def domain(self, domaintype='meshpy'):
if domaintype is 'meshpy':
from meshpy.triangle import MeshInfo
domain = MeshInfo()
points = np.zeros((16, 2), dtype=np.float)
points[0:4, :] = np.array([(0.0, 0.0), (1.0, 0.0), (1.0, 1.0),
(0.0, 1.0)],
dtype=np.float)
idx = np.arange(5, -1, -1)
points[4:10, 0] = 0.25 + 0.1 * np.cos(idx * np.pi / 3)
points[4:10, 1] = 0.75 + 0.1 * np.sin(idx * np.pi / 3)
points[10:, 0] = 0.6 + 0.1 * np.cos(idx * np.pi / 3)
points[10:, 1] = 0.4 + 0.1 * np.sin(idx * np.pi / 3)
facets = np.zeros((16, 2), dtype=np.int)
facets[0:4, :] = np.array([(0, 1), (1, 2), (2, 3), (3, 0)],
dtype=np.int)
facets[4:10, :] = np.array([(4, 5), (5, 6), (6, 7), (7, 8), (8, 9),
(9, 4)],
dtype=np.int)
facets[10:, :] = np.array([(10, 11), (11, 12), (12, 13), (13, 14),
(14, 15), (15, 10)],
dtype=np.int)
domain.set_points(points)
domain.set_facets(facets)
domain.set_holes([(0.25, 0.75), (0.6, 0.4)])
return domain
def triangulate(self, options=None):
if options is None:
options = self._get_triangle_options()
mesh_info = MeshInfo()
mesh_info.set_points(self.vertices)
if self.boundary is not None:
segments = []
for b in self.boundary:
segments += self.get_segments(b)
mesh_info.set_facets(segments)
if self.holes is not None:
mesh_info.set_holes(self.holes)
try:
import locale
except ImportError:
use_locale = False
else:
use_locale = True
prev_num_locale = locale.getlocale(locale.LC_NUMERIC)
locale.setlocale(locale.LC_NUMERIC, "C")
try:
mesh = MeshInfo()
internals.triangulate(options, mesh_info, mesh, MeshInfo(), None)
finally:
# restore previous locale if we've changed it
if use_locale:
locale.setlocale(locale.LC_NUMERIC, prev_num_locale)
return mesh
def make_mesh(max_volume):
def round_trip_connect(seq):
result = []
for i in range(len(seq)):
result.append((i, (i+1)%len(seq)))
return result
shapes = read_shape()
#from matplotlib.pyplot import plot,show
#plot(shapes[0][:,0], shapes[0][:,1])
#show()
from meshpy.geometry import GeometryBuilder, Marker
builder = GeometryBuilder()
for shape in shapes:
from meshpy.geometry import make_box
points = shape
facets = round_trip_connect(range(len(points)))
builder.add_geometry(points=points, facets=facets,
facet_markers=Marker.FIRST_USER_MARKER)
points, facets, facet_markers = make_box((-200, -600), (400, -300))
builder.add_geometry(points=points, facets=facets,
facet_markers=facet_markers)
def transform(pt):
x, y = pt
return -0.01*x, -0.01*y
builder.apply_transform(transform)
from meshpy.triangle import MeshInfo, build
mi = MeshInfo()
builder.set(mi)
holes = []
for shape, sign, frac in zip(shapes, [1, 1, -1, 1, 1, 1], [0.5, 0, 0, 0, 0, 0]):
avg = np.average(shape, axis=0)
start_idx = int(frac*shape.shape[0])
start = shape[start_idx]
holes.append(transform(start + sign*0.01*(avg-start)))
mi.set_holes(holes)
mesh = build(mi,
allow_boundary_steiner=True,
generate_faces=True,
max_volume=max_volume)
return mesh
def make_squaremesh():
def round_trip_connect(seq):
result = []
for i in range(len(seq)):
result.append((i, (i + 1) % len(seq)))
return result
def needs_refinement(vertices, area):
x = sum(numpy.array(v) for v in vertices) / 3
max_area_volume = 0.7e-2 + 0.03 * (0.05 * x[1]**2 +
0.3 * min(x[0] + 1, 0)**2)
max_area_corners = 1e-3 + 0.001 * max(
la.norm(x - corner)**4 for corner in obstacle_corners)
return bool(area > 2.5 * min(max_area_volume, max_area_corners))
from meshpy.geometry import make_box
points, facets, _, _ = make_box((-0.5, -0.5), (0.5, 0.5))
obstacle_corners = points[:]
from meshpy.geometry import GeometryBuilder, Marker
profile_marker = Marker.FIRST_USER_MARKER
builder = GeometryBuilder()
builder.add_geometry(points=points,
facets=facets,
facet_markers=profile_marker)
points, facets, _, facet_markers = make_box((-16, -22), (25, 22))
builder.add_geometry(points=points,
facets=facets,
facet_markers=facet_markers)
from meshpy.triangle import MeshInfo, build
mi = MeshInfo()
builder.set(mi)
mi.set_holes([(0, 0)])
mesh = build(mi,
refinement_func=needs_refinement,
allow_boundary_steiner=True,
generate_faces=True)
print("%d elements" % len(mesh.elements))
from meshpy.triangle import write_gnuplot_mesh
write_gnuplot_mesh("mesh.dat", mesh)
fvi2fm = mesh.face_vertex_indices_to_face_marker
face_marker_to_tag = {
profile_marker: "noslip",
Marker.MINUS_X: "inflow",
Marker.PLUS_X: "outflow",
Marker.MINUS_Y: "inflow",
Marker.PLUS_Y: "inflow"
}
def bdry_tagger(fvi, el, fn, all_v):
face_marker = fvi2fm[fvi]
return [face_marker_to_tag[face_marker]]
from grudge.mesh import make_conformal_mesh_ext
vertices = numpy.asarray(mesh.points, dtype=float, order="C")
from grudge.mesh.element import Triangle
return make_conformal_mesh_ext(vertices, [
Triangle(i, el_idx, vertices) for i, el_idx in enumerate(mesh.elements)
], bdry_tagger)
def make_nacamesh():
def round_trip_connect(seq):
result = []
for i in range(len(seq)):
result.append((i, (i + 1) % len(seq)))
return result
pt_back = numpy.array([1, 0])
#def max_area(pt):
#max_area_front = 1e-2*la.norm(pt)**2 + 1e-5
#max_area_back = 1e-2*la.norm(pt-pt_back)**2 + 1e-4
#return min(max_area_front, max_area_back)
def max_area(pt):
x = pt[0]
if x < 0:
return 1e-2 * la.norm(pt)**2 + 1e-5
elif x > 1:
return 1e-2 * la.norm(pt - pt_back)**2 + 1e-5
else:
return 1e-2 * pt[1]**2 + 1e-5
def needs_refinement(vertices, area):
barycenter = sum(numpy.array(v) for v in vertices) / 3
return bool(area > max_area(barycenter))
from meshpy.naca import get_naca_points
points = get_naca_points(naca_digits="2412", number_of_points=80)
from meshpy.geometry import GeometryBuilder, Marker
from meshpy.triangle import write_gnuplot_mesh
profile_marker = Marker.FIRST_USER_MARKER
builder = GeometryBuilder()
builder.add_geometry(points=points,
facets=round_trip_connect(points),
facet_markers=profile_marker)
builder.wrap_in_box(4, (10, 8))
from meshpy.triangle import MeshInfo, build
mi = MeshInfo()
builder.set(mi)
mi.set_holes([builder.center()])
mesh = build(
mi,
refinement_func=needs_refinement,
#allow_boundary_steiner=False,
generate_faces=True)
write_gnuplot_mesh("mesh.dat", mesh)
print("%d elements" % len(mesh.elements))
fvi2fm = mesh.face_vertex_indices_to_face_marker
face_marker_to_tag = {
profile_marker: "noslip",
Marker.MINUS_X: "inflow",
Marker.PLUS_X: "outflow",
Marker.MINUS_Y: "inflow",
Marker.PLUS_Y: "inflow"
#Marker.MINUS_Y: "minus_y",
#Marker.PLUS_Y: "plus_y"
}
def bdry_tagger(fvi, el, fn, all_v):
face_marker = fvi2fm[fvi]
return [face_marker_to_tag[face_marker]]
from grudge.mesh import make_conformal_mesh_ext
vertices = numpy.asarray(mesh.points, order="C")
from grudge.mesh.element import Triangle
return make_conformal_mesh_ext(
vertices,
[
Triangle(i, el_idx, vertices)
for i, el_idx in enumerate(mesh.elements)
],
bdry_tagger,
#periodicity=[None, ("minus_y", "plus_y")]
)
def make_squaremesh():
def round_trip_connect(seq):
result = []
for i in range(len(seq)):
result.append((i, (i+1)%len(seq)))
return result
def needs_refinement(vertices, area):
x = sum(numpy.array(v) for v in vertices)/3
max_area_volume = 0.7e-2 + 0.03*(0.05*x[1]**2 + 0.3*min(x[0]+1,0)**2)
max_area_corners = 1e-3 + 0.001*max(
la.norm(x-corner)**4 for corner in obstacle_corners)
return bool(area > 2.5*min(max_area_volume, max_area_corners))
from meshpy.geometry import make_box
points, facets, _, _ = make_box((-0.5,-0.5), (0.5,0.5))
obstacle_corners = points[:]
from meshpy.geometry import GeometryBuilder, Marker
profile_marker = Marker.FIRST_USER_MARKER
builder = GeometryBuilder()
builder.add_geometry(points=points, facets=facets,
facet_markers=profile_marker)
points, facets, _, facet_markers = make_box((-16, -22), (25, 22))
builder.add_geometry(points=points, facets=facets,
facet_markers=facet_markers)
from meshpy.triangle import MeshInfo, build
mi = MeshInfo()
builder.set(mi)
mi.set_holes([(0,0)])
mesh = build(mi, refinement_func=needs_refinement,
allow_boundary_steiner=True,
generate_faces=True)
print "%d elements" % len(mesh.elements)
from meshpy.triangle import write_gnuplot_mesh
write_gnuplot_mesh("mesh.dat", mesh)
fvi2fm = mesh.face_vertex_indices_to_face_marker
face_marker_to_tag = {
profile_marker: "noslip",
Marker.MINUS_X: "inflow",
Marker.PLUS_X: "outflow",
Marker.MINUS_Y: "inflow",
Marker.PLUS_Y: "inflow"
}
def bdry_tagger(fvi, el, fn, all_v):
face_marker = fvi2fm[fvi]
return [face_marker_to_tag[face_marker]]
from hedge.mesh import make_conformal_mesh_ext
vertices = numpy.asarray(mesh.points, dtype=float, order="C")
from hedge.mesh.element import Triangle
return make_conformal_mesh_ext(
vertices,
[Triangle(i, el_idx, vertices)
for i, el_idx in enumerate(mesh.elements)],
bdry_tagger)
def make_nacamesh():
def round_trip_connect(seq):
result = []
for i in range(len(seq)):
result.append((i, (i + 1) % len(seq)))
return result
pt_back = numpy.array([1, 0])
# def max_area(pt):
# max_area_front = 1e-2*la.norm(pt)**2 + 1e-5
# max_area_back = 1e-2*la.norm(pt-pt_back)**2 + 1e-4
# return min(max_area_front, max_area_back)
def max_area(pt):
x = pt[0]
if x < 0:
return 1e-2 * la.norm(pt) ** 2 + 1e-5
elif x > 1:
return 1e-2 * la.norm(pt - pt_back) ** 2 + 1e-5
else:
return 1e-2 * pt[1] ** 2 + 1e-5
def needs_refinement(vertices, area):
barycenter = sum(numpy.array(v) for v in vertices) / 3
return bool(area > max_area(barycenter))
from meshpy.naca import get_naca_points
points = get_naca_points(naca_digits="2412", number_of_points=80)
from meshpy.geometry import GeometryBuilder, Marker
from meshpy.triangle import write_gnuplot_mesh
profile_marker = Marker.FIRST_USER_MARKER
builder = GeometryBuilder()
builder.add_geometry(points=points, facets=round_trip_connect(points), facet_markers=profile_marker)
builder.wrap_in_box(4, (10, 8))
from meshpy.triangle import MeshInfo, build
mi = MeshInfo()
builder.set(mi)
mi.set_holes([builder.center()])
mesh = build(
mi,
refinement_func=needs_refinement,
# allow_boundary_steiner=False,
generate_faces=True,
)
write_gnuplot_mesh("mesh.dat", mesh)
print "%d elements" % len(mesh.elements)
fvi2fm = mesh.face_vertex_indices_to_face_marker
face_marker_to_tag = {
profile_marker: "noslip",
Marker.MINUS_X: "inflow",
Marker.PLUS_X: "outflow",
Marker.MINUS_Y: "inflow",
Marker.PLUS_Y: "inflow"
# Marker.MINUS_Y: "minus_y",
# Marker.PLUS_Y: "plus_y"
}
def bdry_tagger(fvi, el, fn, all_v):
face_marker = fvi2fm[fvi]
return [face_marker_to_tag[face_marker]]
from hedge.mesh import make_conformal_mesh_ext
vertices = numpy.asarray(mesh.points, order="C")
from hedge.mesh.element import Triangle
return make_conformal_mesh_ext(
vertices,
[Triangle(i, el_idx, vertices) for i, el_idx in enumerate(mesh.elements)],
bdry_tagger,
# periodicity=[None, ("minus_y", "plus_y")]
)