This page shows the mathematical forms of the auxiliary equation pieces that each boundary condition class represents. Note that \(u\) is used in some places to denote a generic variable. Elsewhere typical literature symbols are used, e.g. \(\phi\) denotes the neutron flux, \(T\) denotes the temperature, and \(C\) denotes precursor concentrations.

Moltres BCs

VacuumBC

\[\vec{n} \cdot -D_g \nabla \phi_g = \frac{\phi_g}{2}\]

Squirrel BCs

OutflowBC

\begin{align} \vec{n} \cdot \vec{\Gamma} &= \vec{n} \cdot \vec{a} u \ \ \mathsf{if} \ \ \vec{n} \cdot \vec{a} > 0\
&= 0 \ \ \mathsf{if} \ \ \vec{n} \cdot \vec{a} \le 0\
\end{align}

InflowBC

\[\vec{n} \cdot \vec{\Gamma} = \vec{n} \cdot \vec{a} u_{in}\]

TemperatureOutflowBC

\begin{align} \vec{n} \cdot \vec{\Gamma} &= \rho c_p \vec{n} \cdot \vec{a} T \ \ \mathsf{if} \ \ \vec{n} \cdot \vec{a} > 0\
&= 0 \ \ \mathsf{if} \ \ \vec{n} \cdot \vec{a} \le 0 \end{align}

TemperatureInflowBC

\[\vec{n} \cdot \vec{\Gamma} = \rho c_p \vec{n} \cdot \vec{a} T_{in}\]