Test for conservation of mass

test/mass_conservation.jl

@@ -0,0 +1,106 @@
+using Revise
+using Infiltrator
+using Test 
+
+using Huginn
+
+"""
+    unit_mass_test(; H₀, B, A, t_sim, Δx, Δy, rtol=0.02, atol=1.0, distance_to_border=3, save_plot=false)
+
+Test one single run of the forward model with customized physical parameters and 
+initial condition. It checks that the total mass of ice is conserved during the solver 
+when no mass balance is applied. 
+
+Arguments 
+=================
+    - `H₀`: Initial ice thickness profile
+    - `B`: Bed topography
+    - `A`: Glen coefficient 
+    - `t_sim`: Total time for the simulation
+    - `Δx`, `Δy`: Spacial width
+    - `rtol`: Relative tolerance
+    - `save_plot`: Optional bool to save plot during simulation
+"""
+function unit_mass_test(; H₀, B, A, t_sim, Δx, Δy, rtol=0.02, save_plot=false)
+
+    # Get parameters for a simulation 
+    parameters = Parameters(simulation=SimulationParameters(tspan=(0.0, t_sim),
+                                                            use_MB=false,
+                                                            use_iceflow=true,
+                                                            multiprocessing=true,
+                                                            workers=1),
+                            physical=PhysicalParameters(A=A),
+                            solver=SolverParameters(reltol=1e-12))
+
+    model = Model(iceflow = SIA2Dmodel(parameters))
+
+    # Surface
+    S = B + H₀
+    nx, ny = size(H₀)
+
+    # Define glacier object
+    glacier = Glacier(rgi_id = "toy", H₀ = H₀, S = S, B = B, 
+                      Δx=Δx, Δy=Δy, nx=nx, ny=ny)
+    glaciers = Vector{Sleipnir.AbstractGlacier}([glacier])
+
+    prediction = Prediction(model, glaciers, parameters)
+    run!(prediction) 
+
+    # Final solution
+    H₁_pred = prediction.results[1].H[end]
+
+    # Optional plot
+    if save_plot
+        fig = Figure(resolution = (800, 800))
+
+        Axis(fig[1, 1], title = "Initial Condition")
+        heatmap!(H₀, colormap=:viridis, colorrange=(0, maximum(H₀)))
+
+        Axis(fig[1, 2], title = "Final State")
+        heatmap!(H₁, colormap=:viridis, colorrange=(0, maximum(H₀)))
+
+        Axis(fig[2,1], title="Difference")
+        heatmap!(H₁_pred .- H₀, colormap=Reverse(:balance), colorrange=(-10, 10))
+
+        save("test/mass_conservation_test.png", fig)
+    end
+
+    # Initial total mass 
+    mass₀ = sum(H₀)
+    mass₁ = sum(H₁_pred)
+    Δmass = mass₁ - mass₀
+    # @show Δmass, Δmass / mass₀
+
+    # No mass in the borders of the domain
+    @test maximum(maximum([H₁_pred[2,:], H₁_pred[:,2]])) < 1.0e-7
+    @test Δmass / mass₀ < rtol
+end
+
+
+"""
+    unit_mass_flatbed_test(; rtol, atol)
+
+Tests a combination of bed topographies and initial conditions 
+
+Arguments 
+=================
+    - `rtol`: Relative tolerance
+"""
+function unit_mass_flatbed_test(; rtol)
+    for nx in 80:20:140
+        ny = nx
+        for shape in ["parabolic", "square"]
+            for A in [4e-17, 8e-17]
+                B = zeros((nx, ny))
+                if shape == "parabolic"
+                    H₀ = [ 0.5 * ( (nx/4)^2 - (i - nx/2)^2 - (j - ny/2)^2 ) for i in 1:nx, j in 1:ny]
+                    H₀[H₀ .< 0.0] .= 0.0
+                elseif shape == "square"
+                    H₀ = zeros((nx,ny))
+                    @views H₀[floor(Int,nx/3):floor(Int,2nx/3), floor(Int,ny/3):floor(Int,2ny/3)] .= 400
+                end
+                unit_mass_test(; H₀=H₀, B=B, A=A, t_sim=10.0, Δx=50.0, Δy=50.0, rtol=rtol, save_plot=false)
+            end
+        end
+    end
+end

test/runtests.jl

@@ -11,7 +11,7 @@ using Huginn
 
 # include("PDE_UDE_solve.jl")
 include("halfar.jl")
-# include("mass_conservation.jl")
+include("mass_conservation.jl")
 
 # Activate to avoid GKS backend Plot issues in the JupyterHub
 ENV["GKSwstype"]="nul"
@@ -24,4 +24,4 @@ atol = 2.0
 
 @testset "Halfar Solution" halfar_test(rtol=0.02, atol=1.0)
 
-# @testset "Conservation of Mass - Flat Bed" unit_mass_flatbed_test(rtol=1.0e-7, atol=1000)
+@testset "Conservation of Mass - Flat Bed" unit_mass_flatbed_test(rtol=1.0e-7)