r3.gwflowgrass - Online in the Cloud

PROGRAM:

NAME

r3.gwflow - Numerical calculation program for transient, confined groundwater flow in
three dimensions.

KEYWORDS

raster3d, groundwater flow, voxel, hydrology

SYNOPSIS

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]

Flags:
-m
Use 3D raster 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

--help
Print usage summary

--verbose
Verbose module output

--quiet
Quiet module output

--ui
Force launching GUI dialog

Parameters:
phead=name [required]
Input 3D raster map with initial piezometric heads in [m]

status=name [required]
Input 3D raster map providing the status for each cell, = 0 - inactive, 1 - active, 2
- dirichlet

hc_x=name [required]
Input 3D raster map with the x-part of the hydraulic conductivity tensor in [m/s]

hc_y=name [required]
Input 3D raster map with the y-part of the hydraulic conductivity tensor in [m/s]

hc_z=name [required]
Input 3D raster map with the z-part of the hydraulic conductivity tensor in [m/s]

sink=name
Input 3D raster map with sources and sinks in [m^3/s]

yield=name [required]
Specific yield [1/m] input 3D raster map

recharge=name
Recharge input 3D raster map in m^3/s

output=name [required]
Output 3D raster map storing the piezometric head result of the numerical calculation

velocity_x=name
Output 3D raster map storing the groundwater filter velocity vector part in x
direction [m/s]

velocity_y=name
Output 3D raster map storing the groundwater filter velocity vector part in y
direction [m/s]

velocity_z=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]

dtime=float [required]
The calculation time in seconds
Default: 86400

maxit=integer
Maximum number of iteration used to solve the linear equation system
Default: 10000

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 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.

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 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

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.

EXAMPLE 1

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

EXAMPLE 2

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

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