Equations

The three-dimensional flow of water through the porous material between the cells is solved as a partial differential equation. Where K is the hydraulic conductivity [L/T] along the three axis, S the specific storage and W is the volumentric flux per unit volume in and out of the groundwater system. The hydraulic conductivity between two cells is calculated by using the harmonic mean. The equation is solved using a conjugate gradient approach and an Incomplete LUT preconditioner.

$\frac{\partial}{\partial&space;x}\left&space;(&space;K_{x}&space;\frac{\partial&space;h}{\partial&space;x}&space;\right&space;)&space;+&space;\frac{\partial}{\partial&space;y}\left&space;(&space;K_{y}&space;\frac{\partial&space;h}{\partial&space;y}&space;\right&space;)&space;+&space;\frac{\partial}{\partial&space;z}\left&space;(&space;K_{z}&space;\frac{\partial&space;h}{\partial&space;z}&space;\right&space;)&space;+&space;W&space;=&space;S_{s}&space;\frac{\partial&space;h}{\partial&space;t}$

Additional information on the equations can be found in the very detailed MODFLOW documentation: Modflow 2005

Boundary Conditions

G³M support multiple boundary condition types:

• No-flow boundary