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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 calculated, 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

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, Germany.

       Last changed: $Date: 2017-02-17 22:14:15 +0100 (Fri, 17 Feb 2017) $

SOURCE CODE

       Available at: r3.gwflow source code (history)

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