# realGasEqn¶

Real gas using a real gas equation of state. Requires the computation of specific heat and temperature and assignment of zero point energy outside of the equation. Assumes single temperature. The equations are solved in conservative form.

\notag \begin{align} \frac{\partial}{\partial t}\left( \begin{array}{c} \rho \\ \rho\,u_{x} \\ \rho\,u_{y} \\ \rho\,u_{z} \\ e \\ \end{array} \right) + \nabla\cdot\left( \begin{array}{ccc} \rho\,u_{x} & \rho\,u_{y} & \rho\,u_{z} \\ \rho\,u_{x}^{2}+P & \rho\,u_{x}\,u_{y} & \rho\,u_{x}\,u_{z} \\ \rho\,u_{y}\,u_{x} & \rho\,u_{y}\,u_{y} + P & \rho\,u_{y}\,u_{z} \\ \rho\,u_{z}\,u_{x} & \rho\,u_{z}\,u_{y} & \rho\,u_{z}\,u_{z} + P \\ u_{x}\left(e+P\right) & u_{y}\left(e+P\right) & u_{z}\left(e+P\right)\\ \end{array} \right) = 0 \end{align}

The energy is given by

$\begin{equation} e=\frac{1}{2}\rho\left(u_{x}^{2}+u_{y}^{2}+u_{z}^{2}\right)+\sum_{i}n_{i}\left(Cv_{i}T+e_{0\,i}\right) \end{equation}$

## Parameters¶

numSpecies (float)
The number of species modeled in the real gas system.
basementPressure (float)
The minimum pressure allowed. Defaults to 0.
basementDensity (float)

The minimum density allowed. Defaults to 0.

Note

basementPressure and basementDensity are only used if correct=true

correct (boolean)

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). Defaults to false.

Note

Setting correctNans or correct to true can lead to energy conservation errors

## Parent Updater Data¶

in (string vector, required)
Vector of conserved quantities
1. $$\rho$$ mass density
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
2nd variable (3n+1)

3n+1 auxiliary variables with n the number of species

1. variables 0-(n-1). $$n_{i}$$ species number density
2. variables n-(2n-1). $$Cv_{i}$$ species specific heat at constant volume
3. variables n-(3n-1). $$e_{0\,i}$$ species zero point energy density
4. variables 3n. $$T$$ Temperature in Kelvin

## Example¶

An example realGas equation block is given below

<Equation realGas>
kind = realGasEqn
numSpecies = 7
</Equation>