# momentumEnergyExchange¶

Computes the momentum and energy exchange between multiple fluids due to ‘friction’. The momentum and energy exchange terms are given by the RHS of the euler equations below. Note that this does NOT include thermal relaxation as that is part of the temperatureRelaxation source.

The source for the continuity equation is zero, but added for convenience.

$$$\frac{\partial \rho_{i}}{\partial t}+\nabla\cdot\left[\rho_{i}U_{i}\right]=0$$$

The momentum term contains the species exchange term $$R_{i}$$

$$$\frac{\partial \rho_{i}U_{i}}{\partial t}+\nabla\cdot\left[\rho U_{i}U_{i}+P_{i}\right]=R_{i}$$$

And the energy term has a source due to changes in momentum $$V\cdot R_{i}$$

$$$\frac{\partial e_{i}}{\partial t}+\nabla\cdot\left[U_{i}\cdot\left(e_{i}+P_{i}\right)\right]=V\cdot R_{i}$$$

Where $$V$$ is the bulk velocity given by

$$$V=\frac{\sum_{i}\rho_{i}U_{i}}{\sum_{i}\rho_{i}}$$$

and the momentum exchange term as

$$$R_{i}=-\sum_{j}n_{i}\mu_{i\,j}\tau_{i\,j}^{-1}\left(U_{i}-U_{j}\right)$$$

Descriptions of this model can be found in

Zhdanov, Viktor Mikhailovich. “Transport processes in multicomponent plasma.” Plasma Physics and Controlled Fusion 44.10 (2002): 2283.

## Parameters¶

speciesMass (vector float)
The particle mass of each fluid species

## 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. $$e$$ total energy density, fluid and field

2nd 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. $$e$$ total energy density, fluid and field

Nth 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. $$e$$ total energy density, fluid and field

(N+1)th Variable

This variable is the collision frequency matrix that can be computed by the source collisionFrequency. The order of species should be the same as provided to collisionFrequency.
out (string vector, required)
There are N outputs each at least length 5 corresponding to the source terms for the 1st through Nth inputs. The first component (corresponding to mass density) is always 0 while the remaining 4 components have non-zero values.

## Example¶

<Equation thisGas>
kind = momentumEnergyExchange
speciesMass = [ELECTRON_MASS, ION_MASS, ION_MASS]
</Equation>