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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-inactive, 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 system
           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 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.

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  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 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:

           ·   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 calculation, inner sources
               and recharge can be defined for those cells

           ·   2 == Dirichlet - cells of this type will have a fixed piezometric head value which
               do not change over the 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).  Always prefer a sparse matrix 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.

       Last changed: $Date: 2018-12-26 13:09:47 +0100 (Wed, 26 Dec 2018) $

SOURCE CODE

       Available at: r.gwflow source code (history)

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