def make_geom(length: float, lcar: float) -> Geometry:
# Barkley et al (2002, figure 3 a - c)
geom = Geometry()
points = []
for point in [[0, -1, 0],
[length, -1, 0],
[length, 1, 0],
[-1, 1, 0],
[-1, 0, 0],
[0, 0, 0]]:
points.append(geom.add_point(point, lcar))
lines = []
for termini in zip(points,
islice(cycle(points), 1, None)):
lines.append(geom.add_line(*termini))
for k, label in [([1], 'outlet'),
([2], 'ceiling'),
([3], 'inlet'),
([0, 4, 5], 'floor')]:
geom.add_physical(list(np.array(lines)[k]), label)
geom.add_physical(
geom.add_plane_surface(geom.add_line_loop(lines)), 'domain')
return geom
def make_mesh(halfheight: float, # mm
length: float,
thickness: float) -> MeshTri:
geom = Geometry()
points = []
lines = []
lcar = halfheight / 2**2
for xy in [(0., halfheight),
(0., -halfheight),
(length, -halfheight),
(length, halfheight),
(0., -halfheight - thickness),
(length, -halfheight - thickness)]:
points.append(geom.add_point([*xy, 0.], lcar))
lines.append(geom.add_line(*points[:2]))
geom.add_physical(lines[-1], 'fluid-inlet')
lines.append(geom.add_line(*points[1:3]))
lines.append(geom.add_line(*points[2:4]))
geom.add_physical(lines[-1], 'fluid-outlet')
lines.append(geom.add_line(points[3], points[0]))
geom.add_physical(geom.add_plane_surface(geom.add_line_loop(lines)),
'fluid')
lines.append(geom.add_line(points[1], points[4]))
geom.add_physical(lines[-1], 'solid-inlet')
lines.append(geom.add_line(*points[4:6]))
geom.add_physical(lines[-1], 'heated')
lines.append(geom.add_line(points[5], points[2]))
geom.add_physical(lines[-1], 'solid-outlet')
geom.add_physical(geom.add_plane_surface(geom.add_line_loop(
[*lines[-3:], -lines[1]])), 'solid')
return from_meshio(generate_mesh(geom, dim=2))
try:
m = from_file(mesh_file)
except FileNotFoundError:
from pygmsh import generate_mesh
from pygmsh.built_in import Geometry
geom = Geometry()
points = []
lines = []
points.append(geom.add_point([0., 0., 0.], .1))
points.append(geom.add_point([0., 1., 0.], .1))
points.append(geom.add_point([0., -1., 0.], .1))
lines.append(geom.add_circle_arc(points[2], points[0], points[1]))
geom.add_physical(lines[-1], 'contact')
lines.append(geom.add_line(points[1], points[2]))
geom.add_physical(lines[-1], 'dirichlet')
geom.add_physical(geom.add_plane_surface(geom.add_line_loop(lines)),
'domain')
m = from_meshio(generate_mesh(geom, dim=2))
to_file(m, mesh_file)
M = MeshLine(np.linspace(0, 1, 6)) * MeshLine(np.linspace(-1, 1, 10))
M.translate((1.0, 0.0))
M.refine()
# define elements and bases
e1 = ElementTriP2()
e = ElementVectorH1(e1)
E1 = ElementQuad2()
E = ElementVectorH1(E1)
lines = []
radii = [1., 2.]
lcar = .1
points.append(geom.add_point([0.] * 3, lcar)) # centre
for x in radii:
points.append(geom.add_point([x, 0., 0.], lcar))
for y in reversed(radii):
points.append(geom.add_point([0., y, 0.], lcar))
lines.append(geom.add_line(*points[1:3]))
geom.add_physical_line(lines[-1], 'ground')
lines.append(geom.add_circle_arc(points[2], points[0], points[3]))
lines.append(geom.add_line(points[3], points[4]))
geom.add_physical_line(lines[-1], 'positive')
lines.append(geom.add_circle_arc(points[4], points[0], points[1]))
geom.add_physical_surface(
geom.add_plane_surface(geom.add_line_loop(lines)), 'domain')
pts, cells, _, cell_data, field_data = generate_mesh(
geom, prune_vertices=False)
mesh = MeshTri(pts[:, :2].T, cells['triangle'].T)
boundaries = {bc:
np.unique(cells['line'][cell_data['line']['gmsh:physical'] ==
field_data[bc][0]])
for bc in field_data if field_data[bc][1] == 1}
elements = ElementTriP1()
basis = InteriorBasis(mesh, elements, MappingAffine(mesh), 2)
A = asm(laplace, basis)
b = asm(unit_load, basis)