
NAME
r3.gwflow - Numerical calculation program for transient, confined groundwater flow in three dimensions
KEYWORDS
raster3d, voxel, groundwater, numeric, simulation
SYNOPSIS
r3.gwflow
r3.gwflow help
r3.gwflow [-mf] phead=name status=name hc_x=name hc_y=name hc_z=name [q=name] s=name [r=name] output=name [vx=name] [vy=name] [vz=name] [budget=name] dt=float [maxit=integer] [error=float] [solver=name] [--overwrite] [--verbose] [--quiet]
Flags:
- -m
- Use G3D mask (if exists)
- -f
- Use a full filled quadratic linear equation system, default is a sparse linear equation system.
- --overwrite
- Allow output files to overwrite existing files
- --verbose
- Verbose module output
- --quiet
- Quiet module output
Parameters:
- phead=name
- Input 3d-raster map with initial piezometric heads in [m]
- status=name
- Input 3d-raster map providing the status for each cell, = 0 - inactive, 1 - active, 2 - dirichlet
- hc_x=name
- Input 3d-raster map with the x-part of the hydraulic conductivity tensor in [m/s]
- hc_y=name
- Input 3d-raster map with the y-part of the hydraulic conductivity tensor in [m/s]
- hc_z=name
- Input 3d-raster map with the z-part of the hydraulic conductivity tensor in [m/s]
- q=name
- Input 3d-raster map with sources and sinks in [m^3/s]
- s=name
- Specific yield [1/m] input 3d-raster map
- r=name
- Recharge input 3d-raster map in m^3/s
- output=name
- Output 3d-raster map storing the piezometric head result of the numerical calculation
- vx=name
- Output 3d-raster map storing the groundwater filter velocity vector part in x direction [m/s]
- vy=name
- Output 3d-raster map storing the groundwater filter velocity vector part in y direction [m/s]
- vz=name
- Output 3d-raster map storing the groundwater filter velocity vector part in z direction [m/s]
- budget=name
- Output 3d-raster map Storing the groundwater budget for each cell [m^3/s]
- 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: cg,pcg,cholesky
- Default: cg
DESCRIPTION
This numerical program calculates implicit transient and steady state,
confined groundwater flow in three dimensions
based on volume maps and the current 3d region settings.
All initial- and boundary-conditions must be provided as volume maps.
The unit in the location must be meters.
This module is sensitive to mask settings. All cells which are outside the mask
are ignored and handled as no flow boundaries.
This 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 stady state computation 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 numerical implicit
finite volume discretization. The discretization results in a symmetric and positive definit
linear equation system in form of Ax = b, which must be solved. The groundwater flow partial
differential equation is of the following form:
(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 supportet:
- 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
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.
Aditionally 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).
Always prefer a sparse matrix solver.
EXAMPLE 1
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 a confined aquifer
r3.mapcalc --o expression="phead = if(row() == 1 && depth() == 4, 50, 40)"
r3.mapcalc --o expression="status = if(row() == 1 && depth() == 4, 2, 1)"
r3.mapcalc --o expression="well = if(row() == 20 && col() == 20 && depth() == 2, -0.25, 0)"
r3.mapcalc --o expression="hydcond = 0.00025"
r3.mapcalc --o expression="syield = 0.0001"
r.mapcalc --o expression="recharge = 0.0"
r3.gwflow --o 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 vx=vx vy=vy vz=vz budget=budget
# The data can be visulaized 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
This will create a nice 3d model with geolgical layer with different
hydraulic conductivities. Make sure you are not in a lat/lon projection.
# 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 --o expression="phead = if(col() == 1 && depth() == 33, 50, 40)"
r3.mapcalc --o expression="status = if(col() == 1 && depth() == 33, 2, 1)"
r3.mapcalc --o expression="well = if(row() == 20 && col() == 20 && depth() == 3, -0.25, 0)"
r3.mapcalc --o expression="well = if(row() == 50 && col() == 50 && depth() == 3, -0.25, well)"
r3.mapcalc --o expression="hydcond = 0.0025"
r3.mapcalc --o expression="hydcond = if(depth() < 30 && depth() > 23 && col() < 60, 0.000025, hydcond)"
r3.mapcalc --o expression="hydcond = if(depth() < 20 && depth() > 13 && col() > 7, 0.000025, hydcond)"
r3.mapcalc --o expression="hydcond = if(depth() < 10 && depth() > 7 && col() < 60, 0.000025, hydcond)"
r3.mapcalc --o expression="syield = 0.0001"
r3.gwflow --o solver=cg phead=phead status=status hc_x=hydcond hc_y=hydcond \
hc_z=hydcond q=well s=syield output=gwresult dt=8640000 vx=vx vy=vy vz=vz budget=budget
# The data can be visulaized 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
r.gwflow
r.solute.transport
r3.out.vtk
AUTHOR
Sören Gebbert
This work is based on the Diploma Thesis of Sören Gebbert available
here
at Technical University Berlin in Germany.
Last changed: $Date: 2010-01-23 05:49:09 -0800 (Sat, 23 Jan 2010) $
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