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internal_tide.jl
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internal_tide.jl
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using Printf
using CUDA
using Oceananigans
using Oceananigans.TurbulenceClosures: VerticallyImplicitTimeDiscretization
using Oceananigans.MultiRegion
using Oceananigans.ImmersedBoundaries: ImmersedBoundaryGrid, GridFittedBoundary
using LinearAlgebra
using Adapt
function boundary_clustered(N, L, ini)
Δz(k) = k < N / 2 + 1 ? 2 / (N - 1) * (k - 1) + 1 : - 2 / (N - 1) * (k - N) + 1
z_faces = zeros(N+1)
for k = 2:N+1
z_faces[k] = z_faces[k-1] + Δz(k-1)
end
z_faces = z_faces ./ z_faces[end] .* L .+ ini
return z_faces
end
function center_clustered(N, L, ini)
Δz(k) = k < N / 2 + 1 ? 2 / (N - 1) * (k - 1) + 1 : - 2 / (N - 1) * (k - N) + 1
z_faces = zeros(N+1)
for k = 2:N+1
z_faces[k] = z_faces[k-1] + 3 - Δz(k-1)
end
z_faces = z_faces ./ z_faces[end] .* L .+ ini
return z_faces
end
grid = RectilinearGrid(GPU(), size=(512, 256),
x = (-10, 10),
z = (0, 5),
topology = (Periodic, Flat, Bounded))
# Gaussian bump of width "1"
bump(x, y, z) = z < exp(-x^2)
@inline show_name(t) = t() isa ExplicitFreeSurface ? "explicit" : "implicit"
grid_with_bump = ImmersedBoundaryGrid(grid, GridFittedBoundary(bump))
mrg_with_bump = MultiRegionGrid(grid_with_bump, partition=XPartition(2), devices=(0, 1))
# Tidal forcing
tidal_forcing(x, y, z, t) = 1e-4 * cos(t)
for free_surface in (ExplicitFreeSurface, )
model = HydrostaticFreeSurfaceModel(grid = grid_with_bump,
momentum_advection = CenteredSecondOrder(),
free_surface = free_surface(gravitational_acceleration=10),
closure = ScalarDiffusivity(VerticallyImplicitTimeDiscretization(), ν=1e-2, κ=1e-2),
tracers = :b,
buoyancy = BuoyancyTracer(),
coriolis = FPlane(f=sqrt(0.5)),
forcing = (u = tidal_forcing,))
# Linear stratification
set!(model, b = (x, y, z) -> 4 * z)
progress_message(s) = @info @sprintf("[%.2f%%], iteration: %d, time: %.3f, max|w|: %.2e",
100 * s.model.clock.time / s.stop_time, s.model.clock.iteration,
s.model.clock.time, maximum(abs, model.velocities.w))
gravity_wave_speed = sqrt(model.free_surface.gravitational_acceleration * grid.Lz)
Δt = CUDA.@allowscalar 0.1 * minimum(grid.Δxᶜᵃᵃ) / gravity_wave_speed
simulation = Simulation(model, Δt = Δt, stop_time = 50000Δt)
simulation.output_writers[:fields] = JLD2OutputWriter(model, merge(model.velocities, model.tracers),
schedule = TimeInterval(0.1),
filename = "internal_tide_$(show_name(time_stepper))",
init = serialize_grid,
overwrite_existing = true)
simulation.callbacks[:progress] = Callback(progress_message, IterationInterval(10))
run!(simulation)
@info """
Simulation complete.
Output: $(abspath(simulation.output_writers[:fields].filepath))
"""
end
using JLD2
using Plots
ENV["GKSwstype"] = "100"
function nice_divergent_levels(c, clim; nlevels=20)
levels = range(-clim, stop=clim, length=nlevels)
cmax = maximum(abs, c)
clim < cmax && (levels = vcat([-cmax], levels, [cmax]))
return (-clim, clim), levels
end
function nan_solid(x, z, u, bump)
Nx, Nz = size(u)
x2 = reshape(x, Nx, 1)
z2 = reshape(z, 1, Nz)
u[bump.(x2, 0, z2)] .= NaN
return nothing
end
function visualize_internal_tide_simulation(prefix)
filename = prefix * ".jld2"
file = jldopen(filename)
grid = adapt(CPU(), file["serialized/grid"])
bump(x, y, z) = z < exp(-x^2)
xu, yu, zu = nodes((Face, Center, Center), grid)
xw, yw, zw = nodes((Center, Center, Face), grid)
xb, yb, zb = nodes((Center, Center, Center), grid)
b₀ = file["timeseries/b/0"][:, 1, :]
iterations = parse.(Int, keys(file["timeseries/t"]))
anim = @animate for (i, iter) in enumerate(iterations)
@info "Plotting iteration $iter of $(iterations[end])..."
u = file["timeseries/u/$iter"][:, 1, :]
w = file["timeseries/w/$iter"][:, 1, :]
b = file["timeseries/b/$iter"][:, 1, :]
t = file["timeseries/t/$iter"]
b′ = b .- b₀
wlims, wlevels = nice_divergent_levels(w, 1e-4)
ulims, ulevels = nice_divergent_levels(u, 1e-3)
blims, blevels = nice_divergent_levels(b′, 1e-4)
nan_solid(xu, zu, u, bump)
nan_solid(xw, zw, w, bump)
nan_solid(xb, zb, b, bump)
u_title = @sprintf("x velocity, t = %.2f", t)
u_plot = contourf(xu, zu, u'; title = u_title, color = :balance, aspectratio = :equal, linewidth = 0, levels = ulevels, clims = ulims)
w_plot = contourf(xw, zw, w'; title = "z velocity", color = :balance, aspectratio = :equal, linewidth = 0, levels = wlevels, clims = wlims)
b_plot = contourf(xb, zb, b′'; title = "buoyancy perturbation", color = :balance, aspectratio = :equal, linewidth = 0, levels = blevels, clims = blims)
plot(u_plot, w_plot, b_plot, layout = (3, 1), size = (1200, 1200))
end
mp4(anim, prefix * ".mp4", fps = 16)
close(file)
end
function plot_implicit_explicit_difference(filename)
file_explicit = jldopen(filename * "_explicit.jld2")
file_implicit = jldopen(filename * "_implicit.jld2")
iterations = parse.(Int, keys(file_explicit["timeseries/t"]))
comparison_u = zeros(length(iterations))
comparison_w = zeros(length(iterations))
comparison_b = zeros(length(iterations))
for (i, iter) in enumerate(iterations)
u_explicit = file_explicit["timeseries/u/$iter"][:, 1, :]
w_explicit = file_explicit["timeseries/w/$iter"][:, 1, :]
b_explicit = file_explicit["timeseries/b/$iter"][:, 1, :]
u_implicit = file_implicit["timeseries/u/$iter"][:, 1, :]
w_implicit = file_implicit["timeseries/w/$iter"][:, 1, :]
b_implicit = file_implicit["timeseries/b/$iter"][:, 1, :]
comparison_u[i] = norm(u_explicit .- u_implicit)
comparison_w[i] = norm(w_explicit .- w_implicit)
comparison_b[i] = norm(b_explicit .- b_implicit)
end
kwargs = (linewidth = 2, foreground_color_legend = nothing, legendfontsize = 12, legend = :right, grid = false,
xtickfontsize = 12, ytickfontsize=12, xlabel = "time", ylabel = "norm of difference")
plot(iterations, comparison_u, label = "u"; kwargs...)
plot!(iterations, comparison_w, label = "w"; kwargs...)
plot!(iterations, comparison_b, label = "b"; kwargs...)
savefig(filename * "_comparison_implicit_explicit.png")
close(file_explicit)
close(file_implicit)
end
visualize_internal_tide_simulation("internal_tide_explicit")
visualize_internal_tide_simulation("internal_tide_implicit")
plot_implicit_explicit_difference("internal_tide")