def main():
import numpy
from math import pi, cos, sin
from meshpy.tet import MeshInfo, build
from meshpy.geometry import GeometryBuilder, Marker, \
generate_extrusion, make_box
from meshpy.naca import generate_naca
geob = GeometryBuilder()
box_marker = Marker.FIRST_USER_MARKER
wing_length = 2
wing_subdiv = 5
rz_points = [
(0, -wing_length * 1.05),
(0.7, -wing_length * 1.05),
] + [(r, x) for x, r in zip(
numpy.linspace(-wing_length, 0, wing_subdiv, endpoint=False),
numpy.linspace(0.8, 1, wing_subdiv, endpoint=False))] + [(1, 0)] + [
(r, x) for x, r in zip(
numpy.linspace(wing_length, 0, wing_subdiv, endpoint=False),
numpy.linspace(0.8, 1, wing_subdiv, endpoint=False))
][::-1] + [(0.7, wing_length * 1.05), (0, wing_length * 1.05)]
geob.add_geometry(*generate_extrusion(
rz_points=rz_points,
base_shape=generate_naca("0012", verbose=False, number_of_points=20),
ring_markers=(wing_subdiv * 2 + 4) * [box_marker]))
from meshpy.tools import make_swizzle_matrix
swizzle_matrix = make_swizzle_matrix("z:x,y:y,x:z")
geob.apply_transform(lambda p: numpy.dot(swizzle_matrix, p))
def deform_wing(p):
x, y, z = p
return numpy.array([
x, y + 0.1 * abs(x / wing_length)**2,
z + 0.8 * abs(x / wing_length)**1.2
])
geob.apply_transform(deform_wing)
points, facets, _, facet_markers = make_box(
numpy.array([-wing_length - 1, -1, -1.5]),
numpy.array([wing_length + 1, 1, 3]))
geob.add_geometry(points, facets, facet_markers=facet_markers)
mesh_info = MeshInfo()
geob.set(mesh_info)
mesh_info.set_holes([(0, 0, 0.5)])
mesh = build(mesh_info)
print "%d elements" % len(mesh.elements)
mesh.write_vtk("airfoil3d.vtk")
def main():
import numpy
from math import pi, cos, sin
from meshpy.tet import MeshInfo, build
from meshpy.geometry import GeometryBuilder, Marker, make_box
geob = GeometryBuilder()
box_marker = Marker.FIRST_USER_MARKER
extent_small = 0.1*numpy.ones(3, dtype=numpy.float64)
points, facets, _, _ = \
make_box(-extent_small, extent_small)
geob.add_geometry(points, facets, facet_markers=box_marker)
# make small "separator box" for region attribute
geob.wrap_in_box(0.3)
points, facets, _, facet_markers = \
make_box(numpy.array([-1,-1,-1]), numpy.array([1,1,5]))
geob.add_geometry(points, facets, facet_markers=facet_markers)
mesh_info = MeshInfo()
geob.set(mesh_info)
mesh_info.set_holes([(0,0,0)])
# region attributes
mesh_info.regions.resize(1)
mesh_info.regions[0] = (
# point in region
list(extent_small*2) + [
# region number
1,
# max volume in region
0.0001])
mesh = build(mesh_info, max_volume=0.02, volume_constraints=True, attributes=True)
print ("%d elements" % len(mesh.elements))
mesh.write_vtk("box-in-box.vtk")
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 main():
import numpy
from meshpy.tet import MeshInfo, build
from meshpy.geometry import GeometryBuilder, Marker, make_box
geob = GeometryBuilder()
box_marker = Marker.FIRST_USER_MARKER
extent_small = 0.3*numpy.ones(3, dtype=numpy.float64)
points, facets, _, _ = \
make_box(-extent_small, extent_small)
geob.add_geometry(points, facets, facet_markers=box_marker)
points, facets, _, facet_markers = \
make_box(numpy.array([-1, -1, -1]), numpy.array([1, 1, 5]))
geob.add_geometry(points, facets, facet_markers=facet_markers)
mesh_info = MeshInfo()
geob.set(mesh_info)
#mesh_info.set_holes([(0, 0, 0)])
# region attributes
mesh_info.regions.resize(1)
mesh_info.regions[0] = (
# point in region
[0, 0, 0] + [
# region number
1,
# max volume in region
0.001])
mesh = build(mesh_info, max_volume=0.06,
volume_constraints=True, attributes=True)
print(("%d elements" % len(mesh.elements)))
mesh.write_vtk("box-in-box.vtk")
def make_boxmesh():
from meshpy.tet import MeshInfo, build
from meshpy.geometry import GeometryBuilder, Marker, make_box
geob = GeometryBuilder()
box_marker = Marker.FIRST_USER_MARKER
extent_small = 0.1 * numpy.ones(3, dtype=numpy.float64)
geob.add_geometry(*make_box(-extent_small, extent_small))
# make small "separator box" for region attribute
geob.add_geometry(
*make_box(-extent_small *
4, numpy.array([4, 0.4, 0.4], dtype=numpy.float64)))
geob.add_geometry(*make_box(numpy.array([-1, -1, -1], dtype=numpy.float64),
numpy.array([5, 1, 1], dtype=numpy.float64)))
mesh_info = MeshInfo()
geob.set(mesh_info)
mesh_info.set_holes([(0, 0, 0)])
# region attributes
mesh_info.regions.resize(1)
mesh_info.regions[0] = (
# point in region
list(extent_small * 2) + [
# region number
1,
# max volume in region
#0.0001
0.005
])
mesh = build(mesh_info,
max_volume=0.02,
volume_constraints=True,
attributes=True)
print("%d elements" % len(mesh.elements))
#mesh.write_vtk("box-in-box.vtk")
#print "done writing"
fvi2fm = mesh.face_vertex_indices_to_face_marker
face_marker_to_tag = {
box_marker: "noslip",
Marker.MINUS_X: "inflow",
Marker.PLUS_X: "outflow",
Marker.MINUS_Y: "inflow",
Marker.PLUS_Y: "inflow",
Marker.PLUS_Z: "inflow",
Marker.MINUS_Z: "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
return make_conformal_mesh(mesh.points, mesh.elements, bdry_tagger)
def make_box_mesh(a=(0, 0, 0), b=(1, 1, 1),
max_volume=None, periodicity=None,
boundary_tagger=(lambda fvi, el, fn, all_v: []),
return_meshpy_mesh=False):
"""Return a mesh for a brick from the origin to `dimensions`.
*max_volume* specifies the maximum volume for each tetrahedron.
*periodicity* is either None, or a triple of bools, indicating
whether periodic BCs are to be applied along that axis.
See :func:`make_conformal_mesh` for the meaning of *boundary_tagger*.
A few stock boundary tags are provided for easy application
of boundary conditions, namely plus_[xyz] and minus_[xyz] tag
the appropriate faces of the brick.
"""
def count(iterable):
result = 0
for i in iterable:
result += 1
return result
from meshpy.tet import MeshInfo, build
from meshpy.geometry import make_box
points, facets, _, facet_markers = make_box(a, b)
mesh_info = MeshInfo()
mesh_info.set_points(points)
mesh_info.set_facets(facets, facet_markers)
if periodicity is None:
periodicity = (False, False, False)
axes = ["x", "y", "z"]
per_count = count(p for p in periodicity if p)
marker_to_tag = {}
mesh_periodicity = []
periodic_tags = set()
if per_count:
mesh_info.pbc_groups.resize(per_count)
pbc_group_number = 0
for axis, axis_per in enumerate(periodicity):
minus_marker = 1+2*axis
plus_marker = 2+2*axis
minus_tag = "minus_"+axes[axis]
plus_tag = "plus_"+axes[axis]
marker_to_tag[minus_marker] = minus_tag
marker_to_tag[plus_marker] = plus_tag
if axis_per:
pbcg = mesh_info.pbc_groups[pbc_group_number]
pbc_group_number += 1
pbcg.facet_marker_1 = minus_marker
pbcg.facet_marker_2 = plus_marker
translation = [0, 0, 0]
translation[axis] = b[axis]-a[axis]
pbcg.set_transform(translation=translation)
mesh_periodicity.append((minus_tag, plus_tag))
periodic_tags.add(minus_tag)
periodic_tags.add(plus_tag)
else:
mesh_periodicity.append(None)
generated_mesh = build(mesh_info, max_volume=max_volume)
fvi2fm = generated_mesh.face_vertex_indices_to_face_marker
def wrapped_boundary_tagger(fvi, el, fn, all_v):
face_tag = marker_to_tag[fvi2fm[frozenset(fvi)]]
if face_tag in periodic_tags:
return [face_tag]
else:
return [face_tag] + boundary_tagger(fvi, el, fn, all_v)
from hedge.mesh import make_conformal_mesh_ext
from hedge.mesh.element import Tetrahedron
vertices = numpy.asarray(generated_mesh.points, dtype=float, order="C")
result = make_conformal_mesh_ext(
vertices,
[Tetrahedron(i, el_idx, vertices)
for i, el_idx in enumerate(generated_mesh.elements)],
wrapped_boundary_tagger,
periodicity=mesh_periodicity)
if return_meshpy_mesh:
return result, generated_mesh
else:
return result
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_wingmesh():
import numpy
from math import pi, cos, sin
from meshpy.tet import MeshInfo, build
from meshpy.geometry import GeometryBuilder, Marker, \
generate_extrusion, make_box
geob = GeometryBuilder()
profile_marker = Marker.FIRST_USER_MARKER
wing_length = 2
wing_subdiv = 5
rz_points = [
(0, -wing_length * 1.05),
(0.7, -wing_length * 1.05),
] + [(r, x) for x, r in zip(
numpy.linspace(-wing_length, 0, wing_subdiv, endpoint=False),
numpy.linspace(0.8, 1, wing_subdiv, endpoint=False))] + [(1, 0)] + [
(r, x) for x, r in zip(
numpy.linspace(wing_length, 0, wing_subdiv, endpoint=False),
numpy.linspace(0.8, 1, wing_subdiv, endpoint=False))
][::-1] + [(0.7, wing_length * 1.05), (0, wing_length * 1.05)]
from meshpy.naca import get_naca_points
geob.add_geometry(*generate_extrusion(
rz_points=rz_points,
base_shape=get_naca_points("0012", number_of_points=20),
ring_markers=(wing_subdiv * 2 + 4) * [profile_marker]))
def deform_wing(p):
x, y, z = p
return numpy.array([
x + 0.8 * abs(z / wing_length)**1.2,
y + 0.1 * abs(z / wing_length)**2, z
])
geob.apply_transform(deform_wing)
points, facets, facet_markers = make_box(
numpy.array([-1.5, -1, -wing_length - 1], dtype=numpy.float64),
numpy.array([3, 1, wing_length + 1], dtype=numpy.float64))
geob.add_geometry(points, facets, facet_markers=facet_markers)
mesh_info = MeshInfo()
geob.set(mesh_info)
mesh_info.set_holes([(0.5, 0, 0)])
mesh = build(mesh_info)
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.PLUS_Z: "inflow",
Marker.MINUS_Z: "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
return make_conformal_mesh(mesh.points, mesh.elements, bdry_tagger)
def make_boxmesh():
from meshpy.tet import MeshInfo, build
from meshpy.geometry import GeometryBuilder, Marker, make_box
geob = GeometryBuilder()
box_marker = Marker.FIRST_USER_MARKER
extent_small = 0.1*numpy.ones(3, dtype=numpy.float64)
geob.add_geometry(*make_box(-extent_small, extent_small))
# make small "separator box" for region attribute
geob.add_geometry(
*make_box(
-extent_small*4,
numpy.array([4, 0.4, 0.4], dtype=numpy.float64)))
geob.add_geometry(
*make_box(
numpy.array([-1, -1, -1], dtype=numpy.float64),
numpy.array([5, 1, 1], dtype=numpy.float64)))
mesh_info = MeshInfo()
geob.set(mesh_info)
mesh_info.set_holes([(0, 0, 0)])
# region attributes
mesh_info.regions.resize(1)
mesh_info.regions[0] = (
# point in region
list(extent_small*2) + [
# region number
1,
# max volume in region
#0.0001
0.005
])
mesh = build(mesh_info, max_volume=0.02,
volume_constraints=True, attributes=True)
print "%d elements" % len(mesh.elements)
#mesh.write_vtk("box-in-box.vtk")
#print "done writing"
fvi2fm = mesh.face_vertex_indices_to_face_marker
face_marker_to_tag = {
box_marker: "noslip",
Marker.MINUS_X: "inflow",
Marker.PLUS_X: "outflow",
Marker.MINUS_Y: "inflow",
Marker.PLUS_Y: "inflow",
Marker.PLUS_Z: "inflow",
Marker.MINUS_Z: "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
return make_conformal_mesh(
mesh.points, mesh.elements, bdry_tagger)
def make_wingmesh():
import numpy
from math import pi, cos, sin
from meshpy.tet import MeshInfo, build
from meshpy.geometry import GeometryBuilder, Marker, \
generate_extrusion, make_box
geob = GeometryBuilder()
profile_marker = Marker.FIRST_USER_MARKER
wing_length = 2
wing_subdiv = 5
rz_points = [
(0, -wing_length*1.05),
(0.7, -wing_length*1.05),
] + [
(r, x) for x, r in zip(
numpy.linspace(-wing_length, 0, wing_subdiv, endpoint=False),
numpy.linspace(0.8, 1, wing_subdiv, endpoint=False))
] + [(1,0)] + [
(r, x) for x, r in zip(
numpy.linspace(wing_length, 0, wing_subdiv, endpoint=False),
numpy.linspace(0.8, 1, wing_subdiv, endpoint=False))
][::-1] + [
(0.7, wing_length*1.05),
(0, wing_length*1.05)
]
from meshpy.naca import get_naca_points
geob.add_geometry(*generate_extrusion(
rz_points=rz_points,
base_shape=get_naca_points("0012", number_of_points=20),
ring_markers=(wing_subdiv*2+4)*[profile_marker]))
def deform_wing(p):
x, y, z = p
return numpy.array([
x + 0.8*abs(z/wing_length)** 1.2,
y + 0.1*abs(z/wing_length)**2,
z])
geob.apply_transform(deform_wing)
points, facets, facet_markers = make_box(
numpy.array([-1.5,-1,-wing_length-1], dtype=numpy.float64),
numpy.array([3,1,wing_length+1], dtype=numpy.float64))
geob.add_geometry(points, facets, facet_markers=facet_markers)
mesh_info = MeshInfo()
geob.set(mesh_info)
mesh_info.set_holes([(0.5,0,0)])
mesh = build(mesh_info)
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.PLUS_Z: "inflow",
Marker.MINUS_Z: "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
return make_conformal_mesh(mesh.points, mesh.elements, bdry_tagger)
def main():
import numpy
#from math import pi, cos, sin
from meshpy.tet import MeshInfo, build
from meshpy.geometry import GeometryBuilder, Marker, \
generate_extrusion, make_box
from meshpy.naca import get_naca_points
geob = GeometryBuilder()
box_marker = Marker.FIRST_USER_MARKER
wing_length = 2
wing_subdiv = 5
rz_points = [
(0, -wing_length*1.05),
(0.7, -wing_length*1.05),
] + [
(r, x) for x, r in zip(
numpy.linspace(-wing_length, 0, wing_subdiv, endpoint=False),
numpy.linspace(0.8, 1, wing_subdiv, endpoint=False))
] + [(1, 0)] + [
(r, x) for x, r in zip(
numpy.linspace(wing_length, 0, wing_subdiv, endpoint=False),
numpy.linspace(0.8, 1, wing_subdiv, endpoint=False))
][::-1] + [
(0.7, wing_length*1.05),
(0, wing_length*1.05)
]
geob.add_geometry(*generate_extrusion(
rz_points=rz_points,
base_shape=get_naca_points("0012", verbose=False, number_of_points=20),
ring_markers=(wing_subdiv*2+4)*[box_marker]))
from meshpy.tools import make_swizzle_matrix
swizzle_matrix = make_swizzle_matrix("z:x,y:y,x:z")
geob.apply_transform(lambda p: numpy.dot(swizzle_matrix, p))
def deform_wing(p):
x, y, z = p
return numpy.array([
x,
y + 0.1*abs(x/wing_length)**2,
z + 0.8*abs(x/wing_length) ** 1.2])
geob.apply_transform(deform_wing)
points, facets, _, facet_markers = make_box(
numpy.array([-wing_length-1, -1, -1.5]),
numpy.array([wing_length+1, 1, 3]))
geob.add_geometry(points, facets, facet_markers=facet_markers)
mesh_info = MeshInfo()
geob.set(mesh_info)
mesh_info.set_holes([(0, 0, 0.5)])
mesh = build(mesh_info)
print("%d elements" % len(mesh.elements))
mesh.write_vtk("airfoil3d.vtk")
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)
