The governing equations of stationary groundwater flow are 
(also called Darcy's law) and
where is the discharge velocity, is the permeability tensor and is the total head defined by
In the latter equation is the groundwater pressure, is its density and is the height with respect to a reference level. The discharge velocity is the quantity of fluid that flows through a unit of total area of the porous medium in a unit of time.
The resulting equation now reads
Accordingly, by comparison with the heat equation, the correspondence in Table (15) arises. Notice that the groundwater flow equation is a steady state equation, and there is no equivalent to the heat capacity term.
Possible boundary conditions are:
In the direction perpendicular to the free surface must be satisfied. However, the problem is that the exact location of the free surface is not known. It has to be determined iteratively until both equations are satisfied.