def init_rayleigh_benard_benchmark(nx=64, ny=64, nz=16, closure=None):
Lx, Ly, Lz = 25.0, 25.0, 1.0 # Domain
# Parameters
Pr = 1.0 # Prandtl number
f = 0.0 # Coriolis parameter
κ = 1.0 # Thermal diffusivity
ε = 0.8 # Perturbation above criticality
a = 1e-3 # Noise amplitude for initial condition
# Constants
Ra_critical = 1707.762
Ra = Ra_critical + ε
ν = Pr*κ # Viscosity
Bz = -Ra*Pr # Unstable buoyancy gradient
# Construct model
model = dedaLES.BoussinesqChannelFlow(Lx=Lx, Ly=Ly, Lz=Lz, nx=nx, ny=ny, nz=nz,
f=f, ν=ν, κ=κ, B0=Bz*Lz, a=a, closure=closure)
model.set_bc("nopenetration", "top", "bottom")
model.set_bc("freeslip", "top", "bottom")
model.problem.add_bc("right(b) = B0")
model.problem.add_bc("left(b) = 0")
return model
import dedaLES
from dedaLES import mpiprint
# Basics
mpiprint('')
# 1. DNS of Navier-Stokes
dns_model = dedaLES.NavierStokesTriplyPeriodicFlow(nx=4, ny=4, nz=4, ν=1)
dns_model.build_solver()
mpiprint("\nDNS Navier-Stokes model built!\n")
# 2. LES of Navier-Stokes
les_model = dedaLES.NavierStokesTriplyPeriodicFlow(
nx=4, ny=4, nz=4, ν=1, closure=dedaLES.ConstantSmagorinsky())
les_model.build_solver()
mpiprint("\nLES Navier-Stokes model built!\n")
# 2. Boussinesq in a channel
bouss_model = dedaLES.BoussinesqChannelFlow(nx=4, ny=4, nz=4, ν=1, κ=0.1)
for bc in ["no penetration", "no slip", "no flux"]:
bouss_model.set_bc(bc, "top", "bottom")
bouss_model.build_solver()
mpiprint("\nBoussinesq model built!\n")
#dt_safety = params['dt_safety']
stats_cadence = 100
averages_cadence = 10
analysis_cadence = 100
run_time = day
max_writes = 100
if debug:
nx = ny = nz = 8
dt_cadence = np.inf
initial_dt = 1e-16
run_time = 10*initial_dt
stats_cadence = analysis_cadence = averages_cadence = 1
# Construct model
model = dedaLES.BoussinesqChannelFlow(Lx=Lx, Ly=Ly, Lz=Lz, nx=nx, ny=ny, nz=nz, ν=ν, κ=κ, closure=closure, case=int(case),
surface_buoyancy_flux=surface_buoyancy_flux, surface_bz=surface_bz, initial_N2=initial_N2)
Δx = Lx/nx
Δy = Ly/ny
Δz_min, Δz_max = dedaLES.grid_stats(model, 2)
Δmin = min(Δx, Δy, Δz_min)
logger.info("""\n
*** Convection into a linearly stratified fluid ***
Simulation info
---------------
surface heat_flux : {:.2e} W m⁻²
surface buoyancy flux : {:.2e} m² s⁻³
CFL_cadence = 10
stats_cadence = 100
analysis_cadence = 100
run_time = 2*hour
max_writes = 1000
if debug:
nx = ny = nz = 8
CFL_cadence = np.inf
initial_dt = 1e-16
run_time = 10*initial_dt
stats_cadence = analysis_cadence = 1
# Construct model
closure = None
model = dedaLES.BoussinesqChannelFlow(Lx=Lx, Ly=Ly, Lz=Lz, nx=nx, ny=ny, nz=nz, ν=ν, κ=κ, closure=closure,
surface_flux=surface_flux, surface_bz=surface_bz, initial_N2=initial_N2)
Δx = Lx/nx
Δy = Ly/ny
Δz_min, Δz_max = dedaLES.grid_stats(model, 2)
logger.info("""\n
*** Convection into a linearly stratified fluid ***
Simulation info
---------------
Q : {:.2e} m C s⁻¹
surface buoyancy flux : {:.2e} m² s⁻³
1/N : {:.2e} s
initial dt : {:.2e} s
Ra = 1e5 # Rayleigh number. Ra = Δb*L^3 / ν*κ = Δb*L^3*Pr / ν^2
Pr = 0.7 # Prandtl number
a = 1e-1 # Noise amplitude for initial condition
Δb = 1.0 # Buoyancy difference
# Calculated parameters
ν = np.sqrt(Pr / Ra) # Viscosity. ν = sqrt(Pr/Ra) with Lz=Δb=1
κ = ν / Pr # Thermal diffusivity
# Construct model
closure = None #dedaLES.AnisotropicMinimumDissipation() #dedaLES.ConstantSmagorinsky()
model = dedaLES.BoussinesqChannelFlow(Lx=1,
Ly=1,
Lz=6,
nx=64,
ny=64,
nz=32,
ν=ν,
κ=κ,
Δb=1,
closure=closure)
model.set_bc("no penetration", "top", "bottom")
model.set_bc("no slip", "top", "bottom")
model.problem.add_bc("right(b) = 0")
model.problem.add_bc("left(b) = Δb")
model.build_solver()
# Set initial condition: unstable buoyancy grad + random perturbations
noise = a * dedaLES.random_noise(
model.domain) * model.z * (model.Lz - model.z) / model.Lz**2,
nx = ny = 128 # Horizontal resolution
nz = 34 # Vertical resolution
Lx = Ly = 3840.0 # Domain horizontal extent [m]
Lz = 1020 # Domain vertical extent [m]
a = 1e-2 # Non-dimensional initial noise amplitude
dt = 90.0 # Timestep
# Calculated parameters
bz_surf = Q*α*g / (cP*ρ0*κ) # Unstable surface buoyancy gradient [s⁻²]
b_init = (Lz-h0)*bz_deep # Initial buoyancy at bottom of domain
b_noise = a*b_init # Noise amplitude for initial buoyancy condition
# Construct model
closure = dedaLES.ConstantSmagorinsky()
model = dedaLES.BoussinesqChannelFlow(Lx=Lx, Ly=Ly, Lz=Lz, nx=nx, ny=ny, nz=nz, ν=ν, κ=κ, zbottom=-Lz
bz_deep=bz_deep, bz_surf=bz_surf, tb=day/2, closure=closure, H=Lz)
# Boundary conditions
model.set_bc("no penetration", "top", "bottom")
model.set_bc("free slip", "top", "bottom")
model.set_tracer_gradient_bc("b", "top", gradient="bz_surf") #*tanh(t/tb)")
model.set_tracer_gradient_bc("b", "bottom", gradient="bz_deep")
model.build_solver()
# Initial condition
def smoothstep(z, d):
return 0.5*(1 + np.tanh(z/d))
b0 = bz_deep * (model.z + h0) * smoothstep(-model.z-h0, d)
from dedalus.extras import flow_tools
import dedaLES
logger = logging.getLogger(__name__)
a = 10.0
dt = 1e-4
nx = nz = 32
ny = 4
closure = dedaLES.AnisotropicMinimumDissipation()
#closure = dedaLES.ConstantSmagorinsky()
#closure = None
model = dedaLES.BoussinesqChannelFlow(nx=nx,
ny=ny,
nz=nz,
ν=1,
κ=1,
closure=closure)
model.set_bc("no penetration", "top", "bottom")
model.set_bc("no slip", "top", "bottom")
model.set_bc("no flux", "top", "bottom")
model.build_solver()
# Initial condition
fields = {}
for field in ['u', 'v', 'w', 'b']:
noise = dedaLES.random_noise(model.domain)
pert = a * noise * model.z * (1 - model.z)
fields[field] = pert
closure: {}\n\n""".format(Ra, nx, nz, closure_name))
##
## Spinup!
##
nx_spinup = int(nx / spinup_coarsening_factor)
ny_spinup = int(ny / spinup_coarsening_factor)
nz_spinup = int(nz / spinup_coarsening_factor)
spinup_model = dedaLES.BoussinesqChannelFlow(Lx=Lx,
Ly=Ly,
Lz=Lz,
nx=nx_spinup,
ny=ny_spinup,
nz=nz_spinup,
ν=ν,
κ=κ,
Δb=Δb,
closure=closure,
Ra=Ra)
set_rayleigh_benard_bcs(spinup_model)
spinup_model.build_solver(timestepper='SBDF3')
# Set initial condition: unstable buoyancy grad + random perturbations
noise = a * dedaLES.random_noise(
spinup_model.domain) * spinup_model.z * (Lz - spinup_model.z) / Lz**2,
spinup_model.set_fields(u=noise,
v=noise,
w=noise,
b=spinup_model.z / Lz - noise)
# Parameters
Pr = 1.0 # Prandtl number
f = 0.0 # Coriolis parameter
κ = 1.0 # Thermal diffusivity
ε = 0.8 # Perturbation above criticality
a = 1e-3 # Noise amplitude for initial condition
# Constants
Ra_critical = 1707.762
Ra = Ra_critical + ε
ν = Pr*κ # Viscosity
Bz = -Ra*Pr # Unstable buoyancy gradient
# Construct model
model = dedaLES.BoussinesqChannelFlow(Lx=Lx, Ly=Ly, Lz=Lz,
nx=nx, ny=ny, nz=nz,
ν=ν, κ=κ, B0=Bz*Lz, closure=dedaLES.ConstantSmagorinsky())
model.set_bc("nopenetration", "top", "bottom")
model.set_bc("freeslip", "top", "bottom")
model.problem.add_bc("right(b) = B0")
model.problem.add_bc("left(b) = 0")
model.build_solver()
# Random perturbations, initialized globally for same results in parallel
noise = dedaLES.random_noise(model.domain)
# Linear background + perturbations damped at walls
z = model.z
pert = a * noise * z * (Lz - z)
Δb = 1.0 # Buoyancy difference
# Calculated parameters
ν = np.sqrt(Δb * Pr * Lz**3 / Ra) # Viscosity. ν = sqrt(Pr/Ra) with Lz=Δb=1
κ = ν / Pr # Thermal diffusivity
# Construct model
#closure = dedaLES.AnisotropicMinimumDissipation()
#closure = dedaLES.ConstantSmagorinsky()
closure = None
model = dedaLES.BoussinesqChannelFlow(Lx=Lx,
Ly=Ly,
Lz=Lz,
nx=nx,
ny=ny,
nz=nz,
ν=ν,
κ=κ,
Δb=Δb,
closure=closure,
nu=ν,
V=Lx * Ly * Lz)
model.set_bc("no penetration", "top", "bottom")
model.set_bc("no slip", "top", "bottom")
model.problem.add_bc("right(b) = 0")
model.problem.add_bc("left(b) = Δb")
model.problem.substitutions[
'ε'] = "ν*(ux*ux + uy*uy + uz*uz + vx*vx + vy*vy + vz*vz + wx*wx + wy*wy + wz*wz)"
model.build_solver()
