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       r.gwflow    -  Numerical  calculation  program  for  transient,  confined  and  unconfined
       groundwater flow in two dimensions.


       raster, hydrology


       r.gwflow help
       r.gwflow [-s] phead=name  status=name  hc_x=name  hc_y=name   [q=name]   s=name   [r=name]
       top=name   bottom=name  output=name   [velocity=name]    [type=string]    [river_bed=name]
       [river_head=name]    [river_leak=name]    [drain_bed=name]    [drain_leak=name]   dt=float
       [maxit=integer]      [error=float]      [solver=name]      [relax=float]     [--overwrite]
       [--verbose]  [--quiet]

           Use a sparse matrix, only available with iterative solvers

           Allow output files to overwrite existing files

           Verbose module output

           Quiet module output

           The initial piezometric head in [m]

           Boundary condition status, 0-inactive, 1-active, 2-dirichlet

           X-part of the hydraulic conductivity tensor in [m/s]

           Y-part of the hydraulic conductivity tensor in [m/s]

           Water sources and sinks in [m^3/s]

           Specific yield in [1/m]

           Recharge map e.g: 6*10^-9 per cell in [m^3/s*m^2]

           Top surface of the aquifer in [m]

           Bottom surface of the aquifer in [m]

           The map storing the numerical result [m]

           Calculate the groundwater filter velocity vector field [m/s]
           and write the x, and y components to maps named name_[xy]

           The type of groundwater flow
           Options: confined,unconfined
           Default: confined

           The height of the river bed in [m]

           Water level (head) of the river with leakage connection in [m]

           The leakage coefficient of the river bed in [1/s].

           The height of the drainage bed in [m]

           The leakage coefficient of the drainage bed in [1/s]

           The calculation time in seconds
           Default: 86400

           Maximum number of iteration used to solver the linear equation system
           Default: 100000

           Error break criteria for iterative solvers (jacobi, sor, cg or bicgstab)
           Default: 0.0000000001

           The type of solver which should solve the symmetric linear equation system
           Options: gauss,lu,cholesky,jacobi,sor,cg,bicgstab,pcg
           Default: cg

           The relaxation parameter used by the jacobi and sor solver for speedup or stabilizing
           Default: 1


       This numerical program calculates transient, confined and unconfined groundwater  flow  in
       two  dimensions  based  on raster maps and the current region resolution.  All initial and
       boundary conditions must be provided as raster maps.

            | Workflow of r.gwflow

       r.gwflow calculates the piezometric head and optionally 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.  If you want to calculate  stady
       state, set the timestep to a large number (billions of seconds) or set the specific yield/
       effective porosity raster maps to zero.


       The  groundwater  flow  calculation  is  based  on  Darcy's  law  and  a   finite   volume
       discretization.  The  solved  groundwater  flow  partial  differential  equation is of the
       following form:

       (dh/dt)*Ss = 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 yield [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 in meter per second [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 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
       The groundwater flow equation can be solved with several solvers.  Two  iterative  solvers
       with  sparse and quadratic matrices support are implemented.  The conjugate gradients (cg)
       method and the biconjugate gradients-stabilized (bicgstab) method.  Additionally a  direct
       Gauss  solver  and  LU  solver  are  available. Those direct solvers 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.


       Use  this  small  script to create a working groundwater flow area and data. Make sure you
       are not in a lat/lon projection.
       # set the region accordingly
       g.region res=25 res3=25 t=100 b=0 n=1000 s=0 w=0 e=1000
       #now create the input raster maps for confined and unconfined aquifers
       r.mapcalc "phead=if(row() == 1 , 50, 40)"
       r.mapcalc "status=if(row() == 1 , 2, 1)"
       r.mapcalc "well=if(row() == 20 && col() == 20 , -0.001, 0)"
       r.mapcalc "hydcond=0.00025"
       r.mapcalc "recharge=0"
       r.mapcalc "top_conf=20.0"
       r.mapcalc "top_unconf=70.0"
       r.mapcalc "bottom=0.0"
       r.mapcalc "null=0.0"
       r.mapcalc "poros=0.15"
       r.mapcalc "syield=0.0001"
       #confined groundwater flow with cg solver and sparse matrix
       r.gwflow --o -s solver=cg top=top_conf bottom=bottom phead=phead status=status \
       hc_x=hydcond hc_y=hydcond q=well s=syield r=recharge output=gwresult_conf \
       dt=8640000 type=confined velocity=gwresult_conf_velocity
       #unconfined groundwater flow with cg solver and sparse matrix
       r.gwflow --o -s solver=cg top=top_unconf bottom=bottom phead=phead \
       status=status hc_x=hydcond hc_y=hydcond q=well s=poros r=recharge \
       output=gwresult_unconf dt=8640000 type=unconfined velocity=gwresult_unconf_velocity
       # 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
       #now load the data into paraview
       paraview --data=/tmp/gwdata_conf2d.vtk &
       paraview --data=/tmp/gwdata_unconf2d.vtk &




       Soeren Gebbert

       Last changed: $Date: 2013-06-16 05:08:46 +0200 (Sun, 16 Jun 2013) $

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