Rasmus Vest Nielsen

Governing Flow Equations

The groundwater flow equations are a combination of the continuity equation and Darcy's law.
A model node with its surrounding connected neighbors.
A model node with its surrounding connected neighbors.

Continuity Equation

The continuity equation states that the transport of mass in a inifitesimal volume must be conserved, see \eqref{ref1}. E.g. what goes in must go out or accumulate within the CV. \begin{equation} \frac{\delta M}{\delta t} = m_{in} - m_{out}\label{ref1} \end{equation} If you choose a positive direction for the cartesian coordinate system in $x$, $y$, and $z$, $m_{in}$ and $m_{out}$ can be defined as equation \eqref{ref2}: \begin{equation} m^* = \rho Q \label{ref2} \end{equation}

Darcy's Law