## DESCRIPTION

This numerical module calculates transient, confined groundwater flow in three dimensions based on volume maps and the current 3D region resolution. All initial- and boundary-conditions must be provided as volume maps.

The module calculates the piezometric head and optionally the groundwater velocity field. The vector components can be visualized with ParaView if they are exported with r3.out.vtk.

The groundwater flow will always be calculated transient. For steady state computation the user should set the timestep to a large number (billions of seconds) or set the specific yield raster map to zero.

## NOTES

The groundwater flow calculation is based on Darcy's law and a finite volume discretization. The groundwater flow partial differential equation is of the following form:

(dh/dt)*S = Kxx * (d^2h/dx^2) + Kyy * (d^2h/dy^2) + Kzz * (d^2h/dz^2) + q

- h -- the piezometric head im meters [m]
- dt -- the time step for transient calculation in seconds [s]
- S -- the specific yield [1/m]
- b -- the bottom surface of the aquifer meters [m]
- Kxx -- the hydraulic conductivity tensor part in x direction in meter per second [m/s]
- Kyy -- the hydraulic conductivity tensor part in y direction in meter per seconds [m/s]
- Kzz -- the hydraulic conductivity tensor part in z direction in meter per seconds [m/s]
- q - inner source in [1/s]

Two different boundary conditions are implemented, the Dirichlet and Neumann conditions. By default the calculation area is surrounded by homogeneous Neumann boundary conditions. The calculation and boundary status of single cells can be set with the status map, the following cell states are supported:

- 0 == inactive - the cell with status 0 will not be calulated, active cells will have a no flow boundary to an inactive cell
- 1 == active - this cell is used for groundwater calculation, inner sources can be defined for those cells
- 2 == Dirichlet - cells of this type will have a fixed piezometric head value which do not change over time

The groundwater flow equation can be solved with several numerical solvers. Additionally a direct Gauss solver and a LU solver are available. Those direct solvers only work with quadratic matrices, so be careful using them with large maps (maps of size 10.000 cells will need more than one Gigabyte of RAM).

## EXAMPLE

This small script creates a working groundwater flow area and data. It cannot be run in a lat/lon location.

    # set the region accordingly
    g.region res=25 res3=25 t=100 b=0 n=1000 s=0 w=0 e=1000 -p

    #now create the input raster maps for a confined aquifer
    r3.mapcalc "phead = if(row() == 1 && depth() == 4, 50, 40)"
    r3.mapcalc "status = if(row() == 1 && depth() == 4, 2, 1)"
    r3.mapcalc "well = if(row() == 20 && col() == 20 , -0.00025, 0)"
    r3.mapcalc "hydcond = 0.00025"
    r3.mapcalc "syield = 0.0001"
    r.mapcalc  "recharge = 0.0"

    r3.gwflow -s solver=cg phead=phead status=status hc_x=hydcond hc_y=hydcond  \
    hc_z=hydcond q=well s=syield r=recharge output=gwresult dt=8640000 velocity=gwresult_velocity

    # The data can be visualized with ParaView when exported with r3.out.vtk
    r3.out.vtk -p in=gwresult,status vector=gwresult_velocity_x,gwresult_velocity_y,gwresult_velocity_z out=/tmp/gwdata3d.vtk

    #now load the data into ParaView
    paraview --data=/tmp/gwdata3d.vtk

## SEE ALSO

r.gwflow, r3.out.vtk

## AUTHOR

Sören Gebbert

This work is based on the Diploma Thesis of Sören Gebbert available here at Technical University Berlin, Germany.

Last changed: $Date: 2011-09-13 13:13:36 -0700 (Tue, 13 Sep 2011) $