right] = 0 \\ \frac{\partial \rho\,\mathbf{u}}{\partial t} + \nabla\cdot\left[ \rho\,\mathbf{u}\,\mathbf{u}^{T} + \mathbb{I} P \right] = 0 \\ \frac{\partial E}{\partial t} + \nabla\cdot\left[ \left(E + P \right) \mathbf{u} \right] = 0 \\ \frac{\partial E_\mathrm{electron}}{\partial t} + \nabla\cdot\left[ \left(E_\mathrm{electron} + P_\mathrm{electron} \right) \mathbf{u} \right] = 0 \end{align}\]

Here, \(\mathbb{I}\) is the identity matrix, \(P\) is the total (heavy particle and electron) gas pressure and \(P_\mathrm{electron}\) is the electron pressure.

Primary Variables (6)

  1. \(\rho_{l}\) mass density of a species “l”
  2. \(\rho\,u_{x}\) x momentum density
  3. \(\rho\,u_{y}\) y momentum density
  4. \(\rho\,u_{z}\) z momentum density
  5. \(e\) energy density
  6. \(e_{e}\) electron energy density

Auxiliary Variables (4)

1st auxiliary variable is the total pressure

  1. \(P\) total mass density

2nd auxiliary variable the electron pressure

  1. \(P_{e}\) electron pressure

3rd auxiliary variable is an estimate of the sound speed

  1. \(c_{s}\) fluid sound speed

Parameters

basementPressure (float) [0.0]

The minimum pressure allowed

basementDensity (float) [0.0]

The minimum density allowed

Note

basementPressure and basementDensity are only used if correct=true

correct (boolean) [true]

Tells whether or not densities or pressures should be corrected when the fall below basement pressures or basement densities. When set to true pressure=max(basementPressure, pressure) and density = max(basementDensity, density)

Example

An example eulerTwoTemp equation block is given below::

equations = [euler]
<Equation euler>
  kind = eulerTwoTemp
  correct = false
</Equation>