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
- \(\rho\) mass density
- \(\rho\,u_{x}\) x momentum density
- \(\rho\,u_{y}\) y momentum density
- \(\rho\,u_{z}\) z momentum density
- \(e\) energy density
2nd variable (3n+1)3n+1 auxiliary variables with n the number of species
- variables 0-(n-1). \(n_{i}\) species number density
- variables n-(2n-1). \(Cv_{i}\) species specific heat at constant volume
- variables n-(3n-1). \(e_{0\,i}\) species zero point energy density
- variables 3n. \(T\) Temperature in Kelvin
Example
An example realGas equation block is given below
<Equation realGas>
kind = realGasEqn
numSpecies = 7
</Equation>