# tenMomentFluidSrc¶

Computes the “lorentz force” for a 10 moment fluid given, particle mass, charge and permittivity.

\notag \begin{align} s=\left( \begin{array}{c} 0 \\ r\,\rho\left(E_{x}+u_{y}B_{z}-u_{z}B_{y}\right)\\ r\,\rho\left(E_{y}+u_{z}B_{x}-u_{x}B_{z}\right)\\ r\,\rho\left(E_{z}+u_{x}B_{y}-u_{y}B_{x}\right)\\ 2\,r\,\rho\,u_{x}E_{x}+2r\left(B_{z}\mathbf{P_{x\,y}}-B_{y}\mathbf{P_{x\,z}}\right)\\ r\,\rho\left(u_{x}E_{y}+u_{y}E_{x}\right)+r\left(B_{z}\mathbf{P_{y\,y}}+B_{y}\mathbf{P_{y\,z}}-B_{z}\mathbf{P_{x\,x}}+B_{x}\mathbf{P_{x\,z}}\right)\\ r\,\rho\left(u_{x}E_{z}+u_{z}E_{x}\right)+r\left(B_{z}\mathbf{P_{y\,z}}+B_{y}\mathbf{P_{x\,x}}-B_{y}\mathbf{P_{x\,x}}-B_{x}\mathbf{P_{y\,y}}\right)\\ 2r\,\rho\,u_{y}E_{y}+2r\left(B_{x}\mathbf{P_{y\,z}}-B_{z}\mathbf{P_{x\,y}}\right)\\ r\,\rho\left(u_{y}E_{z}+u_{z}E_{y}\right)+r\left(B_{y}\mathbf{P_{x\,y}}-B_{z}\mathbf{P_{x\,z}}+B_{x}\mathbf{P_{z\,z}}-B_{x}\mathbf{P_{y\,y}}\right)\\ 2r\,\rho\,u_{z}E_{z}+2r\left(B_{y}\mathbf{P_{x\,z}}-B_{x}\mathbf{P_{y\,z}}\right)\\ \end{array} \right) \end{align}

where $$q$$ is the species charge, $$m$$ is the species mass $$\epsilon_{0}$$ is the permittivity, $$\rho$$ is the fluid mass density, $$u_{x}$$ is the fluid x velocity, $$u_{y}$$ is the fluid y velocity, $$u_{z}$$ is the fluid z velocity, $$E_{x}$$ is the x electric field, $$E_{y}$$ is the y electric field, $$E_{z}$$ is the z electric field, $$B_{x}$$ is the x magnetic field, $$B_{y}$$ is the y magnetic field and $$B_{z}$$ is the z magnetic field. $$\mathbf{P_{i\,j}}=P_{i\,j}+\rho\,u_{i}u_{j}$$ with $$P_{i\,j}$$ the pressure tensor and $$\rho$$ the mass density and $$r=q/m$$ the charge to mass ratio.

## Parameters¶

mass (float)
The mass of the fluid species
charge (float)
The charge of the fluid species
type (string, default=unsplit)
One of either split or unsplit

## Data¶

inputVariables (string vector)

1st Variable (nodalArray)

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

2nd Variable (nodaArray)

1. $$E_{x}$$ x electric field
2. $$E_{y}$$ y electric field
3. $$E_{z}$$ z electric field
4. $$B_{x}$$ x magnetic field
5. $$B_{y}$$ y magnetic field
6. $$B_{z}$$ z magnetic field

## Parent Updater Data¶

in (string vector, required)

The nodalArrays should match the inputVariables in the source block.

1st Variable (nodalArray)

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

2nd Variable (nodaArray)

1. $$E_{x}$$ x electric field
2. $$E_{y}$$ y electric field
3. $$E_{z}$$ z electric field
4. $$B_{x}$$ x magnetic field
5. $$B_{y}$$ y magnetic field
6. $$B_{z}$$ z magnetic field
out (string vector, required)
The output nodalArray is a length 10 vector, but the first component is 0 so that it works simply as a fluid source for the ten moment equations.

## Example¶

<Updater hyperIons>
kind = classicMuscl2d
onGrid = domain
timeIntegrationScheme = none
numericalFlux = hlleFlux
preservePositivity = true
limiter = [mc,none]

variableForm = conservative

in = [ions, em]
out = [ionsNew]

cfl = CFL
equations = [euler]
sources = [lorentz]

<Equation euler>
kind = tenMomentEqn
basementDensity = BASEMENT_DENSITY
basementPressure = BASEMENT_PRESSURE
</Equation>

<Source lorentz>
kind = tenMomentFluidSrc
type = split
inputVariables = [ions, em]
mass = ION_MASS
charge = ION_CHARGE
</Source>

</Updater>