print(f'v={v} c')
if __name__ == '__main__':
from os.path import splitext
from sys import argv
from skfem.visuals.matplotlib import plot, savefig
import matplotlib.pyplot as plt
B_x = projection(A, global_basis, global_basis, 1)
B_y = -projection(A, global_basis, global_basis, 0)
E_x = -projection(U, global_basis, global_basis, 0)
E_y = -projection(U, global_basis, global_basis, 1)
fig = plt.figure(figsize=(11.52, 5.12))
ax1 = plt.subplot(1, 2, 1)
plot(global_basis, np.sqrt(B_x**2 + B_y**2), ax=ax1, colorbar=True)
ax1.set_title('Magnetic flux density (Tesla)')
ax1.set_aspect('equal')
ax1.set_yticks([])
ax2 = plt.subplot(1, 2, 2)
plot(global_basis, np.sqrt(E_x**2 + E_y**2), ax=ax2, colorbar=True)
ax2.set_title('Electric field strength (V/m)')
ax2.set_aspect('equal')
ax2.set_yticks([])
savefig(splitext(argv[0])[0] + '_solution.png')
exit_interface_temperature = {
'skfem':
temperature[np.intersect1d(dofs['fluid-outlet'].all(),
dofs['solid-outlet'].all())[0]],
'exact':
exact(length, -1.)
}
if __name__ == '__main__':
from pathlib import Path
from skfem.visuals.matplotlib import plot, savefig
plot(mesh, temperature)
savefig(Path(__file__).with_suffix('.png'),
bbox_inches='tight',
pad_inches=0)
fig, ax = subplots()
ax.set_title('transverse temperature profiles')
y = {label: mesh.p[1, d.nodal['u']] for label, d in dofs.items()}
ii = {label: np.argsort(yy) for label, yy in y.items()}
y['exact'] = np.linspace(min(y['solid-inlet']), max(y['fluid-inlet']))
for port, saturation, linestyle in [('inlet', '', '--'),
('outlet', 'dark', '-')]:
for phase, hue, marker in [('fluid', 'green', 'x'),
('solid', 'red', '+')]:
color = saturation + hue
label = f'{phase}-{port}'
psi = solve(*condense(A, vorticity, D=basis['psi'].find_dofs()['floor'].all()))
if __name__ == '__main__':
from functools import partial
from os.path import splitext
from sys import argv
from matplotlib.tri import Triangulation
from skfem.visuals.matplotlib import plot, savefig
name = splitext(argv[0])[0]
plot(mesh, pressure)
savefig(f'{name}-pressure.png', bbox_inches='tight', pad_inches=0)
mesh.save(f'{name}-velocity.vtk',
{'velocity': velocity[basis['u'].nodal_dofs].T})
fig, ax = subplots()
ax.plot(
*mesh.p[:,
mesh.facets[:,
np.concatenate(list(mesh.boundaries.values()))]],
color='k')
n_streamlines = 11
contour = partial(ax.tricontour,
Triangulation(*mesh.p, mesh.t.T),
psi[basis['psi'].nodal_dofs.flatten()],
from matplotlib.tri import Triangulation
from skfem.visuals.matplotlib import plot, draw, savefig
name = splitext(argv[0])[0]
mesh.save(f'{name}_velocity.vtk',
{'velocity': velocity[basis['u'].nodal_dofs].T})
print(basis['psi'].interpolator(psi)(np.zeros((2, 1)))[0],
'(cf. exact 1/64)')
print(
basis['p'].interpolator(pressure)(np.array([[-0.5, 0.5], [0.5, 0.5]])),
'(cf. exact -/+ 1/8)')
ax = draw(mesh)
plot(basis['p'], pressure, ax=ax)
savefig(f'{name}_pressure.png')
ax = draw(mesh)
velocity1 = velocity[basis['u'].nodal_dofs]
ax.quiver(*mesh.p, *velocity1, mesh.p[0, :]) # colour by buoyancy
savefig(f'{name}_velocity.png')
ax = draw(mesh)
ax.tricontour(Triangulation(*mesh.p, mesh.t.T),
psi[basis['psi'].nodal_dofs.flatten()])
savefig(f'{name}_stream-function.png')
@BilinearForm
def hdg(u, ut, v, vt, w):
from skfem.helpers import grad, dot
# outwards normal
n = w.n * (-1.)**w.idx[0]
return dot(n, grad(u)) * (vt - v) + dot(n, grad(v)) * (ut - u)\
+ 1e1 / w.h * (ut - u) * (vt - v)
@LinearForm
def load(v, vt, w):
return 1. * v
A = asm(laplace, ibasis) + asm(hdg, tbasis)
f = asm(load, ibasis)
y = solve(*condense(A, f, D=ibasis.get_dofs()))
(u1, ibasis1), (u2, ibasis2) = ibasis.split(y)
if __name__ == '__main__':
from os.path import splitext
from sys import argv
from skfem.visuals.matplotlib import plot, savefig
plot(ibasis1, u1, Nrefs=3, colorbar=True, shading='gouraud')
savefig(splitext(argv[0])[0] + '_p1dg.png')
plot(ibasis2, u2, Nrefs=4, colorbar=True, shading='gouraud')
savefig(splitext(argv[0])[0] + '_skeleton.png')
