r.gwflow(1grass) | GRASS GIS User's Manual | r.gwflow(1grass) |
r.gwflow - Numerical calculation program for transient, confined and unconfined groundwater flow in two dimensions.
raster, groundwater flow, hydrology
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]
This numerical program calculates implicit transient, confined and unconfined 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 budget 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 seconds) 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.
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 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
Confined and unconfined groundwater flow is supported. Be aware that the storativity input parameter is handled differently in case of unconfined flow. Instead of the storativity, the effective porosity is expected.
To compute unconfined groundwater flow, a simple Picard based linearization 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:
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 &
r.solute.transport, r3.gwflow, r.out.vtk
Sören Gebbert
This work is based on the Diploma Thesis of Sören Gebbert available here at Technical University Berlin in Germany.
Available at: r.gwflow source code (history)
Accessed: Sunday Jan 22 07:36:11 2023
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