diff --git a/examples/t8code_3d_dgsem/elixir_advection_cubed_sphere.jl b/examples/t8code_3d_dgsem/elixir_advection_cubed_sphere.jl new file mode 100644 index 0000000000..556d8a0289 --- /dev/null +++ b/examples/t8code_3d_dgsem/elixir_advection_cubed_sphere.jl @@ -0,0 +1,61 @@ +using OrdinaryDiffEq +using Trixi + +############################################################################### +# semidiscretization of the linear advection equation + +advection_velocity = (0.2, -0.7, 0.5) +equations = LinearScalarAdvectionEquation3D(advection_velocity) + +# Create DG solver with polynomial degree = 3 and (local) Lax-Friedrichs/Rusanov flux as surface flux +solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) + +initial_condition = initial_condition_convergence_test + +boundary_condition = BoundaryConditionDirichlet(initial_condition) +boundary_conditions = Dict(:inside => boundary_condition, + :outside => boundary_condition) + +# Note that the first argument refers to the level of refinement, unlike in for p4est +mesh = Trixi.T8codeMeshCubedSphere(2, 3, 0.5, 0.5; + polydeg = 3, initial_refinement_level = 0) + +# A semidiscretization collects data structures and functions for the spatial discretization +semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, + boundary_conditions = boundary_conditions) + +############################################################################### +# ODE solvers, callbacks etc. + +# Create ODE problem with time span from 0.0 to 1.0 +tspan = (0.0, 1.0) +ode = semidiscretize(semi, tspan) + +# At the beginning of the main loop, the SummaryCallback prints a summary of the simulation setup +# and resets the timers +summary_callback = SummaryCallback() + +# The AnalysisCallback allows to analyse the solution in regular intervals and prints the results +analysis_callback = AnalysisCallback(semi, interval = 100) + +# # The SaveSolutionCallback allows to save the solution to a file in regular intervals +# save_solution = SaveSolutionCallback(interval = 100, +# solution_variables = cons2prim) + +# The StepsizeCallback handles the re-calculation of the maximum Δt after each time step +stepsize_callback = StepsizeCallback(cfl = 1.2) + +# Create a CallbackSet to collect all callbacks such that they can be passed to the ODE solver +callbacks = CallbackSet(summary_callback, analysis_callback, # save_solution, + stepsize_callback) + +############################################################################### +# run the simulation + +# OrdinaryDiffEq's `solve` method evolves the solution in time and executes the passed callbacks +sol = solve(ode, CarpenterKennedy2N54(williamson_condition = false), + dt = 1.0, # solve needs some value here but it will be overwritten by the stepsize_callback + save_everystep = false, callback = callbacks); + +# Print the timer summary +summary_callback() diff --git a/examples/t8code_3d_dgsem/elixir_euler_baroclinic_instability.jl b/examples/t8code_3d_dgsem/elixir_euler_baroclinic_instability.jl new file mode 100644 index 0000000000..2126028899 --- /dev/null +++ b/examples/t8code_3d_dgsem/elixir_euler_baroclinic_instability.jl @@ -0,0 +1,301 @@ +# An idealized baroclinic instability test case +# For optimal results consider increasing the resolution to 16x16x8 trees per cube face. +# +# Note that this elixir can take several hours to run. +# Using 24 threads of an AMD Ryzen Threadripper 3990X (more threads don't speed it up further) +# and `check-bounds=no`, this elixirs takes about one hour to run. +# With 16x16x8 trees per cube face on the same machine, it takes about 28 hours. +# +# References: +# - Paul A. Ullrich, Thomas Melvin, Christiane Jablonowski, Andrew Staniforth (2013) +# A proposed baroclinic wave test case for deep- and shallow-atmosphere dynamical cores +# https://doi.org/10.1002/qj.2241 + +using OrdinaryDiffEq +using Trixi +using LinearAlgebra + +############################################################################### +# Setup for the baroclinic instability test +gamma = 1.4 +equations = CompressibleEulerEquations3D(gamma) + +# Initial condition for an idealized baroclinic instability test +# https://doi.org/10.1002/qj.2241, Section 3.2 and Appendix A +function initial_condition_baroclinic_instability(x, t, + equations::CompressibleEulerEquations3D) + lon, lat, r = cartesian_to_sphere(x) + radius_earth = 6.371229e6 + # Make sure that the r is not smaller than radius_earth + z = max(r - radius_earth, 0.0) + + # Unperturbed basic state + rho, u, p = basic_state_baroclinic_instability_longitudinal_velocity(lon, lat, z) + + # Stream function type perturbation + u_perturbation, v_perturbation = perturbation_stream_function(lon, lat, z) + + u += u_perturbation + v = v_perturbation + + # Convert spherical velocity to Cartesian + v1 = -sin(lon) * u - sin(lat) * cos(lon) * v + v2 = cos(lon) * u - sin(lat) * sin(lon) * v + v3 = cos(lat) * v + + return prim2cons(SVector(rho, v1, v2, v3, p), equations) +end + +# Steady state for RHS correction below +function steady_state_baroclinic_instability(x, t, equations::CompressibleEulerEquations3D) + lon, lat, r = cartesian_to_sphere(x) + radius_earth = 6.371229e6 + # Make sure that the r is not smaller than radius_earth + z = max(r - radius_earth, 0.0) + + # Unperturbed basic state + rho, u, p = basic_state_baroclinic_instability_longitudinal_velocity(lon, lat, z) + + # Convert spherical velocity to Cartesian + v1 = -sin(lon) * u + v2 = cos(lon) * u + v3 = 0.0 + + return prim2cons(SVector(rho, v1, v2, v3, p), equations) +end + +function cartesian_to_sphere(x) + r = norm(x) + lambda = atan(x[2], x[1]) + if lambda < 0 + lambda += 2 * pi + end + phi = asin(x[3] / r) + + return lambda, phi, r +end + +# Unperturbed balanced steady-state. +# Returns primitive variables with only the velocity in longitudinal direction (rho, u, p). +# The other velocity components are zero. +function basic_state_baroclinic_instability_longitudinal_velocity(lon, lat, z) + # Parameters from Table 1 in the paper + # Corresponding names in the paper are commented + radius_earth = 6.371229e6 # a + half_width_parameter = 2 # b + gravitational_acceleration = 9.80616 # g + k = 3 # k + surface_pressure = 1e5 # p₀ + gas_constant = 287 # R + surface_equatorial_temperature = 310.0 # T₀ᴱ + surface_polar_temperature = 240.0 # T₀ᴾ + lapse_rate = 0.005 # Γ + angular_velocity = 7.29212e-5 # Ω + + # Distance to the center of the Earth + r = z + radius_earth + + # In the paper: T₀ + temperature0 = 0.5 * (surface_equatorial_temperature + surface_polar_temperature) + # In the paper: A, B, C, H + const_a = 1 / lapse_rate + const_b = (temperature0 - surface_polar_temperature) / + (temperature0 * surface_polar_temperature) + const_c = 0.5 * (k + 2) * (surface_equatorial_temperature - surface_polar_temperature) / + (surface_equatorial_temperature * surface_polar_temperature) + const_h = gas_constant * temperature0 / gravitational_acceleration + + # In the paper: (r - a) / bH + scaled_z = z / (half_width_parameter * const_h) + + # Temporary variables + temp1 = exp(lapse_rate / temperature0 * z) + temp2 = exp(-scaled_z^2) + + # In the paper: ̃τ₁, ̃τ₂ + tau1 = const_a * lapse_rate / temperature0 * temp1 + + const_b * (1 - 2 * scaled_z^2) * temp2 + tau2 = const_c * (1 - 2 * scaled_z^2) * temp2 + + # In the paper: ∫τ₁(r') dr', ∫τ₂(r') dr' + inttau1 = const_a * (temp1 - 1) + const_b * z * temp2 + inttau2 = const_c * z * temp2 + + # Temporary variables + temp3 = r / radius_earth * cos(lat) + temp4 = temp3^k - k / (k + 2) * temp3^(k + 2) + + # In the paper: T + temperature = 1 / ((r / radius_earth)^2 * (tau1 - tau2 * temp4)) + + # In the paper: U, u (zonal wind, first component of spherical velocity) + big_u = gravitational_acceleration / radius_earth * k * temperature * inttau2 * + (temp3^(k - 1) - temp3^(k + 1)) + temp5 = radius_earth * cos(lat) + u = -angular_velocity * temp5 + sqrt(angular_velocity^2 * temp5^2 + temp5 * big_u) + + # Hydrostatic pressure + p = surface_pressure * + exp(-gravitational_acceleration / gas_constant * (inttau1 - inttau2 * temp4)) + + # Density (via ideal gas law) + rho = p / (gas_constant * temperature) + + return rho, u, p +end + +# Perturbation as in Equations 25 and 26 of the paper (analytical derivative) +function perturbation_stream_function(lon, lat, z) + # Parameters from Table 1 in the paper + # Corresponding names in the paper are commented + perturbation_radius = 1 / 6 # d₀ / a + perturbed_wind_amplitude = 1.0 # Vₚ + perturbation_lon = pi / 9 # Longitude of perturbation location + perturbation_lat = 2 * pi / 9 # Latitude of perturbation location + pertz = 15000 # Perturbation height cap + + # Great circle distance (d in the paper) divided by a (radius of the Earth) + # because we never actually need d without dividing by a + great_circle_distance_by_a = acos(sin(perturbation_lat) * sin(lat) + + cos(perturbation_lat) * cos(lat) * + cos(lon - perturbation_lon)) + + # In the first case, the vertical taper function is per definition zero. + # In the second case, the stream function is per definition zero. + if z > pertz || great_circle_distance_by_a > perturbation_radius + return 0.0, 0.0 + end + + # Vertical tapering of stream function + perttaper = 1.0 - 3 * z^2 / pertz^2 + 2 * z^3 / pertz^3 + + # sin/cos(pi * d / (2 * d_0)) in the paper + sin_, cos_ = sincos(0.5 * pi * great_circle_distance_by_a / perturbation_radius) + + # Common factor for both u and v + factor = 16 / (3 * sqrt(3)) * perturbed_wind_amplitude * perttaper * cos_^3 * sin_ + + u_perturbation = -factor * (-sin(perturbation_lat) * cos(lat) + + cos(perturbation_lat) * sin(lat) * cos(lon - perturbation_lon)) / + sin(great_circle_distance_by_a) + + v_perturbation = factor * cos(perturbation_lat) * sin(lon - perturbation_lon) / + sin(great_circle_distance_by_a) + + return u_perturbation, v_perturbation +end + +@inline function source_terms_baroclinic_instability(u, x, t, + equations::CompressibleEulerEquations3D) + radius_earth = 6.371229e6 # a + gravitational_acceleration = 9.80616 # g + angular_velocity = 7.29212e-5 # Ω + + r = norm(x) + # Make sure that r is not smaller than radius_earth + z = max(r - radius_earth, 0.0) + r = z + radius_earth + + du1 = zero(eltype(u)) + + # Gravity term + temp = -gravitational_acceleration * radius_earth^2 / r^3 + du2 = temp * u[1] * x[1] + du3 = temp * u[1] * x[2] + du4 = temp * u[1] * x[3] + du5 = temp * (u[2] * x[1] + u[3] * x[2] + u[4] * x[3]) + + # Coriolis term, -2Ω × ρv = -2 * angular_velocity * (0, 0, 1) × u[2:4] + du2 -= -2 * angular_velocity * u[3] + du3 -= 2 * angular_velocity * u[2] + + return SVector(du1, du2, du3, du4, du5) +end + +############################################################################### +# Start of the actual elixir, semidiscretization of the problem + +initial_condition = initial_condition_baroclinic_instability + +boundary_conditions = Dict(:inside => boundary_condition_slip_wall, + :outside => boundary_condition_slip_wall) + +# This is a good estimate for the speed of sound in this example. +# Other values between 300 and 400 should work as well. +surface_flux = FluxLMARS(340) +volume_flux = flux_kennedy_gruber +solver = DGSEM(polydeg = 5, surface_flux = surface_flux, + volume_integral = VolumeIntegralFluxDifferencing(volume_flux)) + +# For optimal results, use 4 lat lon levels and 8 layers here +# Note that the first argument refers to the level of refinement, unlike in for p4est +lat_lon_levels = 3 +layers = 4 +mesh = Trixi.T8codeMeshCubedSphere(lat_lon_levels, layers, 6.371229e6, 30000.0, + polydeg = 5, initial_refinement_level = 0) + +semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver, + source_terms = source_terms_baroclinic_instability, + boundary_conditions = boundary_conditions) + +############################################################################### +# ODE solvers, callbacks etc. + +tspan = (0.0, 10 * 24 * 60 * 60.0) # time in seconds for 10 days + +# Save RHS of the steady state and subtract it in every RHS evaluation. +# This trick preserves the steady state exactly (to machine rounding errors, of course). +# Otherwise, this elixir produces entirely unusable results for a resolution of 8x8x4 cells +# per cube face with a polydeg of 3. +# With this trick, even the polydeg 3 simulation produces usable (although badly resolved) results, +# and most of the grid imprinting in higher polydeg simulation is eliminated. +# +# See https://github.com/trixi-framework/Trixi.jl/issues/980 for more information. +u_steady_state = compute_coefficients(steady_state_baroclinic_instability, tspan[1], semi) +# Use a `let` block for performance (otherwise du_steady_state will be a global variable) +let du_steady_state = similar(u_steady_state) + # Save RHS of the steady state + Trixi.rhs!(du_steady_state, u_steady_state, semi, tspan[1]) + + global function corrected_rhs!(du, u, semi, t) + # Normal RHS evaluation + Trixi.rhs!(du, u, semi, t) + # Correct by subtracting the steady-state RHS + Trixi.@trixi_timeit Trixi.timer() "rhs correction" begin + # Use Trixi.@threaded for threaded performance + Trixi.@threaded for i in eachindex(du) + du[i] -= du_steady_state[i] + end + end + end +end +u0 = compute_coefficients(tspan[1], semi) +ode = ODEProblem(corrected_rhs!, u0, tspan, semi) + +summary_callback = SummaryCallback() + +analysis_interval = 5000 +analysis_callback = AnalysisCallback(semi, interval = analysis_interval) + +alive_callback = AliveCallback(analysis_interval = analysis_interval) + +#save_solution = SaveSolutionCallback(interval = 5000, +# save_initial_solution = true, +# save_final_solution = true, +# solution_variables = cons2prim) + +callbacks = CallbackSet(summary_callback, + analysis_callback, + alive_callback) +# , save_solution) + +############################################################################### +# run the simulation + +# Use a Runge-Kutta method with automatic (error based) time step size control +# Enable threading of the RK method for better performance on multiple threads +sol = solve(ode, RDPK3SpFSAL49(thread = OrdinaryDiffEq.True()); abstol = 1.0e-6, + reltol = 1.0e-6, + ode_default_options()..., callback = callbacks); + +summary_callback() # print the timer summary diff --git a/src/meshes/t8code_mesh.jl b/src/meshes/t8code_mesh.jl index 0d440710c2..bd913f6a24 100644 --- a/src/meshes/t8code_mesh.jl +++ b/src/meshes/t8code_mesh.jl @@ -584,7 +584,7 @@ struct AbaqusFile{NDIMS} end """ - T8codeMesh(meshfile::String, NDIMS; kwargs...) + T8codeMesh(filepath::String, NDIMS; kwargs...) Main mesh constructor for the `T8codeMesh` that imports an unstructured, conforming mesh from either a Gmsh mesh file (`.msh`) or Abaqus mesh file (`.inp`) which is determined @@ -769,6 +769,52 @@ function t8_cmesh_new_from_connectivity(connectivity::Ptr{p8est_connectivity}, c return t8_cmesh_new_from_p8est(connectivity, comm, 0) end +""" +T8codeMeshCubedSphere(trees_per_face_dimension, layers, inner_radius, thickness; + polydeg, RealT=Float64, initial_refinement_level=0) + +Construct a cubed spherical shell of given inner radius and thickness as `T8codeMesh` with +`6 * trees_per_face_dimension^2 * layers` trees. The mesh will have two boundaries, +`:inside` and `:outside`. + +# Arguments +- `lat_lon_levels_per_face_dimension::Integer`: number of trees per patch in longitudinal + and latitudinal direction given as level of + refinement. +- `layers::Integer`: the number of trees in the third local dimension of each face, i.e., + the number of layers of the shell. +- `inner_radius::Float64`: Radius of the inner side of the shell. +- `thickness::Float64`: Thickness of the shell. The outer radius will be + `inner_radius + thickness`. +- `polydeg::Integer`: polynomial degree used to store the geometry of the mesh. + The mapping will be approximated by an interpolation polynomial + of the specified degree for each tree. +- `RealT::Type`: the type that should be used for coordinates. +- `initial_refinement_level::Integer`: refine the mesh uniformly to this level before the + simulation starts. +""" +function T8codeMeshCubedSphere(lat_lon_levels_per_face_dimension, layers, inner_radius, + thickness; + polydeg, RealT = Float64, initial_refinement_level = 0) + NDIMS = 3 + cmesh = t8_cmesh_new_cubed_spherical_shell(inner_radius, thickness, + lat_lon_levels_per_face_dimension, + layers, mpi_comm()) + do_face_ghost = mpi_isparallel() + scheme = t8_scheme_new_default_cxx() + forest = t8_forest_new_uniform(cmesh, scheme, initial_refinement_level, do_face_ghost, + mpi_comm()) + + num_trees = t8_cmesh_get_num_trees(cmesh) + boundary_names = fill(Symbol("---"), 2 * NDIMS, num_trees) + for itree in 1:num_trees + boundary_names[5, itree] = :inside + boundary_names[6, itree] = :outside + end + + return T8codeMesh{NDIMS, RealT}(forest, boundary_names; polydeg = polydeg) +end + struct adapt_callback_passthrough adapt_callback::Function user_data::Any diff --git a/src/solvers/dgsem_t8code/containers_3d.jl b/src/solvers/dgsem_t8code/containers_3d.jl index 1375782631..4793d2afdd 100644 --- a/src/solvers/dgsem_t8code/containers_3d.jl +++ b/src/solvers/dgsem_t8code/containers_3d.jl @@ -64,8 +64,7 @@ function calc_node_coordinates!(node_coordinates, current_index += 1), matrix1, matrix2, matrix3, view(mesh.tree_node_coordinates, :, :, :, :, - global_itree + 1), - tmp1) + global_itree + 1), tmp1) end end diff --git a/test/test_t8code_3d.jl b/test/test_t8code_3d.jl index cdce1e1980..27366bca0c 100644 --- a/test/test_t8code_3d.jl +++ b/test/test_t8code_3d.jl @@ -110,6 +110,22 @@ mkdir(outdir) end end + # This test differs from the one in `test_p4est_3d.jl` in the latitudinal and + # longitudinal dimensions. + @trixi_testset "elixir_advection_cubed_sphere.jl" begin + @test_trixi_include(joinpath(EXAMPLES_DIR, "elixir_advection_cubed_sphere.jl"), + l2=[0.002006918015656413], + linf=[0.027655117058380085]) + # Ensure that we do not have excessive memory allocations + # (e.g., from type instabilities) + let + t = sol.t[end] + u_ode = sol.u[end] + du_ode = similar(u_ode) + @test (@allocated Trixi.rhs!(du_ode, u_ode, semi, t)) < 1000 + end + end + # This test is identical to the one in `test_p4est_3d.jl`. @trixi_testset "elixir_advection_restart.jl" begin @test_trixi_include(joinpath(EXAMPLES_DIR, "elixir_advection_restart.jl"), @@ -301,30 +317,29 @@ mkdir(outdir) end end - @trixi_testset "elixir_euler_convergence_pure_fv.jl" begin - @test_trixi_include(joinpath(pkgdir(Trixi, "examples", "tree_3d_dgsem"), - "elixir_euler_convergence_pure_fv.jl"), + # This test is identical to the one in `test_p4est_3d.jl` besides minor + # deviations in the expected error norms. + @trixi_testset "elixir_euler_baroclinic_instability.jl" begin + @test_trixi_include(joinpath(EXAMPLES_DIR, + "elixir_euler_baroclinic_instability.jl"), l2=[ - 0.037182410351406, - 0.032062252638283974, - 0.032062252638283974, - 0.03206225263828395, - 0.12228177813586687 + 6.725093801700048e-7, + 0.00021710076010951073, + 0.0004386796338203878, + 0.00020836270267103122, + 0.07601887903440395, ], linf=[ - 0.0693648413632646, - 0.0622101894740843, - 0.06221018947408474, - 0.062210189474084965, - 0.24196451799555962 + 1.9107530539574924e-5, + 0.02980358831035801, + 0.048476331898047564, + 0.02200137344113612, + 4.848310144356219, ], - mesh=T8codeMesh((4, 4, 4), polydeg = 3, - coordinates_min = (0.0, 0.0, 0.0), - coordinates_max = (2.0, 2.0, 2.0)), - # Remove SaveSolution callback - callbacks=CallbackSet(summary_callback, - analysis_callback, alive_callback, - stepsize_callback)) + tspan=(0.0, 1e2), + # Decrease tolerance of adaptive time stepping to get similar results across different systems + abstol=1.0e-9, reltol=1.0e-9, + coverage_override=(lat_lon_levels = 0, layers = 1, polydeg = 3)) # Prevent long compile time in CI # Ensure that we do not have excessive memory allocations # (e.g., from type instabilities) let