Decaying Homogeneous Isotropic Turbulence - 2D

In this example we consider decaying homogeneous isotropic turbulence, similar to the cases considered in [1] and [2]. The initial velocity field is created randomly, but with a specific energy spectrum. Due to viscous dissipation, the turbulent features eventually group to form larger visible eddies.

using CairoMakie
using IncompressibleNavierStokes

Output directory

output = "output/DecayingTurbulence2D"

"output/DecayingTurbulence2D"

Floating point precision

T = Float64

Float64

Array type

ArrayType = Array
# using CUDA; ArrayType = CuArray
# using AMDGPU; ArrayType = ROCArray
# using oneAPI; ArrayType = oneArray
# using Metal; ArrayType = MtlArray

Array

Viscosity model

Re = T(10_000)

10000.0

A 2D grid is a Cartesian product of two vectors

n = 256
lims = T(0), T(1)
x = LinRange(lims..., n + 1), LinRange(lims..., n + 1)

(LinRange{Float64}(0.0, 1.0, 257), LinRange{Float64}(0.0, 1.0, 257))

Build setup and assemble operators

setup = Setup(x...; Re, ArrayType);

Create random initial conditions

ustart = random_field(setup, T(0));

Solve unsteady problem

state, outputs = solve_unsteady(;
    setup,
    ustart,
    tlims = (T(0), T(1)),
    Δt = T(1e-3),
    processors = (
        # rtp = realtimeplotter(; setup, nupdate = 1),
        ehist = realtimeplotter(;
            setup,
            plot = energy_history_plot,
            nupdate = 10,
            displayfig = false,
        ),
        espec = realtimeplotter(; setup, plot = energy_spectrum_plot, nupdate = 10),
        # anim = animator(; setup, path = "$output/solution.mkv", nupdate = 20),
        # vtk = vtk_writer(; setup, nupdate = 10, dir = output, filename = "solution"),
        # field = fieldsaver(; setup, nupdate = 10),
        log = timelogger(; nupdate = 100),
    ),
);

Iteration 100	t = 0.1	Δt = 0.001	umax = 3.39444
Iteration 200	t = 0.2	Δt = 0.001	umax = 3.21724
Iteration 300	t = 0.3	Δt = 0.001	umax = 2.96
Iteration 400	t = 0.4	Δt = 0.001	umax = 2.73372
Iteration 500	t = 0.5	Δt = 0.001	umax = 2.98374
Iteration 600	t = 0.6	Δt = 0.001	umax = 2.78184
Iteration 700	t = 0.7	Δt = 0.001	umax = 2.78671
Iteration 800	t = 0.8	Δt = 0.001	umax = 3.32722
Iteration 900	t = 0.9	Δt = 0.001	umax = 3.37924
Iteration 1000	t = 1	Δt = 0.001	umax = 3.40912

Post-process

We may visualize or export the computed fields (u, p)

Energy history

outputs.ehist

Energy spectrum

outputs.espec

Export to VTK

save_vtk(setup, state.u, state.t, "$output/solution")

1-element Vector{String}:
 "output/DecayingTurbulence2D/solution.vtr"

Plot field

fieldplot(state; setup)

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