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

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## NAME

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

raster3d, voxel## SYNOPSIS

r3.gwflow r3.gwflow help r3.gwflow[-ms]phead=string status=string hc_x=string hc_y=string hc_z=string[q=string]s=string[r=string]output=string[velocity=string]dt=float[maxit=integer] [error=float] [solver=name] [relax=float] [--overwrite] [--verbose] [--quiet]Flags: -mUse G3D mask (if exists)-sUse a sparse linear equation system, only available with iterative solvers--overwriteAllow output files to overwrite existing files--verboseVerbose module output--quietQuiet module outputParameters: phead=stringThe initial piezometric head in [m]status=stringThe status for each cell, = 0 - inactive, 1 - active, 2 - dirichlethc_x=stringThe x-part of the hydraulic conductivity tensor in [m/s]hc_y=stringThe y-part of the hydraulic conductivity tensor in [m/s]hc_z=stringThe z-part of the hydraulic conductivity tensor in [m/s]q=stringSources and sinks in [m^3/s]s=stringSpecific yield in 1/mr=stringRecharge raster map in m^3/soutput=stringThe piezometric head result of the numerical calculation will be written to this mapvelocity=stringCalculate the groundwater distance velocity vector field and write the x, y, and z components to maps named name_[xyz]. Name is basename for the new raster3d mapsdt=floatThe calculation time in seconds Default:86400 maxit=integerMaximum number of iteration used to solver the linear equation system Default:100000 error=floatError break criteria for iterative solvers (jacobi, sor, cg or bicgstab) Default:0.0000000001 solver=nameThe type of solver which should solve the symmetric linear equation system Options:gauss,lu,cholesky,jacobi,sor,cg,bicgstab,pcgDefault:cg relax=floatThe relaxation parameter used by the jacobi and sor solver for speedup or stabilizing Default:1DESCRIPTION

This numerical program calculates transient, confined groundwater flow in three dimensions based on volume maps and the current 3d region resolution. All initial- and boundary-conditions must be provided as volume maps. This module calculates the piezometric head and optionally the groundwater velocity field. The vector components can be visualized with paraview if they are exported withr3.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 raster maps to zero.## NOTES

The groundwater flow calculation is based on Darcy's law and a finite volume discretization. The groundwater flow partial differential equation is of the following form: (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 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 supportet: 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 The groundwater flow equation can be solved with several solvers. Aditionally a direct Gauss solver and LU solver are available. Those direct solvers only work with quadratic matrices, so be careful using them with large maps (maps of size 10.000 cells will need more than one gigabyte of ram).## EXAMPLE

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 a confined aquifer r3.mapcalc "phead=if(row() == 1 && depth() == 4, 50, 40)" r3.mapcalc "status=if(row() == 1 && depth() == 4, 2, 1)" r3.mapcalc "well=if(row() == 20 && col() == 20 , -0.00025, 0)" r3.mapcalc "hydcond=0.00025" r3.mapcalc "syield=0.0001" r.mapcalc "recharge=0.0" r3.gwflow --o -s solver=cg phead=phead status=status hc_x=hydcond hc_y=hydcond \ hc_z=hydcond q=well s=syield r=recharge output=gwresult dt=8640000 velocity=gwresult_velocity # The data can be visulaized with paraview when exported with r3.out.vtk r3.out.vtk -p in=gwresult,status vector=gwresult_velocity_x,gwresult_velocity_y,gwresult_velocity_z out=/tmp/gwdata3d.vtk #now load the data into paraview## SEE ALSO

r.gwflow r3.out.vtk## AUTHOR

Soeren Gebbert Last changed: $Date: 2007-07-04 09:52:35 +0200 (Wed, 04 Jul 2007) $ Full index (C) 2003-2010 GRASS Development Team R3.GWFLOW(1)

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