add 1D advection test

Author: Iddingsite

test/test_1D_advection.jl

@@ -0,0 +1,158 @@
+@testset "struct tests" begin
+    @testset "1D Shu test" begin
+
+        # Number of grid points
+        nx = 200
+
+        x_min = -1.0
+        x_max = 1.0
+        Lx = x_max - x_min
+
+        x = range(x_min, stop=x_max, length=nx)
+
+        # Courant number
+        CFL = 0.4
+        period = 2
+
+        # Parameters for Shu test
+        z = -0.7
+        δ = 0.005
+        β = log(2)/(36*δ^2)
+        a = 0.5
+        α = 10
+
+        # Functions
+        G(x, β, z) = exp.(-β .* (x .- z).^2)
+        F(x, α, a) = sqrt.(max.(1 .- α^2 .* (x .- a).^2, 0.0))
+
+        # Grid x assumed defined
+        u0_vec = zeros(length(x))
+
+        # Gaussian-like smooth bump at x in [-0.8, -0.6]
+        idx = (x .>= -0.8) .& (x .<= -0.6)
+        u0_vec[idx] .= (1/6) .* (G(x[idx], β, z - δ) .+ 4 .* G(x[idx], β, z) .+ G(x[idx], β, z + δ))
+
+        # Heaviside step at x in [-0.4, -0.2]
+        idx = (x .>= -0.4) .& (x .<= -0.2)
+        u0_vec[idx] .= 1.0
+
+        # Piecewise linear ramp at x in [0, 0.2]
+        # Triangular spike at x=0.1, base width 0.2
+        idx = abs.(x .- 0.1) .<= 0.1
+        u0_vec[idx] .= 1 .- 10 .* abs.(x[idx] .- 0.1)
+
+        # Elliptic/smooth bell at x in [0.4, 0.6]
+        idx = (x .>= 0.4) .& (x .<= 0.6)
+        u0_vec[idx] .= (1/6) .* (F(x[idx], α, a - δ) .+ 4 .* F(x[idx], α, a) .+ F(x[idx], α, a + δ))
+
+
+        u = copy(u0_vec)
+        weno = WENOScheme(u; boundary=(2, 2), stag=true)
+
+        # advection velocity
+        a = ones(nx+1) .* 1
+
+        # grid size
+        Δx = x[2] - x[1]
+        Δt = CFL*Δx^(5/3)
+
+        tmax = period * (Lx + Δx) / maximum(abs.(a))
+
+        t = 0
+
+        while t < tmax
+            WENO_step!(u, a, weno, Δt, Δx)
+
+            t += Δt
+
+            if t + Δt > tmax
+                Δt = tmax - t
+            end
+        end
+
+        @test sum(u) ≈ 51.92724276042664
+        @test maximum(u) ≈ 0.9991824828036449
+    end
+
+    @testset "1D Shu test Chmy CPU" begin#
+
+        backend=CPU()
+        nx=200
+
+        arch = Arch(backend)
+
+        x_min = -1.0
+        x_max = 1.0
+        Lx = x_max - x_min
+
+        x = range(x_min, stop=x_max, length=nx)
+
+        grid   = UniformGrid(arch; origin=(x_min,), extent=(Lx,), dims=(nx,))
+
+        # Courant number
+        CFL = 0.7
+        period = 4
+
+        # Parameters
+        z = -0.7
+        δ = 0.005
+        β = log(2)/(36*δ^2)
+        a = 0.5
+        α = 10
+
+        # Functions
+        G(x, β, z) = exp.(-β .* (x .- z).^2)
+        F(x, α, a) = sqrt.(max.(1 .- α^2 .* (x .- a).^2, 0.0))
+
+        # Grid x assumed defined
+        u0_vec = zeros(length(x))
+
+        # Gaussian-like smooth bump at x in [-0.8, -0.6]
+        idx = (x .>= -0.8) .& (x .<= -0.6)
+        u0_vec[idx] .= (1/6) .* (G(x[idx], β, z - δ) .+ 4 .* G(x[idx], β, z) .+ G(x[idx], β, z + δ))
+
+        # Heaviside step at x in [-0.4, -0.2]
+        idx = (x .>= -0.4) .& (x .<= -0.2)
+        u0_vec[idx] .= 1.0
+
+        # Piecewise linear ramp at x in [0, 0.2]
+        # Triangular spike at x=0.1, base width 0.2
+        idx = abs.(x .- 0.1) .<= 0.1
+        u0_vec[idx] .= 1 .- 10 .* abs.(x[idx] .- 0.1)
+
+        # Elliptic/smooth bell at x in [0.4, 0.6]
+        idx = (x .>= 0.4) .& (x .<= 0.6)
+        u0_vec[idx] .= (1/6) .* (F(x[idx], α, a - δ) .+ 4 .* F(x[idx], α, a) .+ F(x[idx], α, a + δ))
+
+
+        u = Field(backend, grid, Center())
+        set!(u, u0_vec)
+        weno = WENOScheme(u, grid; boundary=(2, 2), stag=true)
+
+        # advection velocity
+        a_vec = ones(nx+1) .* -1
+        a = VectorField(backend, grid)
+        set!(a, a_vec)
+
+        # grid size
+        Δx = x[2] - x[1]
+        Δt = CFL * Δx^(5/3)
+
+        tmax = period * (Lx+Δx) / maximum(abs.(a.x))
+
+        t = 0
+
+        while t < tmax
+            WENO_step!(u, a, weno, Δt, Δx, grid, arch)
+
+            t += Δt
+
+            if t + Δt > tmax
+                Δt = tmax - t
+            end
+        end
+
+        @test sum(u) ≈ 51.92724276042664
+        @test maximum(u) ≈ 0.9991824828036449
+    end
+end