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>