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[ci-skip] First commit of the branch to add a refined mesh test for t…
…he Rosenbrock shallow water test case with the Williamson5 test configuration. This includes the Williamson 5 initial conditions and driver, as well as a change to the Rosenbrock solver to allow for bottom topography
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| # Initial conditions for the zonal flow over an isolated mountain ("Williamson 5") | ||
| # shallow water test case. Involves a balanced geostrophic flow with a Gaussian | ||
| # hill in the northern hemisphere. | ||
| # reference: | ||
| # D.L. Williamson, J.B. Drake, J.J. Hack, R. Jakob, P.N. Swarztrauber, | ||
| # J. Comput. Phys. 102 (1992) 211–224. | ||
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| const Rₑ = 6371220.0 | ||
| const gₑ = 9.80616 | ||
| const U₀ = 20.0 | ||
| const Ωₑ = 7.292e-5 | ||
| const H₀ = 5960.0 | ||
| const α₀ = 0.0 | ||
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| function uθ(θϕr) | ||
| θ,ϕ,r = θϕr | ||
| U₀*(cos(ϕ)*cos(α₀) + cos(θ)*sin(ϕ)*sin(α₀)) | ||
| end | ||
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| function uϕ(θϕr) | ||
| θ,ϕ,r = θϕr | ||
| -U₀*sin(θ)*sin(α₀); | ||
| end | ||
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| # Initial velocity | ||
| function u₀(xyz) | ||
| θϕr = xyz2θϕr(xyz) | ||
| u = uθ(θϕr) | ||
| v = uϕ(θϕr) | ||
| spherical_to_cartesian_matrix(θϕr)⋅VectorValue(u,v,0) | ||
| end | ||
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| # Topography | ||
| function topography(xyz) | ||
| θϕr = xyz2θϕr(xyz) | ||
| θc = -π/2.0 | ||
| ϕc = π/6.0 | ||
| bo = 2000.0 | ||
| rad = π/9.0 | ||
| rsq = (ϕ - ϕc)*(ϕ - ϕc) + (θ - θc)*(θ - θc) | ||
| r = sqrt(rsq) | ||
| b = 0.0 | ||
| if(r < rad) | ||
| b = bo*(1.0 - r/rad) | ||
| end | ||
| b | ||
| end | ||
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| # Initial fluid depth | ||
| function h₀(xyz) | ||
| θϕr = xyz2θϕr(xyz) | ||
| b = -cos(θ)*cos(ϕ)*sin(α₀) + sin(ϕ)*cos(α₀) | ||
| bt = topography(xyz) | ||
| H₀ - (Rₑ*Ωₑ*U₀ + 0.5*U₀*U₀)*b*b/gₑ - bt | ||
| end |
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| module Williamson5ShallowWaterRosenbrock | ||
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| using PartitionedArrays | ||
| using Test | ||
| using FillArrays | ||
| using Gridap | ||
| using GridapPETSc | ||
| using GridapGeosciences | ||
| using GridapDistributed | ||
| using GridapP4est | ||
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| include("Williamson5InitialConditions.jl") | ||
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| function petsc_gamg_options() | ||
| """ | ||
| -ksp_type gmres -ksp_rtol 1.0e-06 -ksp_atol 0.0 | ||
| -ksp_monitor -pc_type gamg -pc_gamg_type agg | ||
| -mg_levels_esteig_ksp_type gmres -mg_coarse_sub_pc_type lu | ||
| -mg_coarse_sub_pc_factor_mat_ordering_type nd -pc_gamg_process_eq_limit 50 | ||
| -pc_gamg_square_graph 9 pc_gamg_agg_nsmooths 1 | ||
| """ | ||
| end | ||
| function petsc_mumps_options() | ||
| """ | ||
| -ksp_type preonly -ksp_error_if_not_converged true | ||
| -pc_type lu -pc_factor_mat_solver_type mumps | ||
| """ | ||
| end | ||
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| order = 0 | ||
| degree = 4 | ||
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| # magnitude of the descent direction of the implicit solve; | ||
| # neutrally stable for 0.5, L-stable for 1+sqrt(2)/2 | ||
| λ = 1.0 + 0.5*sqrt(2.0) | ||
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| dt = 480.0 | ||
| nstep = Int(24*60^2*20/dt) # 20 days | ||
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| function main(distribute,parts) | ||
| ranks = distribute(LinearIndices((prod(parts),))) | ||
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| # Change directory to the location of the script, where the mesh data files are located | ||
| cd(@__DIR__) | ||
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| coarse_model, cell_panels, coarse_cell_wise_vertex_coordinates= | ||
| parse_cubed_sphere_coarse_model("williamson-5-C12/connectivity-gridapgeo.txt","williamson-5-C12/geometry-gridapgeo.txt") | ||
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| num_uniform_refinements=0 | ||
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| GridapPETSc.with(args=split(petsc_mumps_options())) do | ||
| model=CubedSphereDiscreteModel(ranks, | ||
| coarse_model, | ||
| coarse_cell_wise_vertex_coordinates, | ||
| cell_panels, | ||
| num_uniform_refinements; | ||
| radius=rₑ, | ||
| adaptive=true, | ||
| order=0) | ||
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| hf, uf = shallow_water_rosenbrock_time_stepper(model, order, degree, | ||
| h₀, u₀, Ωₑ, gₑ, H₀, | ||
| λ, dt, 60.0, nstep; | ||
| t₀=topography, | ||
| leap_frog=true, | ||
| write_solution=true, | ||
| write_solution_freq=45, | ||
| write_diagnostics=true, | ||
| write_diagnostics_freq=1, | ||
| dump_diagnostics_on_screen=true) | ||
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| end | ||
| end | ||
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| with_mpi() do distribute | ||
| main(distribute,1) | ||
| end | ||
| end # module |