pmgbergen / porepy

Hi,

We tried to create a grid with a single, concave element in 2D and noticed that the normal is not oriented correctly.
Note that we would like all normals to be oriented outward (as specified in cell_faces) but it gets flipped if the cell center is not inside the polygon.

Our guess is that it should not be cell_center but a star-shaped point in the line:

porepy/src/porepy/grids/grid.py

Line 414 in 1533c7e

cc = self.cell_centers[:, ci[idx]]

MWE:

import porepy as pp
import numpy as np
import scipy.sparse as sps


def test(alpha):
    nodes = np.array([[0, 0.5, 1, 0.5], [0, alpha, 0, 1], np.zeros(4)])
    indices = np.array([0, 1, 1, 2, 2, 3, 3, 0])
    face_nodes = sps.csc_matrix((np.ones(8), indices, np.arange(0, 9, 2)))
    cell_faces = sps.csc_matrix(np.ones((4, 1)))

    sd = pp.Grid(2, nodes, face_nodes, cell_faces, "bug")
    sd.compute_geometry()

    print(sd.face_normals[:, :2])


test(0.25)
# correct
# [[ 0.25 -0.25]
#  [-0.5  -0.5 ]
#  [ 0.    0.  ]]
test(0.5)
# incorrect
# [[-0.5  0.5]
#  [ 0.5  0.5]
#  [ 0.   0. ]]

That makes sense.

I am afraid I will not prioritize fixing this for the foreseeable future, but if you make a PR we will include it unless the change has unexpected side effects. If you make the PR, please include the tests as well.

I understand.

However, there are more problems with _compute_geometry_2d(). In particular, for the example above with alpha = 0.5:

The cell centroid should be [0.5, 0.5] but PorePy returns [0.5, 31/72].
The cell area should be 0.25 but PorePy returns 0.375.

Both of these are computed before the face_normals are "flipped".

In 3D, we assume that the nodes in face_nodes are ordered in a specific (counter)clockwise way. Is there any information to the ordering of nodes in face_nodes in 2D? Without this information, I don't quite see an easy fix.

Normals are flipped in concave polygons