r3.gwflow(1grass) | GRASS GIS User's Manual | r3.gwflow(1grass) |
r3.gwflow - Numerical calculation program for transient, confined groundwater flow in three dimensions.
raster3d, groundwater flow, voxel, hydrology
r3.gwflow
r3.gwflow --help
r3.gwflow [-mf] phead=name
status=name hc_x=name hc_y=name
hc_z=name [sink=name] yield=name
[recharge=name] output=name
[velocity_x=name] [velocity_y=name]
[velocity_z=name] [budget=name]
dtime=float [maxit=integer]
[error=float] [solver=name] [--overwrite]
[--help] [--verbose] [--quiet] [--ui]
This numerical module 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.
The 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 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.
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 3 dimensions:
(dh/dt)*S = Kxx * (d^2h/dx^2) + Kyy * (d^2h/dy^2) + Kzz * (d^2h/dz^2) + q
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:
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. 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). The user should always prefer to use a sparse matrix solver.
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 -p3 #now create the input raster maps for a confined aquifer r3.mapcalc expression="phead = if(row() == 1 && depth() == 4, 50, 40)" r3.mapcalc expression="status = if(row() == 1 && depth() == 4, 2, 1)" r3.mapcalc expression="well = if(row() == 20 && col() == 20 && depth() == 2, -0.25, 0)" r3.mapcalc expression="hydcond = 0.00025" r3.mapcalc expression="syield = 0.0001" r.mapcalc expression="recharge = 0.0" r3.gwflow solver=cg phead=phead statuyield=status hc_x=hydcond hc_y=hydcond \
hc_z=hydcond sink=well yield=syield r=recharge output=gwresult dt=8640000 vx=vx vy=vy vz=vz budget=budget # The data can be visualized 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
This will create a nice 3D model with geological 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 expression="phead = if(col() == 1 && depth() == 33, 50, 40)" r3.mapcalc expression="status = if(col() == 1 && depth() == 33, 2, 1)" r3.mapcalc expression="well = if(row() == 20 && col() == 20 && depth() == 3, -0.25, 0)" r3.mapcalc expression="well = if(row() == 50 && col() == 50 && depth() == 3, -0.25, well)" r3.mapcalc expression="hydcond = 0.0025" r3.mapcalc expression="hydcond = if(depth() < 30 && depth() > 23 && col() < 60, 0.000025, hydcond)" r3.mapcalc expression="hydcond = if(depth() < 20 && depth() > 13 && col() > 7, 0.000025, hydcond)" r3.mapcalc expression="hydcond = if(depth() < 10 && depth() > 7 && col() < 60, 0.000025, hydcond)" r3.mapcalc expression="syield = 0.0001" r3.gwflow solver=cg phead=phead statuyield=status hc_x=hydcond hc_y=hydcond \
hc_z=hydcond sink=well yield=syield output=gwresult dt=8640000 vx=vx vy=vy vz=vz budget=budget # The data can be visualized 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
r.gwflow, r.solute.transport, r3.out.vtk
Sören Gebbert
This work is based on the Diploma Thesis of Sören Gebbert available here at Technical University Berlin, Germany.
Available at: r3.gwflow source code (history)
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