r.gwflow(1grass) GRASS GIS User's Manual r.gwflow(1grass)
NAME
r.gwflow - Numerical calculation program for transient, confined and
unconfined groundwater flow in two dimensions.
KEYWORDS
raster, groundwater flow, hydrology
SYNOPSIS
r.gwflow
r.gwflow --help
r.gwflow [-f] phead=name status=name hc_x=name hc_y=name [q=name]
s=name [recharge=name] top=name bottom=name output=name [vx=name]
[vy=name] [budget=name] type=string [river_bed=name]
[river_head=name] [river_leak=name] [drain_bed=name]
[drain_leak=name] dtime=float [maxit=integer] [maxit=integer]
[error=float] [solver=name] [--overwrite] [--help] [--verbose]
[--quiet] [--ui]
Flags:
-f
Allocate a full quadratic linear equation system, default is a
sparse linear equation system.
--overwrite
Allow output files to overwrite existing files
--help
Print usage summary
--verbose
Verbose module output
--quiet
Quiet module output
--ui
Force launching GUI dialog
Parameters:
phead=name [required]
Name of input raster map with initial piezometric head in [m]
status=name [required]
Name of input raster map providing boundary condition status: 0-in-
active, 1-active, 2-dirichlet
hc_x=name [required]
Name of input raster map with x-part of the hydraulic conductivity
tensor in [m/s]
hc_y=name [required]
Name of input raster map with y-part of the hydraulic conductivity
tensor in [m/s]
q=name
Name of input raster map with water sources and sinks in [m^3/s]
s=name [required]
Name of input raster map with storativity for confined or effective
porosity for unconfined groundwater flow booth in [-]
recharge=name
Recharge input raster map e.g: 6*10^-9 per cell in [m^3/s*m^2]
top=name [required]
Name of input raster map describing the top surface of the aquifer
in [m]
bottom=name [required]
Name of input raster map describing the bottom surface of the
aquifer in [m]
output=name [required]
Output raster map storing the numerical result [m]
vx=name
Output raster map to store the groundwater filter velocity vector
part in x direction [m/s]
vy=name
Output raster map to store the groundwater filter velocity vector
part in y direction [m/s]
budget=name
Output raster map to store the groundwater budget for each cell
[m^3/s]
type=string [required]
The type of groundwater flow
Options: confined, unconfined
Default: confined
river_bed=name
Name of input raster map providing the height of the river bed in
[m]
river_head=name
Name of input raster map providing the water level (head) of the
river with leakage connection in [m]
river_leak=name
Name of input raster map providing the leakage coefficient of the
river bed in [1/s].
drain_bed=name
Name of input raster map providing the height of the drainage bed
in [m]
drain_leak=name
Name of input raster map providing the leakage coefficient of the
drainage bed in [1/s]
dtime=float [required]
The calculation time in seconds
Default: 86400
maxit=integer
Maximum number of iteration used to solve the linear equation sys-
tem
Default: 10000
maxit=integer
The maximum number of iterations in the linearization approach
Default: 25
error=float
Error break criteria for iterative solver
Default: 0.000001
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, confined and un-
confined groundwater flow in two dimensions based on raster maps and
the current region settings. All initial and boundary conditions must
be provided as raster 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.
Workflow of r.gwflow
r.gwflow calculates the piezometric head and optionally the water bud-
get and 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. For stady
state computation set the timestep to a large number (billions of sec-
onds) or set the storativity/ effective porosity raster map to zero.
The water budget is calculated for each non inactive cell. The sum of
the budget for each non inactive cell must be near zero. This is an
indicator of the quality of the numerical result.
NOTES
The groundwater flow calculation is based on Darcy’s law and a numeri-
cal implicit finite volume discretization. The discretization results
in a symmetric and positive definite 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 2 dimensions:
(dh/dt)*S = 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 storage [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/sink in meter per second [1/s]
Confined and unconfined groundwater flow is supported. Be aware that
the storativity input parameter is handled differently in case of un-
confined flow. Instead of the storativity, the effective porosity is
expected.
To compute unconfined groundwater flow, a simple Picard based lin-
earization scheme is used to solve the resulting non-linear equation
system.
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 calcula-
tion, inner sources and recharge can be defined for those cells
• 2 == Dirichlet - cells of this type will have a fixed piezomet-
ric head value which do not change over the time
Note that all required raster maps are read into main memory. Addition-
ally the linear equation system will be allocated, so the memory con-
sumption 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 sup-
port 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). Always prefer a sparse ma-
trix 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. It includes
drainage and river input as well.
# 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 confined and unconfined aquifers
r.mapcalc expression="phead = if(row() == 1 , 50, 40)"
r.mapcalc expression="status = if(row() == 1 , 2, 1)"
r.mapcalc expression="well = if(row() == 20 && col() == 20 , -0.01, 0)"
r.mapcalc expression="hydcond = 0.00025"
r.mapcalc expression="recharge = 0"
r.mapcalc expression="top_conf = 20.0"
r.mapcalc expression="top_unconf = 70.0"
r.mapcalc expression="bottom = 0.0"
r.mapcalc expression="null = 0.0"
r.mapcalc expression="poros = 0.15"
r.mapcalc expression="s = 0.0001"
# The maps of the river
r.mapcalc expression="river_bed = if(col() == 35 , 48, null())"
r.mapcalc expression="river_head = if(col() == 35 , 49, null())"
r.mapcalc expression="river_leak = if(col() == 35 , 0.0001, null())"
# The maps of the drainage
r.mapcalc expression="drain_bed = if(col() == 5 , 48, null())"
r.mapcalc expression="drain_leak = if(col() == 5 , 0.01, null())"
#confined groundwater flow with cg solver and sparse matrix, river and drain
#do not work with this confined aquifer (top == 20m)
r.gwflow solver=cg top=top_conf bottom=bottom phead=phead status=status \
hc_x=hydcond hc_y=hydcond q=well s=s recharge=recharge output=gwresult_conf \
dt=8640000 type=confined vx=gwresult_conf_velocity_x vy=gwresult_conf_velocity_y budget=budget_conf
#unconfined groundwater flow with cg solver and sparse matrix, river and drain are enabled
# We use the effective porosity as storativity parameter
r.gwflow solver=cg top=top_unconf bottom=bottom phead=phead \
status=status hc_x=hydcond hc_y=hydcond q=well s=poros recharge=recharge \
river_bed=river_bed river_head=river_head river_leak=river_leak \
drain_bed=drain_bed drain_leak=drain_leak \
output=gwresult_unconf dt=8640000 type=unconfined vx=gwresult_unconf_velocity_x \
budget=budget_unconf vy=gwresult_unconf_velocity_y
# 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
r.solute.transport, r3.gwflow, r.out.vtk
AUTHOR
Sören Gebbert
This work is based on the Diploma Thesis of Sören Gebbert available
here at Technical University Berlin in Germany.
SOURCE CODE
Available at: r.gwflow source code (history)
Accessed: unknown
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