def create_0d_grids(pts, cells):
# Find 0-d grids (points)
# We know the points are 1d, so squeeze the superflous dimension
# All intersection lines and points on boundaries are non-physical in 3d.
# I.e., they are assigned boundary conditions, but are not gridded.
g_0d = []
if "vertex" in cells:
point_cells = cells["vertex"].ravel()
for pi in point_cells:
g = point_grid.PointGrid(pts[pi])
g.global_point_ind = np.atleast_1d(np.asarray(pi))
g_0d.append(g)
return g_0d
def cart_grid_2d(fracs, nx, physdims=None):
"""
Create grids for a domain with possibly intersecting fractures in 2d.
Based on lines describing the individual fractures, the method
constructs grids in 2d (whole domain), 1d (individual fracture), and 0d
(fracture intersections).
Parameters
----------
fracs (list of np.ndarray, each 2x2): Vertexes of the line for each
fracture. The fracture lines must align to the coordinat axis.
The fractures will snap to the closest grid nodes.
nx (np.ndarray): Number of cells in each direction. Should be 2D.
physdims (np.ndarray): Physical dimensions in each direction.
Defaults to same as nx, that is, cells of unit size.
Returns
-------
list (length 3): For each dimension (2 -> 0), a list of all grids in
that dimension.
Examples
--------
frac1 = np.array([[1,4],[2,2]])
frac2 = np.array([[2,2],[1,4]])
fracs = [frac1,frac2]
gb = cart_grid_2d(fracs, [5,5])
"""
nx = np.asarray(nx)
if physdims is None:
physdims = nx
elif np.asarray(physdims).size != nx.size:
raise ValueError("Physical dimension must equal grid dimension")
else:
physdims = np.asarray(physdims)
g_2d = structured.CartGrid(nx, physdims=physdims)
g_2d.global_point_ind = np.arange(g_2d.num_nodes)
g_2d.compute_geometry()
g_1d = []
g_0d = []
# 1D grids:
shared_nodes = np.zeros(g_2d.num_nodes)
for f in fracs:
is_x_frac = f[1, 0] == f[1, 1]
is_y_frac = f[0, 0] == f[0, 1]
assert is_x_frac != is_y_frac, "Fracture must align to x- or y-axis"
if f.shape[0] == 2:
f = np.vstack((f, np.zeros(f.shape[1])))
nodes = _find_nodes_on_line(g_2d, nx, f[:, 0], f[:, 1])
# nodes = np.unique(nodes)
loc_coord = g_2d.nodes[:, nodes]
g = mesh_2_grid.create_embedded_line_grid(loc_coord, nodes)
g_1d.append(g)
shared_nodes[nodes] += 1
# Create 0-D grids
if np.any(shared_nodes > 1):
for global_node in np.argwhere(shared_nodes > 1).ravel():
g = point_grid.PointGrid(g_2d.nodes[:, global_node])
g.global_point_ind = np.asarray(global_node)
g_0d.append(g)
grids = [[g_2d], g_1d, g_0d]
return grids
def cart_grid_3d(fracs, nx, physdims=None):
"""
Create grids for a domain with possibly intersecting fractures in 3d.
Based on rectangles describing the individual fractures, the method
constructs grids in 3d (the whole domain), 2d (one for each individual
fracture), 1d (along fracture intersections), and 0d (meeting between
intersections).
Parameters
----------
fracs (list of np.ndarray, each 3x4): Vertexes in the rectangle for each
fracture. The vertices must be sorted and aligned to the axis.
The fractures will snap to the closest grid faces.
nx (np.ndarray): Number of cells in each direction. Should be 3D.
physdims (np.ndarray): Physical dimensions in each direction.
Defaults to same as nx, that is, cells of unit size.
Returns
-------
list (length 4): For each dimension (3 -> 0), a list of all grids in
that dimension.
Examples
--------
frac1 = np.array([[1,1,4,4], [1,4,4,1], [2,2,2,2]])
frac2 = np.array([[2,2,2,2], [1,1,4,4], [1,4,4,1]])
fracs = [frac1, frac2]
gb = cart_grid_3d(fracs, [5,5,5])
"""
nx = np.asarray(nx)
if physdims is None:
physdims = nx
elif np.asarray(physdims).size != nx.size:
raise ValueError("Physical dimension must equal grid dimension")
else:
physdims = np.asarray(physdims)
# We create a 3D cartesian grid. The global node mapping is trivial.
g_3d = structured.CartGrid(nx, physdims=physdims)
g_3d.global_point_ind = np.arange(g_3d.num_nodes)
g_3d.compute_geometry()
g_2d = []
g_1d = []
g_0d = []
# We set the tolerance for finding points in a plane. This can be any
# small number, that is smaller than .25 of the cell sizes.
tol = 0.1 * physdims / nx
# Create 2D grids
for fi, f in enumerate(fracs):
assert np.all(f.shape == (3, 4)), "fractures must have shape [3,4]"
is_xy_frac = np.allclose(f[2, 0], f[2])
is_xz_frac = np.allclose(f[1, 0], f[1])
is_yz_frac = np.allclose(f[0, 0], f[0])
assert (is_xy_frac + is_xz_frac +
is_yz_frac == 1), "Fracture must align to x-, y- or z-axis"
# snap to grid
f_s = (np.round(f * nx[:, np.newaxis] / physdims[:, np.newaxis]) *
physdims[:, np.newaxis] / nx[:, np.newaxis])
if is_xy_frac:
flat_dim = [2]
active_dim = [0, 1]
elif is_xz_frac:
flat_dim = [1]
active_dim = [0, 2]
else:
flat_dim = [0]
active_dim = [1, 2]
# construct normal vectors. If the rectangle is ordered
# clockwise we need to flip the normals so they point
# outwards.
sign = 2 * pp.geometry_property_checks.is_ccw_polygon(
f_s[active_dim]) - 1
tangent = f_s.take(np.arange(f_s.shape[1]) + 1, axis=1,
mode="wrap") - f_s
normal = tangent
normal[active_dim] = tangent[active_dim[1::-1]]
normal[active_dim[1]] = -normal[active_dim[1]]
normal = sign * normal
# We find all the faces inside the convex hull defined by the
# rectangle. To find the faces on the fracture plane, we remove any
# faces that are further than tol from the snapped fracture plane.
in_hull = half_space.half_space_int(normal, f_s, g_3d.face_centers)
f_tag = np.logical_and(
in_hull,
np.logical_and(
f_s[flat_dim, 0] - tol[flat_dim] <=
g_3d.face_centers[flat_dim],
g_3d.face_centers[flat_dim] < f_s[flat_dim, 0] + tol[flat_dim],
),
)
f_tag = f_tag.ravel()
nodes = sps.find(g_3d.face_nodes[:, f_tag])[0]
nodes = np.unique(nodes)
loc_coord = g_3d.nodes[:, nodes]
g = _create_embedded_2d_grid(loc_coord, nodes)
g.frac_num = fi
g_2d.append(g)
# Create 1D grids:
# Here we make use of the network class to find the intersection of
# fracture planes. We could maybe avoid this by doing something similar
# as for the 2D-case, and count the number of faces belonging to each edge,
# but we use the FractureNetwork class for now.
frac_list = []
for f in fracs:
frac_list.append(fractures.Fracture(f))
# Combine the fractures into a network
network = pp.FractureNetwork3d(frac_list)
# Impose domain boundary. For the moment, the network should be immersed in
# the domain, or else gmsh will complain.
box = {
"xmin": 0,
"ymin": 0,
"zmin": 0,
"xmax": physdims[0],
"ymax": physdims[1],
"zmax": physdims[2],
}
network.impose_external_boundary(box)
# Find intersections and split them.
network.find_intersections()
network.split_intersections()
# Extract geometrical network information.
pts = network.decomposition["points"]
edges = network.decomposition["edges"]
poly = network._poly_2_segment()
# And tags identifying points and edges corresponding to normal
# fractures, domain boundaries and subdomain boundaries. Only the
# entities corresponding to normal fractures should actually be gridded.
edge_tags, intersection_points = network._classify_edges(poly)
const = constants.GmshConstants()
auxiliary_points, edge_tags = network.on_domain_boundary(edges, edge_tags)
bound_and_aux = np.array([const.DOMAIN_BOUNDARY_TAG, const.AUXILIARY_TAG])
edges = np.vstack((edges, edge_tags))
# Loop through the edges to make 1D grids. Ommit the auxiliary edges.
for e in np.ravel(
np.where(edges[2] == const.FRACTURE_INTERSECTION_LINE_TAG)):
# We find the start and end point of each fracture intersection (1D
# grid) and then the corresponding global node index.
if np.isin(edge_tags[e], bound_and_aux):
continue
s_pt = pts[:, edges[0, e]]
e_pt = pts[:, edges[1, e]]
nodes = _find_nodes_on_line(g_3d, nx, s_pt, e_pt)
loc_coord = g_3d.nodes[:, nodes]
assert (loc_coord.shape[1] > 1), "1d grid in intersection should span\
more than one node"
g = mesh_2_grid.create_embedded_line_grid(loc_coord, nodes)
g_1d.append(g)
# Create 0D grids
# Here we also use the intersection information from the FractureNetwork
# class. No grids for auxiliary points.
for p in intersection_points:
if auxiliary_points[p]:
continue
node = np.argmin(pp.distances.point_pointset(pts[:, p], g_3d.nodes))
assert np.allclose(g_3d.nodes[:, node], pts[:, p])
g = point_grid.PointGrid(g_3d.nodes[:, node])
g.global_point_ind = np.asarray(node)
g_0d.append(g)
grids = [[g_3d], g_2d, g_1d, g_0d]
return grids
