def test_curl_implicit_FFF(basis, N, dealias, dtype):
c, d, b, r = basis(N, dealias, dtype)
Lz = b[2].bounds[1]
integ = lambda A: d3.Integrate(
d3.Integrate(d3.Integrate(A, c.coords[0]), c.coords[1]), c.coords[2])
tau1 = d.VectorField(c, name='tau1')
tau2 = d.Field(name='tau2')
# ABC vector field
k = 2 * np.pi * np.array([1 / Lx, 1 / Ly, 1 / Lz])
f = d.VectorField(c, bases=b)
f.preset_scales(dealias)
f['g'][0] = np.sin(k[2] * r[2]) + np.cos(k[1] * r[1])
f['g'][1] = np.sin(k[0] * r[0]) + np.cos(k[2] * r[2])
f['g'][2] = np.sin(k[1] * r[1]) + np.cos(k[0] * r[0])
g = d.VectorField(c, bases=b)
g.preset_scales(dealias)
g['g'][0] = k[2] * np.sin(k[2] * r[2]) + k[1] * np.cos(k[1] * r[1])
g['g'][1] = k[0] * np.sin(k[0] * r[0]) + k[2] * np.cos(k[2] * r[2])
g['g'][2] = k[1] * np.sin(k[1] * r[1]) + k[0] * np.cos(k[0] * r[0])
# Skew LBVP
u = d.VectorField(c, name='u', bases=b)
phi = d.Field(name='phi', bases=b)
problem = d3.LBVP([u, phi, tau1, tau2], namespace=locals())
problem.add_equation("curl(u) + grad(phi) + tau1 = g")
problem.add_equation("div(u) + tau2 = 0")
problem.add_equation("integ(phi) = 0")
problem.add_equation("integ(comp(u,index=0,coord=c['x'])) = 0")
problem.add_equation("integ(comp(u,index=0,coord=c['y'])) = 0")
problem.add_equation("integ(comp(u,index=0,coord=c['z'])) = 0")
solver = problem.build_solver()
solver.print_subproblem_ranks()
solver.solve()
assert np.allclose(u['c'], f['c'])
def test_curl_implicit_FFC(basis, N, dealias, dtype):
c, d, b, r = basis(N, dealias, dtype)
Lz = b[2].bounds[1]
lift_basis = b[2].clone_with(a=1 / 2, b=1 / 2) # First derivative basis
lift = lambda A, n: d3.Lift(A, lift_basis, n)
integ = lambda A: d3.Integrate(
d3.Integrate(d3.Integrate(A, c.coords[0]), c.coords[1]), c.coords[2])
tau1 = d.VectorField(c, name='tau1', bases=b[0:2])
tau2 = d.Field(name='tau2', bases=b[0:2])
# ABC vector field
k = 2 * np.pi * np.array([1 / Lx, 1 / Ly, 1 / Lz])
f = d.VectorField(c, bases=b)
f.preset_scales(dealias)
f['g'][0] = np.sin(k[2] * r[2]) + np.cos(k[1] * r[1])
f['g'][1] = np.sin(k[0] * r[0]) + np.cos(k[2] * r[2])
f['g'][2] = np.sin(k[1] * r[1]) + np.cos(k[0] * r[0])
g = d.VectorField(c, bases=b)
g.preset_scales(dealias)
g['g'][0] = k[2] * np.sin(k[2] * r[2]) + k[1] * np.cos(k[1] * r[1])
g['g'][1] = k[0] * np.sin(k[0] * r[0]) + k[2] * np.cos(k[2] * r[2])
g['g'][2] = k[1] * np.sin(k[1] * r[1]) + k[0] * np.cos(k[0] * r[0])
# Skew LBVP
u = d.VectorField(c, name='u', bases=b)
phi = d.Field(name='phi', bases=b)
problem = d3.LBVP([u, phi, tau1, tau2], namespace=locals())
problem.add_equation("curl(u) + grad(phi) + lift(tau1,-1) = g")
problem.add_equation("div(u) + lift(tau2,-1) = 0")
problem.add_equation("u(z=0) = f(z=0)")
problem.add_equation("phi(z=0) = 0")
solver = problem.build_solver()
solver.solve()
assert np.allclose(u['c'], f['c'])
def test_poisson_1d_fourier(Nx, dtype, matrix_coupling):
# Bases
coord = d3.Coordinate('x')
dist = d3.Distributor(coord, dtype=dtype)
if dtype == np.complex128:
basis = d3.ComplexFourier(coord, size=Nx, bounds=(0, 2 * np.pi))
elif dtype == np.float64:
basis = d3.RealFourier(coord, size=Nx, bounds=(0, 2 * np.pi))
x = basis.local_grid(1)
# Fields
u = dist.Field(name='u', bases=basis)
g = dist.Field(name='c')
# Substitutions
dx = lambda A: d3.Differentiate(A, coord)
integ = lambda A: d3.Integrate(A, coord)
F = dist.Field(bases=basis)
F['g'] = -np.sin(x)
# Problem
problem = d3.LBVP([u, g], namespace=locals())
problem.add_equation("dx(dx(u)) + g = F")
problem.add_equation("integ(u) = 0")
# Solver
solver = problem.build_solver(matrix_coupling=[matrix_coupling])
solver.solve()
# Check solution
u_true = np.sin(x)
assert np.allclose(u['g'], u_true)
τs2 = d.Field(name='τs2', bases=xb) τu1 = d.VectorField(c, name='τu1', bases=(xb, )) τu2 = d.VectorField(c, name='τu2', bases=(xb, )) # Parameters and operators div = lambda A: de.Divergence(A, index=0) lap = lambda A: de.Laplacian(A, c) grad = lambda A: de.Gradient(A, c) #curl = lambda A: de.operators.Curl(A) dot = lambda A, B: de.DotProduct(A, B) cross = lambda A, B: de.CrossProduct(A, B) trace = lambda A: de.Trace(A) trans = lambda A: de.TransposeComponents(A) dt = lambda A: de.TimeDerivative(A) integ = lambda A: de.Integrate(de.Integrate(A, 'x'), 'z') avg = lambda A: integ(A) / (Lx * Lz) #x_avg = lambda A: de.Integrate(A, 'x')/(Lx) x_avg = lambda A: de.Integrate(A, 'x') / (Lx) from dedalus.core.operators import Skew skew = lambda A: Skew(A) ex = d.VectorField(c, name='ex', bases=zb) ez = d.VectorField(c, name='ez', bases=zb) ex['g'][0] = 1 ez['g'][1] = 1 ez2 = d.VectorField(c, name='ez2', bases=zb2) ez2['g'][1] = 1 h0 = d.Field(name='h0', bases=zb)
τ_s1 = d.Field(name='τ_s1') τ_s2 = d.Field(name='τ_s2') τ_u1 = d.VectorField(c, name='τ_u1') τ_u2 = d.VectorField(c, name='τ_u2') # Parameters and operators div = lambda A: de.Divergence(A, index=0) lap = lambda A: de.Laplacian(A, c) grad = lambda A: de.Gradient(A, c) #curl = lambda A: de.operators.Curl(A) cross = lambda A, B: de.CrossProduct(A, B) trace = lambda A: de.Trace(A) trans = lambda A: de.TransposeComponents(A) dt = lambda A: de.TimeDerivative(A) integ = lambda A: de.Integrate(A, 'z') print(c.unit_vector_fields(d)) ez, = c.unit_vector_fields(d) # stress-free bcs e = grad(u) + trans(grad(u)) e.store_last = True viscous_terms = div(e) - 2 / 3 * grad(div(u)) trace_e = trace(e) trace_e.store_last = True Phi = 0.5 * trace(e @ e) - 1 / 3 * (trace_e * trace_e) structure = heated_polytrope(nz, γ, ε, n_h) h0 = d.Field(name='h0', bases=zb)
# Parameters and operators div = lambda A: de.Divergence(A, index=0) lap = lambda A: de.Laplacian(A, c) grad = lambda A: de.Gradient(A, c) curl = lambda A: de.Curl(A) dot = lambda A, B: de.DotProduct(A, B) cross = lambda A, B: de.CrossProduct(A, B) ddt = lambda A: de.TimeDerivative(A) trans = lambda A: de.TransposeComponents(A) radial = lambda A: de.RadialComponent(A) angular = lambda A: de.AngularComponent(A, index=1) trace = lambda A: de.Trace(A) power = lambda A, B: de.Power(A, B) lift_basis = b.clone_with(k=2) lift = lambda A, n: de.LiftTau(A, lift_basis, n) integ = lambda A: de.Integrate(A, c) azavg = lambda A: de.Average(A, c.coords[0]) shellavg = lambda A: de.Average(A, c.S2coordsys) avg = lambda A: de.Integrate(A, c) / (4 / 3 * np.pi * radius**3) # NCCs and variables of the problem ez = d.VectorField(c, name='ez', bases=b) ez['g'][1] = -np.sin(theta) ez['g'][2] = np.cos(theta) ez_g = de.Grid(ez).evaluate() ez_g.name = 'ez_g' r_cyl = d.VectorField(c, name='r_cyl', bases=b) r_cyl['g'][2] = r * np.sin(theta) r_cyl['g'][1] = -r * np.cos(theta)