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NAME
r3.gwflow - Calculates numerically transient, confined groundwater flow in three
dimensions.
KEYWORDS
raster3d, voxel
SYNOPSIS
r3.gwflow
r3.gwflow help
r3.gwflow [-ms] phead=string status=string hc_x=string hc_y=string hc_z=string [q=string]
s=string [r=string] output=string [velocity=string] dt=float [maxit=integer]
[error=float] [solver=name] [relax=float] [--overwrite] [--verbose] [--quiet]
Flags:
-m
Use 3D raster mask (if exists) with input maps
-s
Use a sparse linear equation system, only available with iterative solvers
--overwrite
Allow output files to overwrite existing files
--verbose
Verbose module output
--quiet
Quiet module output
Parameters:
phead=string
Input 3D raster map with initial piezometric heads in [m]
status=string
The status for each cell, = 0 - inactive, 1 - active, 2 - dirichlet
hc_x=string
The x-part of the hydraulic conductivity tensor in [m/s]
hc_y=string
The y-part of the hydraulic conductivity tensor in [m/s]
hc_z=string
The z-part of the hydraulic conductivity tensor in [m/s]
q=string
Sources and sinks in [m^3/s]
s=string
Specific yield in 1/m
r=string
Recharge raster map in m^3/s
output=string
The piezometric head result of the numerical calculation will be written to this map
velocity=string
Calculate the groundwater distance velocity vector field
and write the x, y, and z components to maps named name_[xyz].Name is basename for the
new 3D raster maps.
dt=float
The calculation time in seconds
Default: 86400
maxit=integer
Maximum number of iteration used to solver the linear equation system
Default: 100000
error=float
Error break criteria for iterative solvers (jacobi, sor, cg or bicgstab)
Default: 0.0000000001
solver=name
The type of solver which should solve the symmetric linear equation system
Options: gauss,lu,cholesky,jacobi,sor,cg,bicgstab,pcg
Default: cg
relax=float
The relaxation parameter used by the jacobi and sor solver for speedup or stabilizing
Default: 1
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) $
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