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 22:13:36 +0200 (Tue, 13 Sep 2011) $
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