## NAME

r.gwflow

## DESCRIPTION

This numerical program calculates transient, confined and unconfined groundwater flow in two dimensions based on raster maps and the current region resolution. All initial and boundary conditions must be provided as raster maps.

Workflow of r.gwflow

r.gwflow calculates the piezometric head and optionally the filter velocity field, based on the hydraulic conductivity and the piezometric head. The vector components can be visualized with paraview if they are exported with r.out.vtk.
The groundwater flow will always be calculated transient. If you want to calculate stady state, set the timestep to a large number (billions of seconds) or set the specific yield/ effective porosity raster maps to zero.

## NOTES

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

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

- h -- the piezometric head im [m]
- dt -- the time step for transient calculation in [s]
- S -- the specific yield [1/m]
- Kxx -- the hydraulic conductivity tensor part in x direction in [m/s]
- Kyy -- the hydraulic conductivity tensor part in y direction in [m/s]
- q - inner source in meter per second [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 must be set with a status map, the following states are supportet:

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

The groundwater flow equation can be solved with several solvers. Two iterative solvers with sparse and quadratic matrices support are implemented. The conjugate gradients (cg) method and the biconjugate gradients-stabilized (bicgstab) method. Aditionally a direct Gauss solver and LU solver are available. Those direct solvers only work with normal quadratic matrices, so be careful using them with large maps (maps of size 10.000 cells will need more than one gigabyte of RAM). Always prefer a sparse matrix solver.

## EXAMPLE

Use this small script to create a working groundwater flow area and data. Make sure you are not in a lat/lon projection.

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

    #now create the input raster maps for confined and unconfined aquifers
    r.mapcalc "phead=if(row() == 1 , 50, 40)"
    r.mapcalc "status=if(row() == 1 , 2, 1)"
    r.mapcalc "well=if(row() == 20 && col() == 20 , -0.001, 0)"
    r.mapcalc "hydcond=0.00025"
    r.mapcalc "recharge=0"
    r.mapcalc "top_conf=20.0"
    r.mapcalc "top_unconf=70.0"
    r.mapcalc "bottom=0.0"
    r.mapcalc "null=0.0"
    r.mapcalc "poros=0.15"
    r.mapcalc "syield=0.0001"

    #confined groundwater flow with cg solver and sparse matrix
    r.gwflow --o -s solver=cg top=top_conf bottom=bottom phead=phead status=status \
    hc_x=hydcond hc_y=hydcond q=well s=syield r=recharge output=gwresult_conf \
    dt=8640000 type=confined velocity=gwresult_conf_velocity

    #unconfined groundwater flow with cg solver and sparse matrix
    r.gwflow --o -s solver=cg top=top_unconf bottom=bottom phead=phead \
    status=status hc_x=hydcond hc_y=hydcond q=well s=poros r=recharge \
    output=gwresult_unconf dt=8640000 type=unconfined velocity=gwresult_unconf_velocity

    # The data can be visulaized with paraview when exported with r.out.vtk
    r.out.vtk -p in=gwresult_conf,status vector=gwresult_conf_velocity_x,gwresult_conf_velocity_y,null out=/tmp/gwdata_conf2d.vtk
    r.out.vtk -p elevation=gwresult_unconf in=gwresult_unconf,status vector=gwresult_unconf_velocity_x,gwresult_unconf_velocity_y,null out=/tmp/gwdata_unconf2d.vtk

    #now load the data into paraview
    paraview --data=/tmp/gwdata_conf2d.vtk &
    paraview --data=/tmp/gwdata_unconf2d.vtk &

## SEE ALSO

r3.gwflow
r.out.vtk

## AUTHOR

Soeren Gebbert

Last changed: $Date: 2008-05-16 21:09:06 +0200 (Fri, 16 May 2008) $

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