DESCRIPTION

This module is sensitive to mask settings. All cells which are outside the mask are ignored and handled as no flow boundaries.

The module calculates the piezometric head and optionally the water balance for each cell and the groundwater velocity field in 3 dimensions. 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

(dh/dt)*S = div (K grad h) + q

In detail for 3 dimensions:

(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/sinc 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 calculated, 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

Note that all required raster maps are read into main memory. Additionally the linear equation system will be allocated, so the memory consumption of this module rapidely grow with the size of the input maps.

The resulting linear equation system Ax = b can be solved with several solvers. An iterative solvers with sparse and quadratic matrices support is implemented. The conjugate gradients method with (pcg) and without (cg) precondition. Additionally a direct Cholesky solver is available. This direct solver 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). The user should always prefer to use a sparse matrix solver.

EXAMPLE 1

# set the region accordingly
g.region res=25 res3=25 t=100 b=0 n=1000 s=0 w=0 e=1000 -p3

#now create the input raster maps for a confined aquifer
r3.mapcalc expression="phead = if(row() == 1 && depth() == 4, 50, 40)"
r3.mapcalc expression="status = if(row() == 1 && depth() == 4, 2, 1)"
r3.mapcalc expression="well = if(row() == 20 && col() == 20 && depth() == 2, -0.25, 0)"
r3.mapcalc expression="hydcond = 0.00025"
r3.mapcalc expression="syield = 0.0001"
r.mapcalc  expression="recharge = 0.0"

r3.gwflow solver=cg phead=phead statuyield=status hc_x=hydcond hc_y=hydcond  \
   hc_z=hydcond sink=well yield=syield r=recharge output=gwresult dt=8640000 vx=vx vy=vy vz=vz budget=budget

# The data can be visualized with ParaView when exported with r3.out.vtk
r3.out.vtk -p in=gwresult,status,budget vector=vx,vy,vz out=/tmp/gwdata3d.vtk

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

EXAMPLE 2

# set the region accordingly
g.region res=15 res3=15 t=500 b=0 n=1000 s=0 w=0 e=1000

#now create the input raster maps for a confined aquifer
r3.mapcalc expression="phead = if(col() == 1 && depth() == 33, 50, 40)"
r3.mapcalc expression="status = if(col() == 1 && depth() == 33, 2, 1)"
r3.mapcalc expression="well = if(row() == 20 && col() == 20 && depth() == 3, -0.25, 0)"
r3.mapcalc expression="well = if(row() == 50 && col() == 50 && depth() == 3, -0.25, well)"
r3.mapcalc expression="hydcond = 0.0025"
r3.mapcalc expression="hydcond = if(depth() < 30 && depth() > 23 && col() < 60, 0.000025, hydcond)"
r3.mapcalc expression="hydcond = if(depth() < 20 && depth() > 13 && col() >  7, 0.000025, hydcond)"
r3.mapcalc expression="hydcond = if(depth() < 10 && depth() >  7 && col() < 60, 0.000025, hydcond)"
r3.mapcalc expression="syield = 0.0001"

r3.gwflow solver=cg phead=phead statuyield=status hc_x=hydcond hc_y=hydcond  \
   hc_z=hydcond sink=well yield=syield output=gwresult dt=8640000 vx=vx vy=vy vz=vz budget=budget

# The data can be visualized with paraview when exported with r3.out.vtk
r3.out.vtk -p in=gwresult,status,budget,hydcond,well vector=vx,vy,vz out=/tmp/gwdata3d.vtk

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

SEE ALSO

AUTHOR

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

Last changed: $Date$