One of the promises of the Voronoi meshes on MODFLOW6 Disv is the efficient distribution of cell sizes that allows us to reach small sizes on certain areas of high interest like wells while keeping coarse cells on the areas with lower level of interest. This type of meshing has some issues that now are addressed on mf6Voronoi.

For example, if we want to create a mesh for a place in Netherlands where the cell sizes go from 50m to 1m we can end up with a mesh distribution like this.

Voronoi discretization over the model limit

We can check that the cell sizes reaches the desired discretization.

Refinement of 1m around wells and 5m around drains

But we face a problem when we run the model.

FORTRAN ERROR RELATED TO ISSUES ON THE DISCRETIZATION

But there are tools in mf6Voronoi to adress the short edges on the mesh.

Tutorial

Code

For voronoi generation

Part 1 : Voronoi mesh generation

import warnings ## Org
warnings.filterwarnings('ignore') ## Org

import os, sys ## Org
import geopandas as gpd ## Org
from mf6Voronoi.geoVoronoi import createVoronoi ## Org
from mf6Voronoi.meshProperties import meshShape ## Org
from mf6Voronoi.utils import initiateOutputFolder, getVoronoiAsShp ## Org

#Create mesh object specifying the coarse mesh and the multiplier
vorMesh = createVoronoi(meshName='zaandam',maxRef = 50, multiplier=1.8) ## Org

#Open limit layers and refinement definition layers
vorMesh.addLimit('limit','../shp/modelLimit.shp') ## Org
vorMesh.addLayer('wells','../shp/modelWell.shp',1) ## Org
vorMesh.addLayer('drain','../shp/modelDrain.shp',5) ## Org
vorMesh.addLayer('channels','../shp/modelGhb.shp',5) ## Org

#Generate point pair array
vorMesh.generateOrgDistVertices() ## Org

#Generate the point cloud and voronoi
vorMesh.createPointCloud() ## Org
vorMesh.generateVoronoi() ## Org

build faster, analyze more

/--------Layer wells discretization-------/
Progressive cell size list: [1, 2.8, 6.04, 11.872, 22.3696, 41.265280000000004] m.

/--------Layer drain discretization-------/
Progressive cell size list: [5, 14.0, 30.200000000000003] m.

/--------Layer channels discretization-------/
Progressive cell size list: [5, 14.0, 30.200000000000003] m.

/----Sumary of points for voronoi meshing----/
Distributed points from layers: 3
Points from layer buffers: 11274
Points from max refinement areas: 24
Points from min refinement areas: 2397
Total points inside the limit: 16203
/--------------------------------------------/

Time required for point generation: 2.75 seconds 


/----Generation of the voronoi mesh----/

Time required for voronoi generation: 1.90 seconds

#Uncomment the next two cells if you have strong differences on discretization or you have encounter an FORTRAN error while running MODFLOW6

vorMesh.checkVoronoiQuality(threshold=0.01)

/----Performing quality verification of voronoi mesh----/
Short side on polygon: 16184 with length = 0.00298
Short side on polygon: 16184 with length = 0.00298
Short side on polygon: 16184 with length = 0.00148

vorMesh.fixVoronoiShortSides()
vorMesh.generateVoronoi()
vorMesh.checkVoronoiQuality(threshold=0.01)

/----Generation of the voronoi mesh----/

Time required for voronoi generation: 1.65 seconds 


/----Performing quality verification of voronoi mesh----/
Your mesh has no edges shorter than your threshold

#Export generated voronoi mesh
initiateOutputFolder('../output') ## Org
getVoronoiAsShp(vorMesh.modelDis, shapePath='../output/'+vorMesh.modelDis['meshName']+'.shp') ## Org

The output folder ../output exists and has been cleared

/----Generation of the voronoi shapefile----/

Time required for voronoi shapefile: 3.37 seconds

# Show the resulting voronoi mesh

#open the mesh file
mesh=gpd.read_file('../output/'+vorMesh.modelDis['meshName']+'.shp') ## Org
#plot the mesh
mesh.plot(figsize=(35,25), fc='crimson', alpha=0.3, ec='teal') ## Org

<Axes: >

Part 2 generate disv properties

# open the mesh file
mesh=meshShape('../output/'+vorMesh.modelDis['meshName']+'.shp') ## Org

# get the list of vertices and cell2d data
gridprops=mesh.get_gridprops_disv() ## Org

Creating a unique list of vertices [[x1,y1],[x2,y2],...]


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Extracting cell2d data and grid index


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#create folder
initiateOutputFolder('../json') ## Org

#export disv
mesh.save_properties('../json/disvDict.json') ## Org

The output folder ../json exists and has been cleared

This is the code for model creation and simulation

Part 2a: generate disv properties

import sys, json, os ## Org
import rasterio, flopy ## Org
import numpy as np ## Org
import matplotlib.pyplot as plt ## Org
import geopandas as gpd ## Org
from mf6Voronoi.meshProperties import meshShape ## Org
from shapely.geometry import MultiLineString ## Org

C:\Users\saulm\anaconda3\Lib\site-packages\geopandas\_compat.py:7: DeprecationWarning: The 'shapely.geos' module is deprecated, and will be removed in a future version. All attributes of 'shapely.geos' are available directly from the top-level 'shapely' namespace (since shapely 2.0.0).
  import shapely.geos

# open the json file
with open('../json/disvDict.json') as file: ## Org
    gridProps = json.load(file) ## Org

cell2d = gridProps['cell2d']           #cellid, cell centroid xy, vertex number and vertex id list
vertices = gridProps['vertices']       #vertex id and xy coordinates
ncpl = gridProps['ncpl']               #number of cells per layer
nvert = gridProps['nvert']             #number of verts
centroids=gridProps['centroids']       #cell centroids xy

Part 2b: Model construction and simulation

#Extract dem values for each centroid of the voronois
elevation=[1 for i in range(ncpl)] ## Org

nlay = 5   ## Org

mtop=np.array(elevation) ## Org
zbot=np.zeros((nlay,ncpl)) ## Org

zbot[0,] = -1
zbot[1,] = -3
zbot[2,] = -5
zbot[3,] = -7
zbot[4,] = -9

Create simulation and model

# create simulation
simName = 'mf6Sim' ## Org
modelName = 'mf6Model' ## Org
modelWs = '../modelFiles' ## Org
sim = flopy.mf6.MFSimulation(sim_name=modelName, version='mf6', ## Org
                             exe_name='../bin/mf6.exe', ## Org
                             sim_ws=modelWs) ## Org

# create tdis package
tdis_rc = [(1000.0, 1, 1.0)] ## Org
tdis = flopy.mf6.ModflowTdis(sim, pname='tdis', time_units='SECONDS', ## Org
                             perioddata=tdis_rc) ## Org

# create gwf model
gwf = flopy.mf6.ModflowGwf(sim, ## Org
                           modelname=modelName, ## Org
                           save_flows=True, ## Org
                           newtonoptions="NEWTON UNDER_RELAXATION") ## Org

# create iterative model solution and register the gwf model with it
ims = flopy.mf6.ModflowIms(sim, ## Org
                           complexity='COMPLEX', ## Org
                           outer_maximum=50, ## Org
                           inner_maximum=30, ## Org
                           linear_acceleration='BICGSTAB') ## Org
sim.register_ims_package(ims,[modelName]) ## Org

# disv
disv = flopy.mf6.ModflowGwfdisv(gwf, nlay=nlay, ncpl=ncpl, ## Org
                                top=mtop, botm=zbot, ## Org
                                nvert=nvert, vertices=vertices, ## Org
                                cell2d=cell2d) ## Org

# initial conditions
icArray = np.zeros([ncpl])
ic = flopy.mf6.ModflowGwfic(gwf, strt=np.stack([icArray for i in range(nlay)])) ## Org

Kx =[4E-4,4E-4,4E-4,4E-4,4E-4] ## Org
icelltype = [1,0,0,0,0] ## Org

# node property flow
npf = flopy.mf6.ModflowGwfnpf(gwf, ## Org
                              save_specific_discharge=True, ## Org
                              icelltype=icelltype, ## Org
                              k=Kx) ## Org

# define storage and transient stress periods
sto = flopy.mf6.ModflowGwfsto(gwf, ## Org
                              iconvert=1, ## Org
                              steady_state={ ## Org
                                0:True, ## Org
                              } ## Org
                              ) ## Org

Working with rechage, evapotranspiration

rchr = 0.15/365/86400 ## Org
rch = flopy.mf6.ModflowGwfrcha(gwf, recharge=rchr) ## Org
# evtr = 1.2/365/86400 ## Org
# evt = flopy.mf6.ModflowGwfevta(gwf,ievt=1,surface=mtop,rate=evtr,depth=1.0) ## Org

Definition of the intersect object

For the manipulation of spatial data to determine hydraulic parameters or boundary conditions

# Define intersection object
interIx = flopy.utils.gridintersect.GridIntersect(gwf.modelgrid) ## Org

#open the river shapefile
rivers =gpd.read_file('../shp/modelDrain.shp') ## Org
list_rivers=[] ## Org
for i in range(rivers.shape[0]): ## Org
    list_rivers.append(rivers['geometry'].loc[i]) ## Org
    
riverMls = MultiLineString(lines=list_rivers) ## Org

#intersec rivers with our grid
riverCells=interIx.intersect(riverMls).cellids ## Org
riverCells[:10] ## Org

array([601, 603, 610, 618, 619, 627, 655, 663, 667, 674], dtype=object)

#river package
riverSpd = {} ## Org
riverSpd[0] = [] ## Org
for cell in riverCells: ## Org
    riverSpd[0].append([(0,cell),-0.5,0.01]) ## Org
riv = flopy.mf6.ModflowGwfdrn(gwf, stress_period_data=riverSpd) ## Org

#river plot
riv.plot(mflay=0) ## Org

[<Axes: title={'center': ' drn_0 location stress period 1 layer 1'}>]

from shapely.geometry import MultiPolygon

#open the river shapefile
channels =gpd.read_file('../shp/modelGhb.shp') ## <=== updated
list_channels=[] ## <=== updated
for i in range(channels.shape[0]): ## <=== updated
    list_channels.append(channels['geometry'].loc[i]) ## <=== updated
    
channelsMpl = MultiPolygon(polygons=list_channels) ## <=== updated
channelsMpl

#intersec rivers with our grid
channelCells=interIx.intersect(channelsMpl).cellids ## <=== updated
channelCells[:10] ## <=== updated

#river package
ghbSpd = {} ## <=== updated
ghbSpd[0] = [] ## <=== updated
for cell in channelCells: ## <=== updated
    ghbSpd[0].append([(0,cell),0,0.01]) ## <==== updated
ghb = flopy.mf6.ModflowGwfghb(gwf, stress_period_data=ghbSpd) ## <=== updated
ghb.plot(mflay=0)## <=== updated

[<Axes: title={'center': ' ghb_0 location stress period 1 layer 1'}>]

Set the Output Control and run simulation

#oc
head_filerecord = f"{gwf.name}.hds" ## Org
budget_filerecord = f"{gwf.name}.cbc" ## Org
oc = flopy.mf6.ModflowGwfoc(gwf, ## Org
                            head_filerecord=head_filerecord, ## Org
                            budget_filerecord = budget_filerecord, ## Org
                            saverecord=[("HEAD", "LAST"),("BUDGET","LAST")]) ## Org

# Run the simulation
sim.write_simulation() ## Org
success, buff = sim.run_simulation() ## Org

writing simulation...
  writing simulation name file...
  writing simulation tdis package...
  writing solution package ims_-1...
  writing model mf6Model...
    writing model name file...
    writing package disv...
    writing package ic...
    writing package npf...
    writing package sto...
    writing package rcha_0...
    writing package drn_0...
INFORMATION: maxbound in ('gwf6', 'drn', 'dimensions') changed to 2420 based on size of stress_period_data
    writing package ghb_0...
INFORMATION: maxbound in ('gwf6', 'ghb', 'dimensions') changed to 4273 based on size of stress_period_data
    writing package oc...
FloPy is using the following executable to run the model: ..\bin\mf6.exe
                                   MODFLOW 6
                U.S. GEOLOGICAL SURVEY MODULAR HYDROLOGIC MODEL
                            VERSION 6.6.0 12/20/2024

   MODFLOW 6 compiled Dec 31 2024 17:10:16 with Intel(R) Fortran Intel(R) 64
   Compiler Classic for applications running on Intel(R) 64, Version 2021.7.0
                             Build 20220726_000000

This software has been approved for release by the U.S. Geological 
Survey (USGS). Although the software has been subjected to rigorous 
review, the USGS reserves the right to update the software as needed 
pursuant to further analysis and review. No warranty, expressed or 
implied, is made by the USGS or the U.S. Government as to the 
functionality of the software and related material nor shall the 
fact of release constitute any such warranty. Furthermore, the 
software is released on condition that neither the USGS nor the U.S. 
Government shall be held liable for any damages resulting from its 
authorized or unauthorized use. Also refer to the USGS Water 
Resources Software User Rights Notice for complete use, copyright, 
and distribution information.

 
 MODFLOW runs in SEQUENTIAL mode
 
 Run start date and time (yyyy/mm/dd hh:mm:ss): 2025/07/27 20:59:22
 
 Writing simulation list file: mfsim.lst
 Using Simulation name file: mfsim.nam
 
    Solving:  Stress period:     1    Time step:     1
 
 Run end date and time (yyyy/mm/dd hh:mm:ss): 2025/07/27 20:59:25
 Elapsed run time:  2.856 Seconds
 
 Normal termination of simulation.

Model output visualization

headObj = gwf.output.head() ## Org
headObj.get_kstpkper() ## Org

[(0, 0)]

heads = headObj.get_data() ## Org
heads[2,0,:5] ## Org

array([1.02717938e-05, 9.74176946e-06, 1.13508284e-05, 7.76607206e-06,
       1.08526309e-05])

# Plot the heads for a defined layer and boundary conditions
fig = plt.figure(figsize=(12,8)) ## Org
ax = fig.add_subplot(1, 1, 1, aspect='equal') ## Org
modelmap = flopy.plot.PlotMapView(model=gwf) ## Org

####
levels = np.linspace(heads[heads>-1e+30].min(),heads[heads>-1e+30].max(),num=10) ## Org
contour = modelmap.contour_array(heads[0],ax=ax,levels=levels,cmap='PuBu') ## Org
ax.clabel(contour, fmt='%.2f') ## Org


quadmesh = modelmap.plot_bc('DRN') ## Org
cellhead = modelmap.plot_array(heads[0],ax=ax, cmap='Blues', alpha=0.8) ## Org

linecollection = modelmap.plot_grid(linewidth=0.3, alpha=0.5, color='cyan', ax=ax) ## Org

plt.colorbar(cellhead, shrink=0.75) ## Org

plt.show() ## Org