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) r_vec = d.VectorField(c, name='r_vec', bases=b) r_vec['g'][2] = r r_vec_g = de.Grid(r_vec).evaluate() structure = lane_emden(Nr, n_rho=n_rho, m=1.5, comm=MPI.COMM_SELF) bk2 = b.clone_with(k=2) bk1 = b.clone_with(k=1) T = d.Field(name='T', bases=b.radial_basis)
logger.info("Ra(z=0) = {:.2g}".format(Ra_bot[0][0]))
logger.info("Ra(z={:.1f}) = {:.2g}".format(Lz / 2, Ra_mid[0][0]))
logger.info("Ra(z={:.1f}) = {:.2g}".format(Lz, Ra_top[0][0]))
logger.info("Δs = {:.2g} ({:.2g} to {:.2g})".format(
s_bot[0][0] - s_top[0][0], s_bot[0][0], s_top[0][0]))
logger.info("Δθ = {:.2g} ({:.2g} to {:.2g})".format(
θ_bot[0][0] - θ_top[0][0], θ_bot[0][0], θ_top[0][0]))
logger.info("ΔT = {:.2g} ({:.2g} to {:.2g})".format(
T_bot[0][0] - T_top[0][0], T_bot[0][0], T_top[0][0]))
logger.info("ΔΥ = {:.2g} ({:.2g} to {:.2g})".format(
Υ_bot[0][0] - Υ_top[0][0], Υ_bot[0][0], Υ_top[0][0]))
scale = d.Field(name='scale', bases=zb2)
scale.require_scales(dealias)
scale['g'] = T0['g']
h0_grad_s0_g = de.Grid(h0 * grad(s0)).evaluate()
h0_grad_s0_g.name = 'h0_grad_s0_g'
h0_g = de.Grid(h0).evaluate()
h0_g.name = 'h0_g'
for ncc in [grad(Υ0), grad(T0), T0, np.exp(-Υ0), ρ0_inv]:
logger.info('scaled {:} has {:} terms'.format(ncc, (np.abs(
(scale * ncc).evaluate()['c']) > ncc_cutoff).sum()))
# Υ = ln(ρ), θ = ln(h)
problem = de.IVP([Υ, u, T, τu1, τu2, τs1, τs2])
problem.add_equation((scale * (dt(Υ) + trace(grad_u) + dot(u, grad(Υ0))),
scale * (-dot(u, grad(Υ)))))
problem.add_equation((scale*(dt(u) + grad(T) \
+ T*grad(Υ0) + T0*grad(Υ)
- μ*ρ0_inv*viscous_terms) \
h0 = d.Field(name='h0', bases=zb) h0['g'] = h_bot + z * h_slope #(Lz+1)-z θ0 = np.log(h0).evaluate() Υ0 = (m_ad * θ0).evaluate() Υ0.name = 'Υ0' ρ0 = np.exp(Υ0).evaluate() ρ0.name = 'ρ0' ρ0_inv = np.exp(-Υ0).evaluate() ρ0_inv.name = '1/ρ0' grad_h0 = grad(h0).evaluate() grad_θ0 = grad(θ0).evaluate() grad_Υ0 = grad(Υ0).evaluate() h0_g = de.Grid(h0).evaluate() h0_inv_g = de.Grid(1 / h0).evaluate() grad_h0_g = de.Grid(grad(h0)).evaluate() ρ0_g = de.Grid(ρ0).evaluate() ρ0_grad_h0_g = de.Grid(ρ0 * grad(h0)).evaluate() ρ0_h0_g = de.Grid(ρ0 * h0).evaluate() source = d.Field(name='source', bases=b) source.change_scales(dealias) source['g'] = (ε * scrR / Pr / h0).evaluate()['g'] source_g = de.Grid(source).evaluate() Υ_bot = Υ0(z=0).evaluate()['g'] Υ_top = Υ0(z=Lz).evaluate()['g']