# convert (u,v) to (r,t)
fr, ft = ebdy.convert_uv_to_rt(fu_radial, fv_radial)
lr, lt = ebdy.convert_uv_to_rt(lower_u, lower_v)
ur, ut = ebdy.convert_uv_to_rt(upper_u, upper_v)
re_radial, te_radial, pe_radial = solver.solve(RAG,
fr,
ft,
lr,
lt,
ur,
ut,
verbose=True,
tol=1e-14,
maxiter=200,
restart=50)
ue_radial, ve_radial = ebdy.convert_rt_to_uv(re_radial, te_radial)
# get error
error_u = np.abs(ue_radial - ua_radial).max()
error_v = np.abs(ve_radial - va_radial).max()
error_p = np.abs(pe_radial - pa_radial).max()
print(' Error, u: {:0.2e}'.format(error_u))
print(' Error, v: {:0.2e}'.format(error_v))
print(' Error, p: {:0.2e}'.format(error_p))
# plot the errors
fig, ax = plt.subplots()
clf = ax.pcolormesh(ebdy.radial_x,
ebdy.radial_y,
np.abs(ue_radial - ua_radial),
norm=mpl.colors.LogNorm())
ax.plot(ebdy.bdy.x, ebdy.bdy.y, color='black', label='boundary', linewidth=3)
upper_v = np.zeros(nb)
# solve radial stokes problem
AAG = ApproximateAnnularGeometry(nb, M, ebdy.radial_width, ebdy.approximate_radius)
# construct the preconditioner (for Dirichlet BC)
solver = AnnularStokesSolver(AAG, 1.0)
print('Solving')
# get the real geometry
sp = ebdy.bdy.speed if interior else ebdy.interface.speed
cur = ebdy.bdy.curvature if interior else ebdy.interface.curvature
RAG = RealAnnularGeometry(sp, cur, AAG)
# convert (u,v) to (r,t)
fr, ft = ebdy.convert_uv_to_rt(fur, fvr)
lr, lt = ebdy.convert_uv_to_rt(lower_u, lower_v)
ur, ut = ebdy.convert_uv_to_rt(upper_u, upper_v)
re_radial, te_radial, pe_radial = solver.solve(RAG, fr, ft, lr, lt, ur, ut, verbose=False, tol=1e-12)
ur, vr = ebdy.convert_rt_to_uv(re_radial, te_radial)
U = np.hypot(ur, vr).max()
u = ur/U
v = vr/U
# get derivatives of the velocity field
ux, uy = ebdy.radial_grid_derivatives(u)
vx, vy = ebdy.radial_grid_derivatives(v)
# get a function c to test with
c_func = lambda x, y: np.exp(np.cos(x))*np.sin(y)
c = c_func(xr, yr)
################################################################################
# test advectors
dt = 0.01