def test_disk_bessel_zeros(Nphi, Nr, m, radius, dtype):
# Bases
c = coords.PolarCoordinates('phi', 'r')
d = distributor.Distributor((c, ))
b = basis.DiskBasis(c, (Nphi, Nr), radius=radius, dtype=dtype)
b_S1 = b.S1_basis()
phi, r = b.local_grids((1, 1))
# Fields
f = field.Field(dist=d, bases=(b, ), dtype=dtype)
τ_f = field.Field(dist=d, bases=(b_S1, ), dtype=dtype)
k2 = field.Field(name='k2', dist=d, dtype=dtype)
# Parameters and operators
lap = lambda A: operators.Laplacian(A, c)
Lift = lambda A: operators.Lift(A, b, -1)
# Bessel equation: k^2*f + lap(f) = 0
problem = problems.EVP([f, τ_f], k2)
problem.add_equation((k2 * f + lap(f) + Lift(τ_f), 0))
problem.add_equation((f(r=radius), 0))
# Solver
solver = solvers.EigenvalueSolver(problem)
print(solver.subproblems[0].group)
for sp in solver.subproblems:
if sp.group[0] == m:
break
else:
raise ValueError("Could not find subproblem with m = %i" % m)
solver.solve_dense(sp)
# Compare eigenvalues
n_compare = 5
selected_eigenvalues = np.sort(solver.eigenvalues)[:n_compare]
analytic_eigenvalues = (spec.jn_zeros(m, n_compare) / radius)**2
assert np.allclose(selected_eigenvalues, analytic_eigenvalues)
def build_disk(Nphi, Nr, dealias, dtype):
c = coords.PolarCoordinates('phi', 'r')
d = distributor.Distributor((c, ))
b = basis.DiskBasis(c, (Nphi, Nr),
radius=radius_disk,
dealias=(dealias, dealias),
dtype=dtype)
phi, r = b.local_grids()
x, y = c.cartesian(phi, r)
return c, d, b, phi, r, x, y
def build_disk(Nphi, Nr, radius, alpha, k, dealias, dtype):
c = coords.PolarCoordinates('phi', 'r')
d = distributor.Distributor((c, ))
b = basis.DiskBasis(c, (Nphi, Nr),
dtype=dtype,
radius=radius,
alpha=alpha,
k=k,
dealias=(dealias, dealias))
return c, d, b
def build_disk(Nphi, Nr, radius, dealias, dtype=np.float64, grid_scale=1):
c = coords.PolarCoordinates('phi', 'r')
d = distributor.Distributor((c, ))
dealias_tuple = (dealias, dealias)
b = basis.DiskBasis(c, (Nphi, Nr),
radius=radius,
dealias=dealias_tuple,
dtype=dtype)
grid_scale_tuple = (grid_scale, grid_scale)
phi, r = b.local_grids(grid_scale_tuple)
x, y = c.cartesian(phi, r)
return c, d, b, phi, r, x, y
dtype = np.float64
# Parameters
radius = 1
Mmax = 31
Nmax = 31
Ampl = 1e-6
Pr = 1
Ra = 1e6
nu = np.sqrt(Pr/Ra)
kappa = nu/Pr
# Bases
c = coords.PolarCoordinates('phi', 'r')
d = distributor.Distributor((c,))
b = basis.DiskBasis(c, (Mmax+1, Nmax+1), radius=radius, dtype=dtype)
cb = b.S1_basis(radius=radius)
phi, r = b.local_grids((1, 1, 1))
# Fields
u = field.Field(dist=d, bases=(b,), tensorsig=(c,),dtype=dtype)
T = field.Field(dist=d, bases=(b,), dtype=dtype)
p = field.Field(dist=d, bases=(b,), dtype=dtype)
tau_u = field.Field(dist=d, bases=(cb,), tensorsig=(c,), dtype=dtype)
tau_T = field.Field(dist=d, bases=(cb,), dtype=dtype)
# parameters
S = field.Field(dist=d, bases=(b,), dtype=dtype)
g = field.Field(dist=d, bases=(b,), tensorsig=(c,), dtype=dtype)