lower_v = upper_v
upper_v = temp
# get an approximate geometry
print('Generating preconditioner')
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(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
e1 = np.abs(etx - itx).max()
e2 = np.abs(ety - ity).max()
err = max(e1, e2)
print('Error is: {:0.2e}'.format(err))
# now do this with radial coords using helper functions
solver = VectorHelper(ebdy)
etx, ety = solver.get_interface_traction_uvp(ru, rv, rp)
# get error in this computation
e1 = np.abs(etx - itx).max()
e2 = np.abs(ety - ity).max()
err = max(e1, e2)
print('Error is: {:0.2e}'.format(err))
# test out the method with the other coords
itr, itt = ebdy.convert_uv_to_rt(itx, ity)
rr, rt = ebdy.convert_uv_to_rt(ru, rv)
etr, ett = solver.get_interface_traction_rtp(rr, rt, rp)
e1 = np.abs(etr - itr).max()
e2 = np.abs(ett - itt).max()
err = max(e1, e2)
print('Error is: {:0.2e}'.format(err))
# test this on the boundary, instead
btx = btxx * ebdy.interface.normal_x + btxy * ebdy.interface.normal_y
bty = btxy * ebdy.interface.normal_x + btyy * ebdy.interface.normal_y
etx, ety = solver.get_boundary_traction_uvp(ru, rv, rp)
# get error in this computation
e1 = np.abs(etx - btx).max()
e2 = np.abs(ety - bty).max()
err = max(e1, e2)
fvr = fv_func(rr, tr)
lower_u = np.zeros(nb)
lower_v = np.zeros(nb)
upper_u = np.zeros(nb)
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)
