diff --git a/examples/fluid/vortex_street_2d.jl b/examples/fluid/vortex_street_2d.jl new file mode 100644 index 0000000000..8eb3289bbf --- /dev/null +++ b/examples/fluid/vortex_street_2d.jl @@ -0,0 +1,158 @@ +# ========================================================================================== +# 2D Vortex Street +# +# Flow past a circular cylinder (vortex street), Tafuni et al. (2018). +# Other literature using this validation: +# Vacandio et al. (2013), Marrone et al. (2013), Calhoun (2002), Liu et al. (1998) +# ========================================================================================== +using TrixiParticles +using OrdinaryDiffEq + +# ========================================================================================== +# ==== Resolution +factor_d = 0.1 # Resolution in the paper is `0.01` (5M particles) + +cylinder_diameter = 0.1 +particle_spacing = factor_d * cylinder_diameter + +# Make sure that the kernel support of fluid particles at a boundary is always fully sampled +boundary_layers = 4 + +# Make sure that the kernel support of fluid particles at an open boundary is always +# fully sampled. +# Note: Due to the dynamics at the inlets and outlets of open boundaries, +# it is recommended to use `open_boundary_layers > boundary_layers` +open_boundary_layers = 8 + +# ========================================================================================== +# ==== Experiment Setup +tspan = (0.0, 4.0) + +# Boundary geometry and initial fluid particle positions +# For better results the domain_size should be increased to +# domain_size = (25 * cylinder_diameter, 20 * cylinder_diameter) +domain_size = (20 * cylinder_diameter, 10 * cylinder_diameter) + +flow_direction = [1.0, 0.0] +reynolds_number = 200 +prescribed_velocity = 1.0 +fluid_density = 1000.0 +# Maximum velocity observed in the vortex street is typically around 1.5 +v_max = 1.5 +sound_speed = 10 * v_max + +boundary_size = (domain_size[1] + 2 * particle_spacing * open_boundary_layers, + domain_size[2]) + +pipe = RectangularTank(particle_spacing, domain_size, boundary_size, fluid_density, + n_layers=boundary_layers, velocity=[prescribed_velocity, 0.0], + faces=(false, false, true, true)) + +# Shift pipe walls in negative x-direction for the inflow +pipe.boundary.coordinates[1, :] .-= particle_spacing * open_boundary_layers + +n_buffer_particles = 20 * pipe.n_particles_per_dimension[2]^(ndims(pipe.fluid) - 1) + +cylinder_center = (5 * cylinder_diameter, domain_size[2] / 2) +cylinder = SphereShape(particle_spacing, cylinder_diameter / 2, + cylinder_center, fluid_density, sphere_type=RoundSphere()) + +fluid = setdiff(pipe.fluid, cylinder) + +# ========================================================================================== +# ==== Fluid +smoothing_length = 1.5 * particle_spacing +smoothing_kernel = WendlandC2Kernel{2}() + +fluid_density_calculator = ContinuityDensity() + +kinematic_viscosity = prescribed_velocity * cylinder_diameter / reynolds_number + +state_equation = StateEquationCole(; sound_speed, reference_density=fluid_density, + exponent=1) +viscosity = ViscosityAdami(nu=kinematic_viscosity) +density_diffusion = DensityDiffusionMolteniColagrossi(delta=0.1) + +# shifting_technique = TransportVelocityAdami(background_pressure=5 * fluid_density * +# sound_speed^2) + +shifting_technique = ParticleShiftingTechnique(; sound_speed_factor=0.2, v_max_factor=0) + +fluid_system = WeaklyCompressibleSPHSystem(fluid, fluid_density_calculator, + state_equation, smoothing_kernel, + density_diffusion=density_diffusion, + smoothing_length, viscosity=viscosity, + pressure_acceleration=tensile_instability_control, + shifting_technique=shifting_technique, + buffer_size=n_buffer_particles) + +# ========================================================================================== +# ==== Open Boundary +open_boundary_model = BoundaryModelMirroringTafuni(; mirror_method=ZerothOrderMirroring()) +# open_boundary_model = BoundaryModelDynamicalPressureZhang() + +inflow = BoundaryZone(; boundary_face=([0.0, 0.0], [0.0, domain_size[2]]), + face_normal=flow_direction, open_boundary_layers, + reference_velocity=(pos, t) -> SVector(prescribed_velocity, 0.0), + density=fluid_density, particle_spacing) + +outflow = BoundaryZone(; + boundary_face=([pipe.fluid_size[1], 0.0], + [pipe.fluid_size[1], pipe.fluid_size[2]]), + face_normal=(-flow_direction), particle_spacing, + density=fluid_density, open_boundary_layers) + +# While the outlet velocity is not explicitly prescribed, +# initializing it in the x-direction helps to suppress initial pressure waves. +outflow.initial_condition.velocity[1, :] .= prescribed_velocity + +open_boundary = OpenBoundarySystem(inflow, outflow; fluid_system, + boundary_model=open_boundary_model, + pressure_acceleration=TrixiParticles.inter_particle_averaged_pressure, + buffer_size=n_buffer_particles) + +# ========================================================================================== +# ==== Boundary +boundary_model = BoundaryModelDummyParticles(pipe.boundary.density, pipe.boundary.mass, + AdamiPressureExtrapolation(), + state_equation=state_equation, + smoothing_kernel, smoothing_length) + +boundary_system_wall = WallBoundarySystem(pipe.boundary, boundary_model) + +boundary_model_cylinder = BoundaryModelDummyParticles(cylinder.density, cylinder.mass, + AdamiPressureExtrapolation(), + state_equation=state_equation, + viscosity=viscosity, + smoothing_kernel, smoothing_length) + +boundary_system_cylinder = WallBoundarySystem(cylinder, boundary_model_cylinder) + +# ========================================================================================== +# ==== Simulation +min_corner = minimum(pipe.boundary.coordinates .- 5 * particle_spacing, dims=2) +max_corner = maximum(pipe.boundary.coordinates .+ 5 * particle_spacing, dims=2) +cell_list = FullGridCellList(; min_corner, max_corner) + +neighborhood_search = GridNeighborhoodSearch{2}(; cell_list, + update_strategy=ParallelUpdate()) + +semi = Semidiscretization(fluid_system, open_boundary, boundary_system_wall, + boundary_system_cylinder; neighborhood_search=neighborhood_search, + parallelization_backend=PolyesterBackend()) + +ode = semidiscretize(semi, tspan) + +info_callback = InfoCallback(interval=50) + +saving_callback = SolutionSavingCallback(; dt=0.02, prefix="", output_directory="out") + +extra_callback = nothing + +callbacks = CallbackSet(info_callback, UpdateCallback(), saving_callback, extra_callback) + +sol = solve(ode, RDPK3SpFSAL35(), + abstol=1e-6, # Default abstol is 1e-6 (may need to be tuned to prevent boundary penetration) + reltol=1e-4, # Default reltol is 1e-3 (may need to be tuned to prevent boundary penetration) + dtmax=1e-2, # Limit stepsize to prevent crashing + save_everystep=false, callback=callbacks); diff --git a/test/Project.toml b/test/Project.toml index 583f367bc9..b51d4e60b5 100644 --- a/test/Project.toml +++ b/test/Project.toml @@ -2,6 +2,7 @@ CSV = "336ed68f-0bac-5ca0-87d4-7b16caf5d00b" CairoMakie = "13f3f980-e62b-5c42-98c6-ff1f3baf88f0" DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0" +FFTW = "7a1cc6ca-52ef-59f5-83cd-3a7055c09341" GLM = "38e38edf-8417-5370-95a0-9cbb8c7f171a" Glob = "c27321d9-0574-5035-807b-f59d2c89b15c" JSON = "682c06a0-de6a-54ab-a142-c8b1cf79cde6" diff --git a/test/examples/examples_fluid.jl b/test/examples/examples_fluid.jl index c13a71f724..4f09534684 100644 --- a/test/examples/examples_fluid.jl +++ b/test/examples/examples_fluid.jl @@ -486,6 +486,15 @@ @test count_rhs_allocations(sol, semi) == 0 end + @trixi_testset "fluid/vortex_street_2d.jl" begin + @trixi_test_nowarn trixi_include(@__MODULE__, + joinpath(examples_dir(), "fluid", + "vortex_street_2d.jl"), + tspan=(0.0, 0.2)) + @test sol.retcode == ReturnCode.Success + @test count_rhs_allocations(sol, semi) == 0 + end + @trixi_testset "fluid/lid_driven_cavity_2d.jl (EDAC)" begin @trixi_test_nowarn trixi_include(@__MODULE__, joinpath(examples_dir(), "fluid", diff --git a/test/validation/validation.jl b/test/validation/validation.jl index 58666e1372..68c3870130 100644 --- a/test/validation/validation.jl +++ b/test/validation/validation.jl @@ -112,4 +112,32 @@ @test sol.retcode == ReturnCode.Success @test count_rhs_allocations(sol, semi) == 0 end + + @trixi_testset "vortex_street_2d" begin + @trixi_testset "Validation" begin + @trixi_test_nowarn trixi_include(@__MODULE__, + joinpath(validation_dir(), + "vortex_street_2d", + "validation_vortex_street_2d.jl"), + output_directory=joinpath(validation_dir(), + "vortex_street_2d", + "out_test"), + tspan=(0.0, 1.0)) + @test sol.retcode == ReturnCode.Success + @test count_rhs_allocations(sol, semi) == 0 + end + + @trixi_testset "Plot" begin + @trixi_test_nowarn trixi_include(@__MODULE__, + joinpath(validation_dir(), + "vortex_street_2d", + "plot_vortex_street_2d.jl")) [ + # exact info outputs + r"┌ Info: Strouhal number\n└\s+round\(strouhal_number, digits = 3\) = 0\.228\n", + r"┌ Info: Fraction of the dominant frequency band in the total spectrum\n└\s+round\(integral_peak / integral_total, digits = 3\) = 0\.39\n", + r"┌ Info: C_L_max for the periodic shedding\n└\s+round\(maximum\(f_lift_cut\), digits = 3\) = 0\.7\n", + r"┌ Info: C_D_max for the periodic shedding\n└\s+round\(maximum\(f_drag\[start_index:end\]\), digits = 3\) = 1\.631\n" + ] + end + end end diff --git a/validation/vortex_street_2d/plot_vortex_street_2d.jl b/validation/vortex_street_2d/plot_vortex_street_2d.jl new file mode 100644 index 0000000000..ab65e032a9 --- /dev/null +++ b/validation/vortex_street_2d/plot_vortex_street_2d.jl @@ -0,0 +1,82 @@ +using TrixiParticles +using CSV, DataFrames, Plots +using FFTW + +# Results in 1.2M particles. +# In the Tafuni et al. (2018), the resolution is `0.01` (5M particles). +resolution_factor = 0.02 +cylinder_diameter = 0.1 +prescribed_velocity = 1.0 + +reynolds_number = 200 + +output_directory = joinpath(validation_dir(), "vortex_street_2d") + +# ====================================================================================== +# ==== Read results +data = CSV.read(joinpath(output_directory, "resulting_force.csv"), DataFrame) + +step = 1 +times = data[!, "time"][1:step:end] + +f_lift = data[!, "f_l_fluid_1"][1:step:end] +f_drag = data[!, "f_d_fluid_1"][1:step:end] + +# ====================================================================================== +# ==== Compute strouhal number +t_start = 6.0 +start_index = findfirst(t -> t ≥ t_start, times) +times_cut = times[start_index:end] +dt = times_cut[2] - times_cut[1] + +f_lift_cut = f_lift[start_index:end] + +# Compute the frequency for the FFT. +# For N time samples with uniform time steps dt, the corresponding frequencies are: +# f_k = k / (N * dt), where k = 0, 1, ..., N-1. +# This gives the frequency bins in Hz, matching the order of FFT. +N = length(f_lift_cut) +frequencies = (0:(N - 1)) / (N * dt) + +spectrum = abs.(fft(f_lift_cut)) +spectrum_half = spectrum[1:div(N, 2)] + +# For real-valued signals, the FFT output is symmetric. +# Only the first half (up to the Nyquist frequency) contains unique, physically meaningful frequency components. +# We therefore analyze only the first N/2 values of the frequency spectrum. +f_dominant = frequencies[argmax(spectrum_half)] + +# Verify whether the dominant frequency is indeed unique. +# In theory, for a purely harmonic oscillation, the spectrum should exhibit only a single dominant frequency component. +delta = 2 * (frequencies[2] - frequencies[1]) +frequency_band = (abs.(frequencies[1:div(N, 2)] .- f_dominant) .< delta) + +strouhal_number = f_dominant * cylinder_diameter / prescribed_velocity + +# ====================================================================================== +# ==== Validate the frequency spectrum +integral_total = sum(spectrum_half) +integral_peak = sum(spectrum_half[frequency_band]) + +@info "Strouhal number" round(strouhal_number, digits=3) +@info "Fraction of the dominant frequency band in the total spectrum" round(integral_peak / + integral_total, + digits=3) +@info "C_L_max for the periodic shedding" round(maximum(f_lift_cut), digits=3) +@info "C_D_max for the periodic shedding" round(maximum(f_drag[start_index:end]), digits=3) + +dp = round(Int, 1 / resolution_factor) +plot_title = "Drag and lift force coefficients (Δx = d/$(dp))" +pC = plot(times, f_lift, ylims=(-1, 3), xlims=(0, 20), label="C_L", color=:red, linewidth=2) +plot!(pC, times, f_drag, ylims=(-1, 3), xlims=(0, 20), label="C_D", color=:blue, + linewidth=2, title=plot_title, xlabel="t (s)") +plot!(pC, top_margin=2Plots.mm) + +pS = plot(frequencies[1:div(N, 2)], spectrum_half, xlabel="Frequency (Hz)", size=(400, 200), + ylabel="Amplitude", + title="Frequency Spectrum (St = $(round(strouhal_number, digits=4)))", + label=nothing, linewidth=2) +plot!(pC, top_margin=2Plots.mm) + +p = plot(pC, pS, layout=@layout([a; b{0.3h}]), size=(800, 800)) +plot!(p, right_margin=5Plots.mm) diff --git a/validation/vortex_street_2d/resulting_force.csv b/validation/vortex_street_2d/resulting_force.csv new file mode 100644 index 0000000000..e26916908b --- /dev/null +++ b/validation/vortex_street_2d/resulting_force.csv @@ -0,0 +1,1002 @@ +time,f_l_fluid_1,f_d_fluid_1 +0.0,0.0,0.0 +0.02,1.7229645488114897e-12,2.2277618268160917 +0.04,1.7074913266527243e-7,1.2293013135228 +0.06,-0.000204783153640161,2.7523047665754654 +0.08,-0.0006030161260902993,-0.047140730662440386 +0.1,-0.000729604111279531,1.4155801989073884 +0.12,-0.01264214888213393,1.6133710804876276 +0.14,-0.02872992523061666,1.366784537317961 +0.16,0.015600658195840375,0.3391149436691562 +0.18,-0.0021770607971640437,1.368301627147613 +0.2,0.02610472829694564,1.3186207116981723 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(2018), the resolution is `0.01` (5M particles). +# Results in 1.3M particles and acceptable results compared to Tafuni et al. (2018). +# resolution_factor = 0.02 # (runtime: ~6-10h) +# Results in 100k particles and much noisier results compared to Tafuni et al. (2018). +resolution_factor = 0.05 + +reynolds_number = 200 +cylinder_diameter = 0.1 + +open_boundary_model = BoundaryModelMirroringTafuni(; mirror_method=ZerothOrderMirroring()) + +trixi_include(@__MODULE__, joinpath(examples_dir(), "fluid", "vortex_street_2d.jl"), + reynolds_number=reynolds_number, saving_callback=nothing, + open_boundary_model=open_boundary_model, factor_d=resolution_factor, + domain_size=(25 * cylinder_diameter, 20 * cylinder_diameter), tspan=tspan, + sol=nothing) + +shifting_technique = TransportVelocityAdami(background_pressure=5 * fluid_density * + sound_speed^2) + +output_directory = joinpath(validation_dir(), "vortex_street_2d") + +# ========================================================================================== +# ==== Postprocessing +circle = SphereShape(0.002, cylinder_diameter / 2, cylinder_center, fluid_density, + n_layers=1, sphere_type=RoundSphere()) + +# Points for pressure interpolation, located at the wall interface +const data_points = copy(circle.coordinates) +const center = SVector(cylinder_center) +# Arc length per surface point +const ds = pi * cylinder_diameter / nparticles(circle) + +calculate_lift_force(system, dv_ode, du_ode, v_ode, u_ode, semi, t) = nothing +function calculate_lift_force(system::TrixiParticles.AbstractFluidSystem, dv_ode, du_ode, + v_ode, u_ode, semi, t) + force = zero(SVector{ndims(system), eltype(system)}) + + values = interpolate_points(data_points, semi, system, v_ode, u_ode; cut_off_bnd=false, + clip_negative_pressure=false) + pressure = Array(values.pressure) + + for i in axes(data_points, 2) + point = TrixiParticles.current_coords(data_points, system, i) + + # F = ∑ -p_i * A_i * n_i + force -= pressure[i] * ds * TrixiParticles.normalize(point - center) + end + + return 2 * force[2] / (fluid_density * prescribed_velocity^2 * cylinder_diameter) +end + +calculate_drag_force(system, dv_ode, du_ode, v_ode, u_ode, semi, t) = nothing +function calculate_drag_force(system::TrixiParticles.AbstractFluidSystem, dv_ode, du_ode, + v_ode, u_ode, semi, t) + force = zero(SVector{ndims(system), eltype(system)}) + + values = interpolate_points(data_points, semi, system, v_ode, u_ode; cut_off_bnd=false, + clip_negative_pressure=false) + pressure = Array(values.pressure) + + for i in axes(data_points, 2) + point = TrixiParticles.current_coords(data_points, system, i) + + # F = ∑ -p_i * A_i * n_i + force -= pressure[i] * ds * TrixiParticles.normalize(point - center) + end + + return 2 * force[1] / (fluid_density * prescribed_velocity^2 * cylinder_diameter) +end + +pp_callback = PostprocessCallback(; dt=0.02, + f_l=calculate_lift_force, f_d=calculate_drag_force, + output_directory, filename="resulting_force", + write_csv=true, write_file_interval=10) + +# ====================================================================================== +# ==== Run the simulation +trixi_include(joinpath(examples_dir(), "fluid", "vortex_street_2d.jl"), + parallelization_backend=PolyesterBackend(), reynolds_number=reynolds_number, + output_directory=output_directory, + open_boundary_model=open_boundary_model, + shifting_technique=shifting_technique, + factor_d=resolution_factor, extra_callback=pp_callback)