# multiSpeciesSingleVelocityEqn¶

This equation represents continuity equations for n species. The species continuity equation is given by

$\begin{equation} \frac{\partial n_{i}}{\partial t}+\nabla_{j}\left(n_{i}\,u_{j}\right)=0 \end{equation}$

## Parameters¶

basementNumberDensity (float)
The minimum species number density allowed
basementDensity (float)
The minimum auxiliary variable mass density allowed. Defaults to 0.
numberOfSpecies (integer)
The number of species that have continuity equations.
useParentEigenvalues (boolean)
When set to true the eigenvalues of the parent system are used in computing dissipation in fluxes such as the localLaxFlux as well as time step restrictions. When set to false, the eigenvalue is simply $$u$$ normal to the direction of interest.

## Sub-Blocks¶

Equation (block)
Defines the parent equation type of the system. The parent equation could be eulerEqn or idealMhdEqn for example. The first 4 components must be density, followed by the 3 components of momentum. This equation is used to compute the advection velocity and if useParentEigenvalues=true then the eigenvalues of this system are used to compute the level of dissipation in the flux functions.

## Parent Updater Data¶

in (string vector, required)
Species densities

Entries 1-$$N$$ where $$N$$ is the number of species

1. variables 0-(N-1) $$n_{i}$$ number density of species i
Vector of conserved quantities

Entries are determined by the Equation sub-block and only the first 4 entries are used in this equation. Entries 1-$$N$$ where $$N$$ the number variables in the parent equation

1. $$\rho$$ species density
2. $$\rho\,u_{x}$$ species x momentum
3. $$\rho\,u_{y}$$ species y momentum
4. $$\rho\,u_{z}$$ species z momentum
5. all components beyond 3 are ignored.

## Example¶

An example multiSpeciesSingleVelocity equation block is given below

<Equation speciesContinuity>
kind = multiSpeciesSingleVelocityEqn
useParentEigenvalues = true
inputVariables = [qSpecies, q]
numberOfSpecies = NSPECIES

<Equation realGas>
kind = realGasEqn
inputVariables = [q, realGasVariables]
numSpecies = NSPECIES
</Equation>

</Equation>