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))
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(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(lines[-1], 'positive')
lines.append(geom.add_circle_arc(points[4], points[0], points[1]))
geom.add_physical(geom.add_plane_surface(geom.add_line_loop(lines)), 'domain')
mesh = from_meshio(generate_mesh(geom, dim=2))
elements = ElementTriP2()
basis = InteriorBasis(mesh, elements)
A = asm(laplace, basis)
boundary_dofs = basis.get_dofs(mesh.boundaries)
interior_dofs = basis.complement_dofs(boundary_dofs)
u = np.zeros(basis.N)
u[boundary_dofs['positive'].all()] = 1.
u = solve(*condense(A, 0.*u, u, interior_dofs))
M = asm(mass, basis)
u_exact = 2 * np.arctan2(*basis.doflocs[::-1]) / np.pi
u_error = u - u_exact