# tenMomentEqn¶

Ideal compressible 10 moment fluid equations. 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} \\ \rho\,u_{x}^{2}+P_{x\,x} \\ \rho\,u_{x}\,u_{y}+P_{x\,y}\\ \rho\,u_{x}\,u_{z}+P_{x\,z}\\ \rho\,u_{y}^{2}+P_{y\,y}\\ \rho\,u_{y}\,u_{z}+P_{y\,z}\\ \rho\,u_{z}^{2}+P_{z\,z}\\ \end{array} \right) + \nabla\cdot\ P = 0 \end{align}

where $$P$$ is defined as

$\begin{split}\begin{pmatrix} \rho\,u_{x} & \rho\,u_{y} & \rho\,u_{z} \\ \rho\,u_{x}^{2}+P_{x\,x} & \rho\,u_{x}\,u_{y}+P_{x\,y} & \rho\,u_{x}\,u_{z}+P_{x\,z} \\ \rho\,u_{y}\,u_{x} +P_{x\,y}& \rho\,u_{y}\,u_{y} + P_{y\,y} & \rho\,u_{y}\,u_{z}+P_{y\,z} \\ \rho\,u_{z}\,u_{x} +P_{x\,z}& \rho\,u_{z}\,u_{y} +P_{y\,z}& \rho\,u_{z}\,u_{z} + P_{z\,z} \\ \rho\,u_{x}^{3}+3u_{x}P_{x\,x} & \rho\,u_{y}u_{x}^{2}+u_{x}P_{y\,y}+2u_{x}P_{x\,y} & \rho\,u_{z}u_{x}^{2}+u_{z}P_{x\,x}+2u_{x}P_{x\,z}\\ \rho\,u_{x}^{2}u_{y}+2\,u_{x}\,P_{x\,y}+u_{y}P_{x\,x} & 0 & 0 \\ \rho\,u_{x}^{2}u_{z}+2\,u_{x}\,P_{x\,z}+u_{z}P_{x\,x} & 0 & 0\\ \rho\,u_{x}u_{y}^{2}+u_{x}P_{y\,y}+2u_{y}P_{x\,y} & \rho\,u_{y}^{3}+3u_{y}P_{y\,y} & 0\\ \rho\,u_{x}u_{y}u_{z}+u_{x}P_{y\,z}+u_{y}P_{x\,z}+u_{z}P_{x\,y} & 0 & 0 \\ \rho\,u_{x}u_{z}^{2}+u_{x}P_{z\,z}+2u_{z}P_{x\,z} & 0 & \rho\,u_{z}^{3}+3u_{z}P_{z\,z}\\ \end{pmatrix}\end{split}$

## Parameters¶

basementPressure (float)
The minimum pressure allowed. Defaults to 0.
basementDensity (float)
The minimum density allowed. Defaults to 0.

## Parent Updater Data¶

in (string vector, required)
1st variable
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. $$\rho\,u_{x}^{2}+P_{x\,x}$$ xx energy density
6. $$\rho\,u_{x}\,u_{y}+P_{x\,y}$$ xy energy density
7. $$\rho\,u_{x}\,u_{z}+P_{x\,z}$$ xz energy density
8. $$\rho\,u_{y}^{2}+P_{y\,y}$$ yy energy density
9. $$\rho\,u_{y}\,u_{z}+P_{y\,z}$$ yz energy density
10. $$\rho\,u_{z}^{2}+P_{z\,z}$$ zz energy density

## Example¶

An example tenMoment equation block is given below:

<Equation tenMoment>
kind = tenMomentEqn
</Equation>