Mesh#

See Mesh in MIKE IO Documentation

import numpy as np
import matplotlib.pyplot as plt
import mikeio

A simple mesh#

Let’s consider a simple mesh consisting of 2 triangular elements.

fn = "data/two_elements.mesh"
with open(fn, "r") as f:
    print(f.read())
100079 1000 4  UTM-31
1 0.0 0.0 -10.0 1 
2 3.0 0.0 -10.0 2 
3 3.0 3.0 -10.0 2 
4 0.0 3.0 -10.0 1 
2 3 21
1 1 2 4
2 2 3 4 
msh = mikeio.open(fn)
msh
Flexible Mesh
number of elements: 2
number of nodes: 4
projection: UTM-31
msh.plot(show_mesh=True);
_images/mesh_6_0.png
msh.node_coordinates
array([[  0.,   0., -10.],
       [  3.,   0., -10.],
       [  3.,   3., -10.],
       [  0.,   3., -10.]])
msh.element_table
[array([0, 1, 3], dtype=int32), array([1, 2, 3], dtype=int32)]
msh.element_coordinates
array([[  1.,   1., -10.],
       [  2.,   2., -10.]])
msh.get_element_area()
array([4.5, 4.5])

Let’s plot the node and element coordinates:

xn, yn = msh.node_coordinates[:,0], msh.node_coordinates[:,1]
xe, ye = msh.element_coordinates[:,0], msh.element_coordinates[:,1]

ax = msh.plot(show_mesh=True)
ax.plot(xn, yn, 'ro', markersize=10)
ax.plot(xe, ye, 'bx', markersize=10)
[<matplotlib.lines.Line2D at 0x7f9fba6b38b0>]
_images/mesh_12_1.png

Boundary polylines#

It can sometimes be convenient to have mesh boundary as a polyline (or multiple in case of more complex meshes).

bxy = msh.boundary_polylines.exteriors[0].xy
plt.plot(bxy[:,0], bxy[:,1])
plt.axis("equal");
_images/mesh_14_0.png

Inside domain?#

MIKE IO has a method for determining if a point (or a list of points) is inside the domain:

  • contains()

pt_1 = [2.0, 1.2]
msh.contains(pt_1)[0]
True
# or multiple points at the same time
pt_2 = [4.0, 1.2]
pts = np.array([pt_1, pt_2])
msh.contains(pts)
array([ True, False])
plt.plot(bxy[:,0], bxy[:,1], label='boundary')
plt.plot(xe[0], ye[0], 'b*', markersize=10, label="center, elem 0")
plt.plot(xe[1], ye[1], 'c*', markersize=10, label="center, elem 1")
plt.plot(*pt_1, 'go', markersize=10, label="pt_1")
plt.plot(*pt_2, 'rs', markersize=10, label="pt_2")
plt.axis("equal")
plt.legend(loc="upper right");
_images/mesh_18_0.png

Find element containing point#

MIKE IO has a method for obtaining the index of the element containing a point:

  • find_index()

g = msh.geometry
g.find_index(coords=pt_1)[0]
1

MIKE IO also has a method for obtaining a list of the n closest element centers:

  • find_nearest_elements()

g.find_nearest_elements(pt_1)
1
g.find_nearest_elements(pt_1, return_distances=True)
(1, 0.8)
g.find_nearest_elements(pt_1, n_nearest=2)
array([1, 0])
# for multiple points
g.find_nearest_elements(pts, return_distances=True)
(array([1, 1]), array([0.8       , 2.15406592]))

A larger mesh#

A dfsu file can also be loaded as a Mesh object

fn = "data/FakeLake.dfsu"
msh = mikeio.Mesh(fn)
msh.plot();
_images/mesh_28_0.png

Inline Exercise#

  1. please check if the point A: (x,y)=(-0.5, 0.0) is inside the mesh

  2. please check if the point B: (x,y)=(-0.5, 0.4) is inside the mesh

  3. find index of the 5 closest points to B

# insert code here
msh.max_nodes_per_element
4
msh.plot_boundary_nodes();
_images/mesh_32_0.png
bnd = msh.boundary_polylines
bnd.n_exteriors, bnd.n_interiors
(1, 1)
ext0 = bnd.exteriors[0]
plt.plot(ext0.xy[:,0], ext0.xy[:,1], label='exterior 0')
int0 = bnd.interiors[0]
plt.plot(int0.xy[:,0], int0.xy[:,1], label='interior 0')
plt.legend();
_images/mesh_34_0.png
# msh.to_shapely()

Change depth#

msh = mikeio.Mesh(fn)
msh.plot();
_images/mesh_37_0.png
# zn == nodes, not elements!
msh.zn = np.clip(msh.zn, -15, 0) # clip depth to interval [-15,0]
msh.plot();
_images/mesh_39_0.png
msh.write('Fake_lake_clip15.mesh')   # save to a new file

Visualisation#

msh = mikeio.open("data/southern_north_sea.mesh")
msh
Flexible Mesh
number of elements: 958
number of nodes: 570
projection: LONG/LAT

The default is to plot the elements and color them according to the bathymetry.

msh.plot();
_images/mesh_44_0.png
msh.plot.outline();
_images/mesh_45_0.png
msh.plot.mesh();
_images/mesh_46_0.png

Maybe we would like to higlight the bathymetric variations in some range, in this case in the -40, -20m range.

msh.plot(vmin=-40, vmax=-20);
_images/mesh_48_0.png

There are other options as well, such as explicit specification of which contour lines to show or choosing a specific colormap (matplotlib colormaps)

msh.plot.contour(show_mesh=True, 
         levels=[-50,-30,-20,-10,-5], cmap="tab10",
         figsize=(12,12), title="Coarse North Sea model");
_images/mesh_50_0.png

See the MIKE IO Mesh Example notebook for more Mesh operations (including shapely operations).