From 2488bf681faab59deb0be362fcd92867f36ae5cc Mon Sep 17 00:00:00 2001 From: nj19721 Date: Wed, 12 Apr 2023 10:14:50 +0100 Subject: [PATCH 1/8] work in progress --- src/DiscSimulations.jl | 15 +++++++++------ src/Euler_with_source.jl | 2 +- src/burgers/trixi.jl | 2 +- src/solution.jl | 18 +++++++++++------- src/test.jl | 9 +++++---- test.jl | 9 +++++++++ 6 files changed, 36 insertions(+), 19 deletions(-) create mode 100644 test.jl diff --git a/src/DiscSimulations.jl b/src/DiscSimulations.jl index e113c97..9280ce1 100644 --- a/src/DiscSimulations.jl +++ b/src/DiscSimulations.jl @@ -1,4 +1,4 @@ -module DiscSimulationsjl +module DiscSimulations using LinearAlgebra using Plots @@ -14,16 +14,19 @@ include("younsi-2012.jl") include("Euler_with_source.jl") include("burgers/trixi.jl") -struct Parameters{} - N - xmin - xmax +##need to add functype constructors?? + +#struct Parameters{T,DensityFuncType,SourceFuncType} +struct Parameters{T} + N::Int + xmin::T + xmax::T ρ source end abstract type SimulationType end -main(p::Parameters, ::SimulationType) = error("Unknown simulation type.") +main(p::Parameters, ::SimulationType) = error("Unknown simulation type: $(typeof(t))") struct BurgersSimulation <: SimulationType end struct EulerWithSourceSimulation <: SimulationType end diff --git a/src/Euler_with_source.jl b/src/Euler_with_source.jl index 7382557..80c97d7 100644 --- a/src/Euler_with_source.jl +++ b/src/Euler_with_source.jl @@ -20,7 +20,7 @@ using Plots du1 = -cos(ϕ)*ρ*(G*mₛ/(r^2)) du2 = -sin(ϕ)*ρ*(G*mₛ/(r^2)) du3 = -(ux*cos(ϕ) + uy*sin(ϕ))*ρ*(G*mₛ/(r^2)) - return SVector(du1, du2, du3) + return SVector(0, du1, du3) end source_zero(u, x, t, equations) = SVector(0, 0, 0) diff --git a/src/burgers/trixi.jl b/src/burgers/trixi.jl index d035a4c..d3fec65 100644 --- a/src/burgers/trixi.jl +++ b/src/burgers/trixi.jl @@ -30,7 +30,7 @@ end function solve_disc(N, x_max, init = BurgerUtils.STANDARD_BURGER_INIT, t_span = BurgerUtils.STANDARD_BURGER_TSPAN) semi, problem = setup(N, x_max, init, t_span) sol = solve(problem, RDPK3SpFSAL49(), abstol = 1.0e-7, reltol = 1.0e-7) - return DiscSolution(sol, semi) + return DiscSolution(sol, semi, OneDimension()) end end # module BurgerTrixi diff --git a/src/solution.jl b/src/solution.jl index 64c9b7f..8b8ec68 100644 --- a/src/solution.jl +++ b/src/solution.jl @@ -7,7 +7,6 @@ struct OneDimension <: AbstractDimension end struct DiscSolution{Dimension,SolutionType,DiscretiziationType} sol::SolutionType semi::DiscretiziationType - #to add: keyword args end function DiscSolution(sol, semi, dimension_type::AbstractDimension) @@ -15,25 +14,30 @@ function DiscSolution(sol, semi, dimension_type::AbstractDimension) end #1D version of plot -function dataplot(solution::DiscSolution{OneDimension}) +function dataplot(solution::DiscSolution{<:OneDimension}, t) return PlotData1D(solution.sol(t), solution.semi) end #2D version of plot -function dataplot(solution::DiscSolution{TwoDimension}) +function dataplot(solution::DiscSolution{<:TwoDimension}, t) return PlotData2D(solution.sol(t), solution.semi) end -function plotgif(solution, tmin, tmax) +dataplot(solution::DiscSolution{<:AbstractDimension}, t) = error("Unknown simulation type: $(typeof(t))") + +function plotgif(solution, tmin, tmax, kwargs...) ts = range(tmin, tmax, 150) frames = Plots.@animate for t in ts - pd = dataplot(solution) + pd = dataplot(solution, t) plot( pd, label = Printf.@sprintf("t = %1.2f", t), - ylims = (-0.1, 2.1), - legend = :topright, + kwargs ) end gif(frames, "temp.gif", fps = 10) |> display end + +#function Base.show(io::IO, sol::DiscSolution) +# println(io, sol.sol, sol.semi) +#end \ No newline at end of file diff --git a/src/test.jl b/src/test.jl index fd312ba..4f1a7d3 100644 --- a/src/test.jl +++ b/src/test.jl @@ -1,9 +1,10 @@ include("DiscSimulations.jl") -using .DiscSimulationsjl +using .DiscSimulations initial_condition_sine(x, t, equation) = sinpi(x[1]) source_zero(u, x, t, equations) = SVector(0, 0, 0) -params = DiscSimulationsjl.Parameters(512, 0, 2π, initial_condition_sine, source_zero) +params = DiscSimulations.Parameters(512, 0.0, 2π, initial_condition_sine, source_zero) -solution = DiscSimulationsjl.main(params, DiscSimulationsjl.BurgersSimulation()) -DiscSimulationsjl.plotgif(solution, 0.0, 2.0) \ No newline at end of file +solution = DiscSimulations.main(params, DiscSimulations.BurgersSimulation()) +DiscSimulations.Base.show(IO, solution) +DiscSimulations.plotgif(solution, 0.0, 2.0) \ No newline at end of file diff --git a/test.jl b/test.jl new file mode 100644 index 0000000..ea3aa49 --- /dev/null +++ b/test.jl @@ -0,0 +1,9 @@ +include("src/DiscSimulations.jl") +using .DiscSimulations + +initial_condition_sine(x, t, equation) = sinpi(x[1]) +source_zero(u, x, t, equations) = SVector(0, 0, 0) +params = DiscSimulations.Parameters(512, 0, 2π, initial_condition_sine, source_zero) + +solution = DiscSimulations.main(params, DiscSimulations.BurgersSimulation()) +DiscSimulations.plotgif(solution, 0.0, 2.0) \ No newline at end of file From aade2156c6df41d6f54fa6897053f12fbfc310ae Mon Sep 17 00:00:00 2001 From: nj19721 Date: Fri, 14 Apr 2023 14:35:31 +0100 Subject: [PATCH 2/8] fixed some errors --- Project.toml | 1 + src/DiscSimulations.jl | 26 ++++++++++++++------------ src/burgers/trixi.jl | 17 ++++++----------- src/burgers/utils.jl | 8 +------- src/simpleGravitySim/simulation.jl | 4 ++-- src/solution.jl | 23 +++++++++++++---------- src/test.jl | 5 +++-- temp.gif | Bin 135341 -> 567309 bytes 8 files changed, 40 insertions(+), 44 deletions(-) diff --git a/Project.toml b/Project.toml index 206dd51..4ed9adb 100644 --- a/Project.toml +++ b/Project.toml @@ -15,3 +15,4 @@ Revise = "295af30f-e4ad-537b-8983-00126c2a3abe" Roots = "f2b01f46-fcfa-551c-844a-d8ac1e96c665" StaticArrays = "90137ffa-7385-5640-81b9-e52037218182" Trixi = "a7f1ee26-1774-49b1-8366-f1abc58fbfcb" +TruncatedStacktraces = "781d530d-4396-4725-bb49-402e4bee1e77" diff --git a/src/DiscSimulations.jl b/src/DiscSimulations.jl index 9280ce1..f1f55c6 100644 --- a/src/DiscSimulations.jl +++ b/src/DiscSimulations.jl @@ -3,18 +3,8 @@ module DiscSimulations using LinearAlgebra using Plots using Printf - -include("solution.jl") - -include("burgers/utils.jl") -#include("burgers/spectral.jl") -#include("burgers/simple.jl") -include("simpleGravitySim/simulation.jl") -include("younsi-2012.jl") -include("Euler_with_source.jl") -include("burgers/trixi.jl") - -##need to add functype constructors?? +using TruncatedStacktraces +TruncatedStacktraces.VERBOSE[] = true #struct Parameters{T,DensityFuncType,SourceFuncType} struct Parameters{T} @@ -36,6 +26,18 @@ main(p::Parameters, ::BurgersSimulation) = BurgerTrixi.solve_disc(p.N, p.xmax) main(p::Parameters, ::EulerWithSourceSimulation) = EulerSource.solve_euler(p.source) main(p::Parameters, ::SimpleGravitySimulation) = SimpleGravitySimulation.solve_gravity_sim(p.ρ) +include("solution.jl") + +include("burgers/utils.jl") +include("burgers/trixi.jl") +#include("burgers/spectral.jl") +#include("burgers/simple.jl") +include("simpleGravitySim/simpleGravity.jl") +include("simpleGravitySim/simulation.jl") +include("younsi-2012.jl") +include("Euler_with_source.jl") + + export Parameters, SimulationType, BurgersSimulation, EulerWithSourceSimulation, SimpleGravitySimulation end # module DiscSimulations diff --git a/src/burgers/trixi.jl b/src/burgers/trixi.jl index d3fec65..29eee80 100644 --- a/src/burgers/trixi.jl +++ b/src/burgers/trixi.jl @@ -5,15 +5,10 @@ using DifferentialEquations using Plots using Printf -include("utils.jl") -using .BurgerUtils +import DiscSimulations: + STANDARD_BURGER_INIT, STANDARD_BURGER_TSPAN, DiscSolution, OneDimension -include("../solution.jl") - -#import DiscSimulations: -# BurgerUtils.STANDARD_BURGER_INIT, BurgerUtils.STANDARD_BURGER_TSPAN, DiscSolution, OneDimension - -function setup(N, x_max, init = BurgerUtils.STANDARD_BURGER_INIT, t_span = BurgerUtils.STANDARD_BURGER_TSPAN) +function setup(N, x_max, init = STANDARD_BURGER_INIT, t_span = STANDARD_BURGER_TSPAN) x_min = 0.0 equations = InviscidBurgersEquation1D() @@ -22,12 +17,12 @@ function setup(N, x_max, init = BurgerUtils.STANDARD_BURGER_INIT, t_span = Burge mesh = TreeMesh(x_min, x_max, initial_refinement_level = 3, n_cells_max = N) semi = SemidiscretizationHyperbolic(mesh, equations, (x, t, eqs) -> init(x), solver) - problem = semidiscretize(semi, t_span) + ode = semidiscretize(semi, t_span) - semi, problem + semi, ode end -function solve_disc(N, x_max, init = BurgerUtils.STANDARD_BURGER_INIT, t_span = BurgerUtils.STANDARD_BURGER_TSPAN) +function solve_disc(N, x_max, init = STANDARD_BURGER_INIT, t_span = STANDARD_BURGER_TSPAN) semi, problem = setup(N, x_max, init, t_span) sol = solve(problem, RDPK3SpFSAL49(), abstol = 1.0e-7, reltol = 1.0e-7) return DiscSolution(sol, semi, OneDimension()) diff --git a/src/burgers/utils.jl b/src/burgers/utils.jl index b537f3f..eb8c32b 100644 --- a/src/burgers/utils.jl +++ b/src/burgers/utils.jl @@ -1,5 +1,3 @@ -module BurgerUtils - function central_difference(Δu, N) lower = -ones(Float64, N - 1) mid = zeros(Float64, N) @@ -11,8 +9,4 @@ function STANDARD_BURGER_INIT(x) @. 1 - cos(x) end -const STANDARD_BURGER_TSPAN = (0.0, 1.0) - -end # module BurgerUtils - -export BurgerUtils \ No newline at end of file +const STANDARD_BURGER_TSPAN = (0.0, 1.0) \ No newline at end of file diff --git a/src/simpleGravitySim/simulation.jl b/src/simpleGravitySim/simulation.jl index d32ff4d..ab0d228 100644 --- a/src/simpleGravitySim/simulation.jl +++ b/src/simpleGravitySim/simulation.jl @@ -1,7 +1,7 @@ module simpleGravitySimulation -include("./simpleGravity.jl") -using .simpleGravity +import DiscSimulations: + simpleGravity using Trixi using OrdinaryDiffEq using Plots diff --git a/src/solution.jl b/src/solution.jl index 8b8ec68..5db658c 100644 --- a/src/solution.jl +++ b/src/solution.jl @@ -14,30 +14,33 @@ function DiscSolution(sol, semi, dimension_type::AbstractDimension) end #1D version of plot -function dataplot(solution::DiscSolution{<:OneDimension}, t) - return PlotData1D(solution.sol(t), solution.semi) +function dataplot(solution::DiscSolution{<:OneDimension}, solver, t) + return PlotData1D(solver(t), solution.semi) end #2D version of plot -function dataplot(solution::DiscSolution{<:TwoDimension}, t) - return PlotData2D(solution.sol(t), solution.semi) +function dataplot(solution::DiscSolution{<:TwoDimension}, solver, t) + return PlotData2D(solver(t), solution.semi) end dataplot(solution::DiscSolution{<:AbstractDimension}, t) = error("Unknown simulation type: $(typeof(t))") -function plotgif(solution, tmin, tmax, kwargs...) +function plotgif(solution::DiscSolution, tmin, tmax)#, kwargs...) ts = range(tmin, tmax, 150) + solver = @time solution.sol frames = Plots.@animate for t in ts - pd = dataplot(solution, t) + pd = dataplot(solution, solver, t) plot( pd, label = Printf.@sprintf("t = %1.2f", t), - kwargs + #ylims = (-1, 1.1), + legend = :topright + #kwargs ) end gif(frames, "temp.gif", fps = 10) |> display end -#function Base.show(io::IO, sol::DiscSolution) -# println(io, sol.sol, sol.semi) -#end \ No newline at end of file +function Base.show(io::IO, sol::DiscSolution) + println(io, string(typeof(sol))) +end \ No newline at end of file diff --git a/src/test.jl b/src/test.jl index 4f1a7d3..595e9fe 100644 --- a/src/test.jl +++ b/src/test.jl @@ -6,5 +6,6 @@ source_zero(u, x, t, equations) = SVector(0, 0, 0) params = DiscSimulations.Parameters(512, 0.0, 2π, initial_condition_sine, source_zero) solution = DiscSimulations.main(params, DiscSimulations.BurgersSimulation()) -DiscSimulations.Base.show(IO, solution) -DiscSimulations.plotgif(solution, 0.0, 2.0) \ No newline at end of file +s = DiscSimulations.DiscSolution(solution.sol, solution.semi, DiscSimulations.OneDimension()) +kwargs = ["ylims = (-1, 1.1)", "legend = :topright"] +DiscSimulations.plotgif(s, 0.0, 2.0)#, kwargs) \ No newline at end of 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Sa0G~R3brsdBYZdk0RTHs3BV=* From 5959ef65ccba3085eb60e4a6e9528a8b97ce7daa Mon Sep 17 00:00:00 2001 From: Alice Date: Fri, 21 Apr 2023 15:49:48 +0100 Subject: [PATCH 3/8] small changes and burgers test case --- .gitignore | 5 +- examples/younsi-2012.jl | 25 ------- src/BurgersTestCase.jl | 27 ++++++++ src/DiscSimulations.jl | 5 +- src/burgers/simple.jl | 32 --------- src/burgers/spectral.jl | 48 -------------- src/burgers/trixi.jl | 8 +-- src/solution.jl | 14 ++-- src/test.jl | 14 +++- src/younsi-2012.jl | 143 +++++++--------------------------------- temp.gif | Bin 567309 -> 377895 bytes 11 files changed, 76 insertions(+), 245 deletions(-) delete mode 100644 examples/younsi-2012.jl create mode 100644 src/BurgersTestCase.jl delete mode 100644 src/burgers/simple.jl delete mode 100644 src/burgers/spectral.jl diff --git a/.gitignore b/.gitignore index 5798e24..c58a275 100644 --- a/.gitignore +++ b/.gitignore @@ -23,4 +23,7 @@ docs/site/ # environment. Manifest.toml -.vscode \ No newline at end of file +.vscode + +#Julia system image +JuliaSysimage.dll \ No newline at end of file diff --git a/examples/younsi-2012.jl b/examples/younsi-2012.jl deleted file mode 100644 index 40fc411..0000000 --- a/examples/younsi-2012.jl +++ /dev/null @@ -1,25 +0,0 @@ -using DiscSimulations -using Plots - -# black hole mass -M = 1.0 - -# black hole spin -a = 0.2 - -# keplerian radius -rₖ = 12.0 - -# angular velocity profile index of the torus -n = 0.21 - -begin - p = plot(xlabel = "r", ylabel = "z", legend = :outertopright) - for a in [0.0, 0.2, 0.4, 0.6, 0.8] - r, z = @time isobar(M, a, n, rₖ) - plot!(r, z, label = "a = $a") - # plot but upside down - plot!(r, -z, label = "a = $a") - end - p -end diff --git a/src/BurgersTestCase.jl b/src/BurgersTestCase.jl new file mode 100644 index 0000000..d0488ed --- /dev/null +++ b/src/BurgersTestCase.jl @@ -0,0 +1,27 @@ +include("DiscSimulations.jl") +using .DiscSimulations + +xmin = 0.0 +xmax = 1.0 +N = 256 + +tmax = (xmax - xmin)/1.0 +t_span = (0.0, tmax) + +function initial_condition_burgers(x) + u = 1.0 + if(x[1] >= 0.333 && x[1] <= 0.666) + u = u + 0.5*sin(2.0*π*(x[1]-0.333)/0.333) + end + return u +end + +#params expects this so we're defining a dummy one +source_zero(u, x, t, equations) = SVector(0, 0, 0) + +params = DiscSimulations.Parameters(N, xmin, xmax, initial_condition_burgers, source_zero, t_span) + +solution = DiscSimulations.main(params, DiscSimulations.BurgersSimulation()) +s = DiscSimulations.DiscSolution(solution.sol, solution.semi, DiscSimulations.OneDimension()) + +DiscSimulations.plotgif(s, t_span[1], t_span[2]; xlims = (0, 1), ylims = (0, 2), legend = :topright) \ No newline at end of file diff --git a/src/DiscSimulations.jl b/src/DiscSimulations.jl index f1f55c6..fce8ecb 100644 --- a/src/DiscSimulations.jl +++ b/src/DiscSimulations.jl @@ -13,6 +13,7 @@ struct Parameters{T} xmax::T ρ source + t_span end abstract type SimulationType end @@ -22,7 +23,7 @@ struct BurgersSimulation <: SimulationType end struct EulerWithSourceSimulation <: SimulationType end struct SimpleGravitySimulation <: SimulationType end -main(p::Parameters, ::BurgersSimulation) = BurgerTrixi.solve_disc(p.N, p.xmax) +main(p::Parameters, ::BurgersSimulation) = BurgerTrixi.solve_disc(p.N, p.xmin, p.xmax, p.ρ, p.t_span) main(p::Parameters, ::EulerWithSourceSimulation) = EulerSource.solve_euler(p.source) main(p::Parameters, ::SimpleGravitySimulation) = SimpleGravitySimulation.solve_gravity_sim(p.ρ) @@ -34,7 +35,7 @@ include("burgers/trixi.jl") #include("burgers/simple.jl") include("simpleGravitySim/simpleGravity.jl") include("simpleGravitySim/simulation.jl") -include("younsi-2012.jl") +#include("younsi-2012.jl") include("Euler_with_source.jl") diff --git a/src/burgers/simple.jl b/src/burgers/simple.jl deleted file mode 100644 index fedaf28..0000000 --- a/src/burgers/simple.jl +++ /dev/null @@ -1,32 +0,0 @@ -module BurgerSimple - -using DifferentialEquations - -import DiscSimulations: STANDARD_BURGER_INIT, STANDARD_BURGER_TSPAN, central_difference - -function burger(du, u, p, t) - # unpack additional paramters - D = p - # dirichlet boundary condition - u[1] = u[end] = 0.0 - step = -u .* (D * u) - du .= step -end - -function setup(N, x_max, init = STANDARD_BURGER_INIT, t_span = STANDARD_BURGER_TSPAN) - Δx = x_max / N - - x = collect(range(0.0, x_max, N)) - u0 = init(x) - - # get central difference operator as matrix - D = central_difference(Δx, N) - - problem = ODEProblem{true}(burger, u0, t_span, D) - - x, u0, problem -end - -end # module BurgerSimple - -export BurgerSimple diff --git a/src/burgers/spectral.jl b/src/burgers/spectral.jl deleted file mode 100644 index c990b3c..0000000 --- a/src/burgers/spectral.jl +++ /dev/null @@ -1,48 +0,0 @@ -module BurgerSpectral - -using ApproxFun -using LinearAlgebra -using DifferentialEquations - -import DiscSimulations: STANDARD_BURGER_INIT, STANDARD_BURGER_TSPAN - -function burger_fourier(du_f, u_f, p, t) - # unpack parameters - D, T, Ti, tmp1, tmp2 = p - # calculate derivative in fourier space - mul!(tmp1, D, u_f) - # transform derivative to regular space - mul!(tmp2, Ti, tmp1) - # transform u to regular space - mul!(tmp1, Ti, u_f) - # D * u - @. tmp1 = tmp2 * tmp1 - # transform back to fourier space - mul!(tmp2, T, tmp1) - du_f .= -tmp2 -end - -function setup(N, x_max, init = STANDARD_BURGER_INIT, t_span = STANDARD_BURGER_TSPAN) - space = Fourier() - x = points(space, N) - - D = (Derivative(space)→space)[1:N, 1:N] - - # fourier transform - T = ApproxFun.plan_transform(space, N) - # inverse fourier transform - Ti = ApproxFun.plan_itransform(space, N) - - u0 = T * init(x) - # pre-allocate temporary arrays - tmp1 = similar(u0) - tmp2 = similar(u0) - - problem = ODEProblem{true}(burger_fourier, u0, t_span, (D, T, Ti, tmp1, tmp2)) - - x, u0, T, Ti, problem -end - -end # module BurgerSpectral - -export BurgerSpectral diff --git a/src/burgers/trixi.jl b/src/burgers/trixi.jl index 29eee80..7adf7cc 100644 --- a/src/burgers/trixi.jl +++ b/src/burgers/trixi.jl @@ -8,9 +8,7 @@ using Printf import DiscSimulations: STANDARD_BURGER_INIT, STANDARD_BURGER_TSPAN, DiscSolution, OneDimension -function setup(N, x_max, init = STANDARD_BURGER_INIT, t_span = STANDARD_BURGER_TSPAN) - x_min = 0.0 - +function setup(N, x_min, x_max, init, t_span) equations = InviscidBurgersEquation1D() solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) @@ -22,8 +20,8 @@ function setup(N, x_max, init = STANDARD_BURGER_INIT, t_span = STANDARD_BURGER_T semi, ode end -function solve_disc(N, x_max, init = STANDARD_BURGER_INIT, t_span = STANDARD_BURGER_TSPAN) - semi, problem = setup(N, x_max, init, t_span) +function solve_disc(N, x_min, x_max, init = STANDARD_BURGER_INIT, t_span = STANDARD_BURGER_TSPAN) + semi, problem = setup(N, x_min, x_max, init, t_span) sol = solve(problem, RDPK3SpFSAL49(), abstol = 1.0e-7, reltol = 1.0e-7) return DiscSolution(sol, semi, OneDimension()) end diff --git a/src/solution.jl b/src/solution.jl index 5db658c..b942179 100644 --- a/src/solution.jl +++ b/src/solution.jl @@ -25,22 +25,16 @@ end dataplot(solution::DiscSolution{<:AbstractDimension}, t) = error("Unknown simulation type: $(typeof(t))") -function plotgif(solution::DiscSolution, tmin, tmax)#, kwargs...) +function plotgif(solution::DiscSolution, tmin, tmax; kwargs...) ts = range(tmin, tmax, 150) solver = @time solution.sol frames = Plots.@animate for t in ts pd = dataplot(solution, solver, t) - plot( - pd, - label = Printf.@sprintf("t = %1.2f", t), - #ylims = (-1, 1.1), - legend = :topright - #kwargs - ) + plot(pd ; kwargs...) end gif(frames, "temp.gif", fps = 10) |> display end -function Base.show(io::IO, sol::DiscSolution) - println(io, string(typeof(sol))) +function Base.show(io::IO, sol::DiscSolution, x) + println(io, string(typeof(sol).parameters[x])) end \ No newline at end of file diff --git a/src/test.jl b/src/test.jl index 595e9fe..ae5a749 100644 --- a/src/test.jl +++ b/src/test.jl @@ -2,10 +2,18 @@ include("DiscSimulations.jl") using .DiscSimulations initial_condition_sine(x, t, equation) = sinpi(x[1]) +#at the moment, the burgers trixi sim is expecting a function that only takes x - this could be modified for more flexibility +initial_condition_burgers(x) = sinpi(x[1]) + +t_span = (0.0, 2.0) + source_zero(u, x, t, equations) = SVector(0, 0, 0) -params = DiscSimulations.Parameters(512, 0.0, 2π, initial_condition_sine, source_zero) +params = DiscSimulations.Parameters(512, 0.0, 2π, initial_condition_burgers, source_zero, t_span) solution = DiscSimulations.main(params, DiscSimulations.BurgersSimulation()) s = DiscSimulations.DiscSolution(solution.sol, solution.semi, DiscSimulations.OneDimension()) -kwargs = ["ylims = (-1, 1.1)", "legend = :topright"] -DiscSimulations.plotgif(s, 0.0, 2.0)#, kwargs) \ No newline at end of file + +#NOTE: SHOW FUNCTION STILL NOT QUITE WORKING +#DiscSimulations.Base.show(IO, solution) + +DiscSimulations.plotgif(s, t_span[1], t_span[2]; ylims = (-1, 1.1), legend = :topright) \ No newline at end of file diff --git a/src/younsi-2012.jl b/src/younsi-2012.jl index e4f8b0b..40fc411 100644 --- a/src/younsi-2012.jl +++ b/src/younsi-2012.jl @@ -1,120 +1,25 @@ -module PolishDoughnut - -using DifferentialEquations -using StaticArrays -using ForwardDiff -using Roots - -# define a derivative functor -D(f) = x -> ForwardDiff.derivative(f, x) - -# metric components for the Kerr spacetime -Σ(r, θ, a) = r^2 + a^2 * cos(θ)^2 -Δ(r, M, a) = r^2 - 2 * M * r + a^2 -function metric_components(r, θ, M, a) - R = 2M - Σ₀ = Σ(r, a, θ) - sinθ2 = sin(θ)^2 - - tt = -(1 - (R * r) / Σ₀) - rr = Σ₀ / Δ(r, R, a) - θθ = Σ₀ - ϕϕ = sinθ2 * (r * r + a * a + (sinθ2 * R * r * a * a) / Σ₀) - - tϕ = (-R * r * a * sinθ2) / Σ₀ - @SVector [tt, rr, θθ, ϕϕ, tϕ] -end - -# younsi et al. 2012 equations -# eq. (32) -Ω(z, M, a, n, rₖ) = (√M / (z^(3 / 2) + a * √M)) * (rₖ / z)^n -Ω(r, θ, M, a, n, rₖ) = Ω((r * sin(θ)), M, a, n, rₖ) - -# eq. (30) -Ψ₁(r, θ, M, a, Ω, Σ) = M * ((Σ - 2r^2) / (Σ^2)) * (Ω - a * sin(θ))^2 + r * sin(θ)^2 -Ψ₁(r, θ, M, a, Ω) = Ψ₁(r, θ, M, a, Ω, Σ(r, θ, a)) - -# eq. (31) -Ψ₂(r, θ, M, a, Ω, Σ, Δ) = sin(2θ) * ((M * r / (Σ^2)) * (a * Ω - (r^2 + a^2))^2 + Δ / 2) -Ψ₂(r, θ, M, a, Ω) = Ψ₂(r, θ, M, a, Ω, Σ(r, θ, a), Δ(r, M, a)) - -# eq. (28) and (29) -function drdθ(u, p, λ) - # unpack parameters - r, θ = u - - Ω₀ = inv(Ω(r, θ, p.M, p.a, p.n, p.rₖ)) - ψ₁ = Ψ₁(r, θ, p.M, p.a, Ω₀) - ψ₂ = Ψ₂(r, θ, p.M, p.a, Ω₀) - Δ₀ = Δ(r, p.M, p.a) - Σ₀ = Σ(r, θ, p.a) - - denom = √(Δ₀ * ψ₁^2 + ψ₂^2) * √inv(Δ₀ / Σ₀) - dr = ψ₂ / denom - dθ = -ψ₁ / denom - - # use a static vector to avoid heap allocation - @SVector [dr, dθ] -end - -function energy(r, θ, M, a, n, rₖ) - Ω₀ = Ω(r, θ, M, a, n, rₖ) - # analytic solution for energy of a circular orbit - g = metric_components(r, θ, M, a) - -(g[1] + g[5] * Ω₀) / √(-g[1] - 2g[5] * Ω₀ - g[4] * Ω₀^2) +using DiscSimulations +using Plots + +# black hole mass +M = 1.0 + +# black hole spin +a = 0.2 + +# keplerian radius +rₖ = 12.0 + +# angular velocity profile index of the torus +n = 0.21 + +begin + p = plot(xlabel = "r", ylabel = "z", legend = :outertopright) + for a in [0.0, 0.2, 0.4, 0.6, 0.8] + r, z = @time isobar(M, a, n, rₖ) + plot!(r, z, label = "a = $a") + # plot but upside down + plot!(r, -z, label = "a = $a") + end + p end - -function energy_minima(θ, M, a, n, rₖ, init_r) - # capture all but radius in a closure - closure = r -> energy(r, θ, M, a, n, rₖ) - # we want to find r for which dE/dr == 0 - dEdr = D(closure) - # we give the function to find the zero for and the gradient of the function - # to the root finder, so we can use something like the Newton solver, which - # is pretty fast and accurate - R = find_zero((dEdr, D(dEdr)), init_r, Roots.Newton()) - R -end - -const terminate_if_negative = - DiscreteCallback((u, t, integrator) -> u[1] * cos(u[2]) < 0, terminate!) - -""" - isobar(M, a, n, rₖ; θ = π/2, init_r = 5.0, max_λ = 40.0) - -Calculate the isobar surface of a pressure supported accretion disc as in Younsi et al. (2012). -- `M`: black hole mass, -- `a`: (dimensionless) black hole spin, -- `n`: angular velocity profile index of the torus, -- `rₖ`: central Keplerian radius of the torus. - -The inclination of the disc from the spin axis may be set by altering `θ`. The minima of ``E(r)`` as a function of ``r`` -is numerically solved using a root finder, starting at `init_r`, and `max_λ` is the maximum integration time for the -differential equation solver. -""" -function isobar(M, a, n, rₖ; θ = π / 2, init_r = 5.0, max_λ = 40.0) - r = energy_minima(θ, M, a, n, rₖ, init_r) - u0 = @SVector [r, θ] - - λ_span = (0.0, max_λ) - # named tuple syntax - params = (; M = M, a = a, n = n, rₖ = rₖ) - prob = ODEProblem{false}(drdθ, u0, λ_span, params) - - sol = solve(prob, Tsit5(), callback = terminate_if_negative, dtmax = 5e-2) - - # quick and dirty unpack - r = first.(sol.u) - θ = last.(sol.u) - - # then translate to cartesian coordinates - z = @. r * cos(θ) - - # and only return those with z > 0 - I = @. z > 0 - r[I], z[I] -end - -end # module PolishDoughnut - -export PolishDoughnut diff --git a/temp.gif b/temp.gif index 2af17b21c03253c5cc7132fa2c7aa2f52d7a0b05..4ce63e4ab68285d95f291985eba1df5a9878b2db 100644 GIT binary patch literal 377895 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z|8qVI!S)sEt)9y+z(g$SHh=+(VbV#xBEcJX7w<;j;Z0=MP`NJm8_PM4zU%meZB zM-V}0mG|M75GKiNzRISLqz`yw1zoo0V;LO=PY%@6@3&?C>ulzqd!>+#xaKkD_^-3s zg^?k)`fE0^oe|jFRp6#M9d6-ZQWx!7x<2_fS-8;kDRv`GAYMF9=XX~{lG|=JcNd;})e(*uq%pG8Uk$-mvP2y@4DIlGJYq*Dw1Z$mJ){n<1z5q}&K`#@k-W-%!L} z24&AZdpy-RfVqV@;VK2K@}20p$A3%WNe{DN%$bSOtd?XKFN{W3I#bg)GeKTumG5Mp z&p#*wS$JIioIitm?Ey2~%}hK4K`I z?!55T?_xod>pwi|V$_9_>MU`;S0-ol#cMOFCzAWDH9h_$As$a&QHwm|5mv4yrdMSU zc56Hgrq{>LIBLIM>d1!W5Q-H3(@TW_i+;>4L{~DEyIky)_<17qwuac@tn;TND;{m1 zPm%28YNpQhv`-FfoNiVXjcydnys(I`CtP{qVv=<8N6Yf_Ky$5Xu%_5p>237xXTK`x zC!%hP5ATgs4pu#fUW%1WWz)H2+ah(R8rRn2A|s(Z*c$M>FoB#@HPTeM{`@B|Gasq& xw+d)uKv&sn%T{&8Ux3XfB)L6{dRe9K^)JKVnRa49?^BH+St*t-O!kuQ{{nJrCENf2 From 8d90254eee1df6337de15fedeb7e235fc35d54fb Mon Sep 17 00:00:00 2001 From: Alice Date: Wed, 26 Apr 2023 12:46:22 +0100 Subject: [PATCH 4/8] Modified refinement level and time span of Burgers test case --- src/BurgersTestCase.jl | 6 +++--- src/DiscSimulations.jl | 3 ++- src/burgers/trixi.jl | 8 ++++---- temp.gif | Bin 377895 -> 307976 bytes 4 files changed, 9 insertions(+), 8 deletions(-) diff --git a/src/BurgersTestCase.jl b/src/BurgersTestCase.jl index d0488ed..947c6a9 100644 --- a/src/BurgersTestCase.jl +++ b/src/BurgersTestCase.jl @@ -3,10 +3,10 @@ using .DiscSimulations xmin = 0.0 xmax = 1.0 -N = 256 +N = 1024 tmax = (xmax - xmin)/1.0 -t_span = (0.0, tmax) +t_span = (0.0, 0.2*tmax) function initial_condition_burgers(x) u = 1.0 @@ -19,7 +19,7 @@ end #params expects this so we're defining a dummy one source_zero(u, x, t, equations) = SVector(0, 0, 0) -params = DiscSimulations.Parameters(N, xmin, xmax, initial_condition_burgers, source_zero, t_span) +params = DiscSimulations.Parameters(N, xmin, xmax, initial_condition_burgers, source_zero, t_span, 8) solution = DiscSimulations.main(params, DiscSimulations.BurgersSimulation()) s = DiscSimulations.DiscSolution(solution.sol, solution.semi, DiscSimulations.OneDimension()) diff --git a/src/DiscSimulations.jl b/src/DiscSimulations.jl index fce8ecb..5351aeb 100644 --- a/src/DiscSimulations.jl +++ b/src/DiscSimulations.jl @@ -14,6 +14,7 @@ struct Parameters{T} ρ source t_span + refinement_level::Int end abstract type SimulationType end @@ -23,7 +24,7 @@ struct BurgersSimulation <: SimulationType end struct EulerWithSourceSimulation <: SimulationType end struct SimpleGravitySimulation <: SimulationType end -main(p::Parameters, ::BurgersSimulation) = BurgerTrixi.solve_disc(p.N, p.xmin, p.xmax, p.ρ, p.t_span) +main(p::Parameters, ::BurgersSimulation) = BurgerTrixi.solve_disc(p.N, p.xmin, p.xmax, p.refinement_level, p.ρ, p.t_span) main(p::Parameters, ::EulerWithSourceSimulation) = EulerSource.solve_euler(p.source) main(p::Parameters, ::SimpleGravitySimulation) = SimpleGravitySimulation.solve_gravity_sim(p.ρ) diff --git a/src/burgers/trixi.jl b/src/burgers/trixi.jl index 7adf7cc..e7a973d 100644 --- a/src/burgers/trixi.jl +++ b/src/burgers/trixi.jl @@ -8,11 +8,11 @@ using Printf import DiscSimulations: STANDARD_BURGER_INIT, STANDARD_BURGER_TSPAN, DiscSolution, OneDimension -function setup(N, x_min, x_max, init, t_span) +function setup(N, x_min, x_max, init, t_span, refinement_level) equations = InviscidBurgersEquation1D() solver = DGSEM(polydeg = 3, surface_flux = flux_lax_friedrichs) - mesh = TreeMesh(x_min, x_max, initial_refinement_level = 3, n_cells_max = N) + mesh = TreeMesh(x_min, x_max, initial_refinement_level = refinement_level, n_cells_max = N) semi = SemidiscretizationHyperbolic(mesh, equations, (x, t, eqs) -> init(x), solver) ode = semidiscretize(semi, t_span) @@ -20,8 +20,8 @@ function setup(N, x_min, x_max, init, t_span) semi, ode end -function solve_disc(N, x_min, x_max, init = STANDARD_BURGER_INIT, t_span = STANDARD_BURGER_TSPAN) - semi, problem = setup(N, x_min, x_max, init, t_span) +function solve_disc(N, x_min, x_max, refinement_level, init = STANDARD_BURGER_INIT, t_span = STANDARD_BURGER_TSPAN) + semi, problem = setup(N, x_min, x_max, init, t_span, refinement_level) sol = solve(problem, RDPK3SpFSAL49(), abstol = 1.0e-7, reltol = 1.0e-7) return DiscSolution(sol, semi, OneDimension()) end diff --git a/temp.gif b/temp.gif index 4ce63e4ab68285d95f291985eba1df5a9878b2db..2870bc685e8a5006cccb832d43bc0b705be300d4 100644 GIT binary patch literal 307976 zcmeF(S5Q;&`!4!4lF*Y7AoS2Xf}j*B3B5{CRI1WJ0RaW22_dvlqzg!sE+8r(DxgT{ z2uKG3ks^Y00qHG=-~R78XP4O*=k8pb&#cL;i`-?N_00R7cSX-YS4r940+a;Y2Lb*g z`v^b> zAb;-7vHaU31qB7AbJa&GDk`cqM{4hm)Ya8-I2^wANK;c&>;18|wzlrM4@dgvJ{}pJ zt2;Kn_vGri`eOotaP8Ca_3PJfocnxYajx;$%F4>d#>Vzs)A8-5liQS&J9q9lI5;?- zYd&^%c6M=baXr_1?B0It;o))r{(Y~GV;>)%hv&MEAD#Pp?CbvF8R)}mDvX-!SdyV;Z4UuW;%zyEmd*IC{CS$%!|r*pqgKY#w**x2}G z;jHQ0;#u>##nYC#oz`=6|62c?wf#A3Z*T8Bw|w?>>FDdqS@*g5t?rexp5Om^R!)1* zt)6{bJ?rc1>t8z?IJdApaDKCXHn_AuG&D54aW*nCGP-d(x^Xr(Ha5O_HgRtAY;tvX za`WuRx#g{?t+Su!w$G-w&t}eTpUwU|o7>p?b#CWue&_7>@81iHiwnDFi@Vf6fBr1( zQJ2rHtSs+QSI_NJ*U$YsSU;d{{Qdj)fVz3^kh;CS{qMgVp8Y$b?(XjHo!j5vJ3iar z-#<7wI6OH!IyyQ&K0Y~jNgyt^l?;`i$NTf5d+&p?l4Zne}e 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Thu, 27 Apr 2023 17:12:17 +0100 Subject: [PATCH 5/8] added python burgers files --- Project.toml | 1 + .../benchmarkedBurgers.cpython-310.pyc | Bin 0 -> 5832 bytes Python Burgers example/benchmarkedBurgers.py | 318 ++++++++++++++++++ Python Burgers example/fv-burger-sine.pdf | Bin 0 -> 13978 bytes Python Burgers example/originalBurgers.py | 304 +++++++++++++++++ Python Burgers example/python-data.csv | 43 +++ Python Burgers example/run-burgers.py | 12 + julia-output.csv | 1 + src/BurgersTestCase.jl | 7 +- 9 files changed, 685 insertions(+), 1 deletion(-) create mode 100644 Python Burgers example/__pycache__/benchmarkedBurgers.cpython-310.pyc create mode 100644 Python Burgers example/benchmarkedBurgers.py create mode 100644 Python Burgers example/fv-burger-sine.pdf create mode 100644 Python Burgers example/originalBurgers.py create mode 100644 Python Burgers example/python-data.csv create mode 100644 Python Burgers example/run-burgers.py create mode 100644 julia-output.csv diff --git a/Project.toml b/Project.toml index 4ed9adb..ce81cc2 100644 --- a/Project.toml +++ b/Project.toml @@ -5,6 +5,7 @@ version = "0.1.2" [deps] ApproxFun = "28f2ccd6-bb30-5033-b560-165f7b14dc2f" +BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf" DifferentialEquations = "0c46a032-eb83-5123-abaf-570d42b7fbaa" ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210" LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" diff --git a/Python Burgers example/__pycache__/benchmarkedBurgers.cpython-310.pyc b/Python Burgers example/__pycache__/benchmarkedBurgers.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..9c1955c381653cf567420e1ffcf87bf1680cb4d8 GIT binary patch literal 5832 zcmai2%a0sK8SkooOwV&49(&hu5}GJVG9g}KD@urCvc`^L5@0b|kYHFe>h0>;?b)8` zadppncjys^b&kGq0Yzw+n=c#?7moZ1NO0*3Laeb^D*s_L(*zOKht zzwc2M)$0`v&-!N{i$8xw)BZt)(~p6|Eu{D}WI_`x)Y?pad0%fEEUz=$mZ~eYOX_R4 zZNYu3R~GtBO&E$YL0O6_fwC1<231j1^`>@L6E#tPsEN8?IndixlpA6WkzAu6idhG^VBk8XsK@$4(hesoxesmOW 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z72JJPVM9z4~uhd3g_5agX^?XlajxNB&;v#JFoNa3yN#V<}{_@_-$VM-Z7rVPxH`PtcRSJk#hN3&38>$*yyWzC*gH)yu!=$ZyxD_IVL5mRiWi_0@yB#kYkqggEb*Cg1qGw@r zW_ZzXUlN+z#xRT$6-A$%ED=v9vTf~!?xr8Mt^NF4irrlwcY>J_4gCRJx(pHo*dfceu?AE;sQzoph= 0.333, + self.grid.x <= 0.666)] = 1.0 + + elif type == "sine": + self.grid.u[:] = 1.0 + + index = np.logical_and(self.grid.x >= 0.333, + self.grid.x <= 0.666) + self.grid.u[index] += \ + 0.5*np.sin(2.0*np.pi*(self.grid.x[index]-0.333)/0.333) + + elif type == "rarefaction": + self.grid.u[:] = 1.0 + self.grid.u[self.grid.x > 0.5] = 2.0 + + + + def timestep(self, C): + return C*self.grid.dx/max(abs(self.grid.u[self.grid.ilo: + self.grid.ihi+1])) + + + def states(self, dt): + """ compute the left and right interface states """ + + g = self.grid + # compute the piecewise linear slopes -- 2nd order MC limiter + # we pick a range of cells that includes 1 ghost cell on either + # side + ib = g.ilo-1 + ie = g.ihi+1 + + u = g.u + + # this is the MC limiter from van Leer (1977), as given in + # LeVeque (2002). Note that this is slightly different than + # the expression from Colella (1990) + + dc = g.scratch_array() + dl = g.scratch_array() + dr = g.scratch_array() + + dc[ib:ie+1] = 0.5*(u[ib+1:ie+2] - u[ib-1:ie ]) + dl[ib:ie+1] = u[ib+1:ie+2] - u[ib :ie+1] + dr[ib:ie+1] = u[ib :ie+1] - u[ib-1:ie ] + + # these where's do a minmod() + d1 = 2.0*np.where(np.fabs(dl) < np.fabs(dr), dl, dr) + d2 = np.where(np.fabs(dc) < np.fabs(d1), dc, d1) + ldeltau = np.where(dl*dr > 0.0, d2, 0.0) + + # now the interface states. Note that there are 1 more interfaces + # than zones + ul = g.scratch_array() + ur = g.scratch_array() + + # are these indices right? + # + # --+-----------------+------------------+ + # ^ i ^ ^ i+1 + # ur(i) ul(i+1) ur(i+1) + # + ur[ib:ie+2] = u[ib:ie+2] - \ + 0.5*(1.0 + u[ib:ie+2]*dt/self.grid.dx)*ldeltau[ib:ie+2] + + ul[ib+1:ie+2] = u[ib:ie+1] + \ + 0.5*(1.0 - u[ib:ie+1]*dt/self.grid.dx)*ldeltau[ib:ie+1] + + return ul, ur + + + def riemann(self, ul, ur): + """ + Riemann problem for Burgers' equation. + """ + + S = 0.5*(ul + ur) + ushock = np.where(S > 0.0, ul, ur) + ushock = np.where(S == 0.0, 0.0, ushock) + + # rarefaction solution + urare = np.where(ur <= 0.0, ur, 0.0) + urare = np.where(ul >= 0.0, ul, urare) + + us = np.where(ul > ur, ushock, urare) + + return 0.5*us*us + + + def update(self, dt, flux): + """ conservative update """ + + g = self.grid + + unew = g.scratch_array() + + unew[g.ilo:g.ihi+1] = g.u[g.ilo:g.ihi+1] + \ + dt/g.dx * (flux[g.ilo:g.ihi+1] - flux[g.ilo+1:g.ihi+2]) + + return unew + + + def evolve(self, C, tmax): + + self.t = 0.0 + + g = self.grid + + # main evolution loop + while (self.t < tmax): + + # fill the boundary conditions + g.fill_BCs() + + # get the timestep + dt = self.timestep(C) + + if (self.t + dt > tmax): + dt = tmax - self.t + + # get the interface states + ul, ur = self.states(dt) + + # solve the Riemann problem at all interfaces + flux = self.riemann(ul, ur) + + # do the conservative update + unew = self.update(dt, flux) + + self.grid.u[:] = unew[:] + + self.t += dt + + +def main(): + #----------------------------------------------------------------------------- + # sine + + xmin = 0.0 + xmax = 1.0 + nx = 256 + ng = 2 + g = Grid1d(nx, ng, bc="periodic") + + # maximum evolution time based on period for unit velocity + tmax = (xmax - xmin)/1.0 + + C = 0.8 + + plt.clf() + + s = Simulation(g) + + start = time.perf_counter() + + for i in range(0, 10): + tend = (i+1)*0.02*tmax + s.init_cond("sine") + + uinit = s.grid.u.copy() + + s.evolve(C, tend) + + c = 1.0 - (0.1 + i*0.1) + g = s.grid + plt.plot(g.x[g.ilo:g.ihi+1], g.u[g.ilo:g.ihi+1], color=str(c)) + + timeTaken = time.perf_counter() - start + + #print(f"Completed Execution in {timeTaken} seconds") + + g = s.grid + plt.plot(g.x[g.ilo:g.ihi+1], uinit[g.ilo:g.ihi+1], ls=":", color="0.9", zorder=-1) + + plt.xlabel("$x$") + plt.ylabel("$u$") + plt.savefig("fv-burger-sine.pdf") + + f = open('python-data.csv','w') + f.write('x: ') + #f.write(str(g.x[g.ilo:g.ihi+1])) + f.write(str(g.u[g.ilo:g.ihi+1])) + f.close() + + return timeTaken + + + #----------------------------------------------------------------------------- + # rarefaction + """ + xmin = 0.0 + xmax = 1.0 + nx = 256 + ng = 2 + g = Grid1d(nx, ng, bc="outflow") + + # maximum evolution time based on period for unit velocity + tmax = (xmax - xmin)/1.0 + + C = 0.8 + + plt.clf() + + s = Simulation(g) + + for i in range(0, 10): + tend = (i+1)*0.02*tmax + + s.init_cond("rarefaction") + + uinit = s.grid.u.copy() + + s.evolve(C, tend) + + c = 1.0 - (0.1 + i*0.1) + plt.plot(g.x[g.ilo:g.ihi+1], g.u[g.ilo:g.ihi+1], color=str(c)) + + + plt.plot(g.x[g.ilo:g.ihi+1], uinit[g.ilo:g.ihi+1], ls=":", color="0.9", zorder=-1) + + plt.xlabel("$x$") + plt.ylabel("$u$") + + plt.savefig("fv-burger-rarefaction.pdf")""" + +if __name__ == "__main__": + main() + diff --git a/Python Burgers example/fv-burger-sine.pdf b/Python Burgers example/fv-burger-sine.pdf new file mode 100644 index 0000000000000000000000000000000000000000..2eb5b890a632ef00679f4edf7cc336d7448fccf6 GIT binary patch literal 13978 zcmc(G2|QI__cuZ^B{F5`k~!Sjy|<8gDDxDV=OI&E8A6843MEs9giweiLYaqTh%%3n zAyYD|=so9_>eui0{GaFfzwhVsUY~8Bv(FyZT6>+fziaJ%cs1k{MBt(*O5TDI$iqrX zI0Oc9v2dUi7l%M~yj`s!P+4=lxuc6M1gc?fYwZp}02Q<#l9H6x&Q@SW>~9SeT%7R` zB%uOSU){pN+7b`Je7}|V!YgXy&GFU{)b|1nb3ESK%^89QZz-YLcIH<0&bAP-A5Yy} zEVZri5JO;CIR$_eYcD(ms_X=iAoC-a{gEp}jDI5s{&xmIxC^48Q7J@{fMa6*bp|SvDKx=mh?mKzX&dx5t9UQFs zyD-4V`_fafcDBXaLEt||RIqmh_=P|f904K7SzEeTS%YM|3W~j%Ffcf>Hh@pVEORW^c}nkH2g!YHK^qZaNgIK=N`qb>3GY z)t#IB;*0GsF5lKnYj!q|*L+^x@x1Egd&%$1%%j8KzTUXHw~FujxILSjd)2?`%vEpf zi`^BaCXVas<6Y|T>8zEGw2Zy!Pupu#QRAz(YF0`>PMTJQ{5JMnUa1RVXvAn9d9t6I(vz4hV~?u0-;4!YFEVXO?~U@%+_kp zJQI9TvHiuG=F+Y}Vfi{W7l%mI%_qWp>l7tkd`TnHxwtRg?aohP+mP=YElNwJuSi(f zmEDl9dMm?HxFm2ReeRl|!g+^?tmnrISG7~TPgSIEc)6ytKBe!z<|K6UQw;2Z3zt!3Acu1#0f%-QbtRST8g&qdFtPkmkq5ZyI%a2&Lo z)wuY`F@2^J|HZK@Y&QI6dP}{LQeCKsqx7Zc(S?Fsl{itG{z0=dPZ7C&#SCSoD{T(1 z26mQxInL4C5NS~~h0-ymP^bj&Gh1$a=T;V5)Y;wE%$LtEBsh^H zW7@gi#uo=ieh7Ix2@8&no05@`ILCI-rLXQ3rQ)k@W(DYAPPeB`rNrfyH#c@y9Y5JM z}m62 zs*`~5nOR#=w>+`UtO@t_&NIorN*=V~mjXD;-t(6>(yY~zzMfH<@?s5ov+$BLVGDiG z=+o?&cVejKrDM;(&}Ecyil?+CAx+(mo-*Gmdu(6{g_-nQyi$+Z65D*!&e<-c`TB$3 z8M}v<)}t@Nyv!N&zr?v8ka~L~s)VzDm*X?H*DcuOvGM-B?S`p^*%+wVWsS&MgX~YY z!lgxIOvlNB`K66S5E0#7i7VaeF~@hxuk1Byh-qd zm9Hzab?1-ot#41Qop)?|lo@ci=IYmmu$KN9cyO4lobTZir^8HA{QVujlCvpeO`~>= zgTu;$sf^t7+2?WFJ?jy5RYq@`qPfg;KC+1WS-A>V*a+LPes%b~Q#YM>S80J&z`K89 zdTF9|yF06Rn%&nPcyMBowTh*W`SmnMaCrL~i9Ki6 z1x^K{67kHldrllH$jr*H=A8}Z8miJN)7}0@8OL83=AMz$V64v_Id(?MQ``6eyFQ^ z8PFltNG!aWU-xFzq_@N6E!S#8hw(L6I@q`1j=dJ^()vBmSDPzecezKod`QB!C_Q)% zy60=>$*u^Fkv$u-Y^B??3o9&+NC*v3ywI2`6j8};9~3!6`gq;Pr6^Yw@@9-~mCukVq`<6pHoq)D zr~XKG58XE0t=(U{Gu6wRcCR9lx=h8DGmo)e+}R*=M#y zdN3_KlALD|!Rp@Si3Sp@8`App{ z+R=Ic-F-?L=M;{#*7W;3>-mH5viQfI8%2Y>v=7`x#?hzedJs=I#5#)9B@G>)*=+_L zrk7ky;pnESPl6bus)B0foLcWV9y}XGmJsFWIb>V^RQ0K)GK&Mv9mn(QbT)Y&A1>Rw zaj*LHFD)8OPB=Ddm)pwgv0Qnva9QtF+`C20Xpt^sItRJ2{I0T(Y-q?tDMTT5Dq`*R z-hhHTlHIui9f+Bl$l1n=1*)Zv8Ak^Q&GWvPDQWeF4quh-;hxpJAW-4Ruvnj~(i;7> z9zAFsQ%c#qh9 z)tPk9?D%ft`-N}kygt?3Puld4#N9$S!z6H1M6^s0Pj7?@YS&AXJg`Vh(wT)(lg8L) zL1E-t%>|*k+aq-k54$?f9;rA0+w|wBu8oosZMx2U6G4qt9$q<)Ie3A3izx{zd-v$t z4to3ualB54PM@!$u5X{^=!B6sL#*fIEZMATdl=191YN=Hmseip7P!(D5{HKhQKi0$ zJZ*SKOgv1XxPX4MF=8&9LS)%X^wgxB#qdh%rhYNH=H0W&h3MDt3BJfjCn}hon(t9} zk*~L%EDMi|+4QyAgIy~*lj{Fiu3LsE=uiv)70%P4&$tQ$&v$f)_sdgHa#&;zMY9ax zn`Ffg``3{T&cRERRLH+j9;$bB?kRggbPIPwiWJV!{(zo+e#LPpEr2|&G$*q9z4Aq8 z8@o=UBkbWJG#_i=(GUvk^`~P|7UH2a;YkL@N3%vhDwBI>vG9uerZ!*JRJkn_qV+1x zVgM0gd}mS~9+0HYzManG(AKCLY%HLFpoT24H5EU%`|w0Nx`Kyncr?T!HM*f|=9YyW z8Qb;yOp%vvk`MMcF*lj@JK5MlLjy(Q*y|oU@He!U;a<}(Q#WkZm+z)SEvkg59dI>K zmm_;JTd(7DIcx^oG&nIsasCtem7h9WJNPWArbAEPFlvrFaWLiCdi|+Jjm4UBSXqglRCS*+q| zQ6U=|^5w;5x^u_P^HU`coa;5M)v{GW*tfYoK97^?2qx)CGndn54Ut^id*l{yenZMz z=|nm*$UIj%pP5X!y&=Iv@{WzM06B`xM4~+v;_CX!j0l^!3*@>s8Z35du*C)E=mdQR;wVkOux)ij&N^

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