r3.gwflow(1)

📦
version 8.4.2 · 8 versions
, in fedora 44

✨ r3.gwflow ✨

okay bestie, welcome to r3.gwflow 💖 this is a page from the GRASS GIS User's Manual (you know, the GRASS 8.4.2 one) and it's about to teach you how to do transient, confined groundwater flow in three whole dimensions. yes. 3D. we're in our voxel era 🦋

🌸 NAME 🌸

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

like. it literally does the math for water moving through the ground in 3D. no cap. 💅

🎀 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 💖

So this numerical module calculates implicit transient and steady state, confined groundwater flow in three dimensions, and it does it based on volume maps plus whatever your current 3D region settings are. Every initial- and boundary-condition has to be handed to it as volume maps, bestie. and the unit of the current coordinate refernce system must be meters. (yes, "refernce" — that's literally what the page says, i don't make the rules 💀)

This module is sensitive to mask settings, lowkey. All cells which are outside the mask are ignored and handled as no flow boundaries. bye. 🚪

It calculates the piezometric head and optionally the water balance for each cell, plus the groundwater velocity field in 3 dimensions. The vector components can be visualized with ParaView if they are exported with r3.out.vtk. iconic combo ngl ✨

and here's the thing: the groundwater flow will always be calculated transient. like always. so 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. those are the two moves, pick one 🎀

📝 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 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, and 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
⚠️ heads up bestie: 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. your RAM is NOT ready 😭

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. always. i said what i said 💅

🌈 EXAMPLE 1 🌈

This small script creates a working groundwater flow area and data. It cannot be run in a lat/lon project. (read that again. cannot. don't do it 🙈)

# 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. (again. not lat/lon. please 🥺)

# 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

go read those too, bestie, they're the friend group 🫶

👑 AUTHOR 👑

Sören Gebbert

This work is based on the Diploma Thesis of Sören Gebbert available here at Technical University Berlin, Germany. 🎓 slay

💜 SOURCE CODE 💜

Available at: r3.gwflow source code (history)

Accessed: Saturday Jan 17 05:41:14 2026

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and that's the whole page, bestie 💖 this was the r3.gwflow(1) manual page from the GRASS GIS 8.4.2 Reference Manual, © 2003-2025 GRASS Development Team — accessed Saturday Jan 17 05:41:14 2026. GRASS 8.4.2 energy only ✨ you ate. periodt. 💅🌸

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