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@JoshuaLampert
JoshuaLampert committed Sep 25, 2023
1 parent 4ea5e4e commit 48e51fc
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Showing 4 changed files with 113 additions and 97 deletions.
2 changes: 1 addition & 1 deletion .github/workflows/Format-check.yml
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Original file line number Diff line number Diff line change
Expand Up @@ -25,7 +25,7 @@ jobs:
- name: Install JuliaFormatter and format
run: |
julia -e 'using Pkg; Pkg.add(PackageSpec(name = "JuliaFormatter"))'
julia -e 'using JuliaFormatter; format(["src", "test", "examples", "create_figures.jl"], verbose = true)'
julia -e 'using JuliaFormatter; format(["src", "test", "examples", "create_figures.jl", "plot_examples.jl"], verbose = true)'
- name: Format check
run: |
julia -e '
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64 changes: 40 additions & 24 deletions create_figures.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -17,17 +17,23 @@ function fig_1()
H = 1.012

b(x) = x * cos.(3 * pi * x) + H
plot(x, b, color = :gray, fill = (0, 0.8, :gray), fillstyle = :/, linewidth = 3, legend = nothing, ticks = nothing, border = :none)
plot(x, b, color = :gray, fill = (0, 0.8, :gray), fillstyle = :/, linewidth = 3,
legend = nothing, ticks = nothing, border = :none)

eta(x) = x / (x^2 + 1) * sin(2 * pi * x) + H + 1.5
plot!(x, eta, color = :blue, fill = (b.(x), 0.4, :blue), linewidth = 3)

x1 = 0.2
plot!([x1, x1], [b(x1), eta(x1)], line = (Plots.Arrow(:open, :both, 2.5, 2.0), :black), annotation = (x1 - 0.08, (eta(x1) + b(x1))/ 2, text(L"h(t, x)", fontsize)), linewidth = 2)
plot!([x1, x1], [b(x1), eta(x1)], line = (Plots.Arrow(:open, :both, 2.5, 2.0), :black),
annotation = (x1 - 0.08, (eta(x1) + b(x1)) / 2, text(L"h(t, x)", fontsize)),
linewidth = 2)
x2 = 0.4
plot!([x2, x2], [0.0, b(x2)], line = (Plots.Arrow(:open, :both, 2.5, 2.0), :black), annotation = (x2 + 0.06, b(x2) / 2, text(L"b(x)", fontsize)), linewidth = 2)
plot!([x2, x2], [0.0, b(x2)], line = (Plots.Arrow(:open, :both, 2.5, 2.0), :black),
annotation = (x2 + 0.06, b(x2) / 2, text(L"b(x)", fontsize)), linewidth = 2)
x3 = 0.8
plot!([x3, x3], [0.0, eta(x3)], line = (Plots.Arrow(:open, :both, 2.5, 2.0), :black), annotation = (x3 - 0.08, eta(x3) / 2, text(L"\eta(t, x)", fontsize)), linewidth = 2)
plot!([x3, x3], [0.0, eta(x3)], line = (Plots.Arrow(:open, :both, 2.5, 2.0), :black),
annotation = (x3 - 0.08, eta(x3) / 2, text(L"\eta(t, x)", fontsize)),
linewidth = 2)

savefig(joinpath(OUT, "bathymetry.pdf"))
end
Expand All @@ -41,28 +47,32 @@ function fig_2()
g = 1.0
c0 = sqrt(g * h0)

k = 0.01:0.5:(8*pi)
k = 0.01:0.5:(8 * pi)
k_zoom = 0.01:0.3:pi
ylim = (0.0, 1.1)


omega_euler(k) = sqrt(g * k) * sqrt(tanh(h0 * k))
c_euler(k) = omega_euler(k) / k
plot(k, c_euler.(k) ./ c0, label = "Euler", ylim = ylim, xguide = L"k", yguide = L"c/c_0", linewidth = linewidth, markershape = :circle, markersize = markersize)
plot!(k_zoom, c_euler.(k_zoom) ./ c0, ylims = (0.54, 1.0), inset = bbox(0.35, 0.1, 0.35, 0.3), subplot = 2, legend = nothing, linewidth = linewidth, markershape = :circle, markersize = markersize)
plot(k, c_euler.(k) ./ c0, label = "Euler", ylim = ylim, xguide = L"k",
yguide = L"c/c_0", linewidth = linewidth, markershape = :circle,
markersize = markersize)
plot!(k_zoom, c_euler.(k_zoom) ./ c0, ylims = (0.54, 1.0),
inset = bbox(0.35, 0.1, 0.35, 0.3), subplot = 2, legend = nothing,
linewidth = linewidth, markershape = :circle, markersize = markersize)

function plot_dispersion_relation(omega, label, markershape)
c(k) = omega(k) / k
plot!(k, c.(k) ./ c0, label = label, linewidth = linewidth, markershape = markershape, markersize = markersize)
plot!(k_zoom, c.(k_zoom) ./ c0, subplot = 2, linewidth = linewidth, markershape = markershape, markersize = markersize)
plot!(k, c.(k) ./ c0, label = label, linewidth = linewidth,
markershape = markershape, markersize = markersize)
plot!(k_zoom, c.(k_zoom) ./ c0, subplot = 2, linewidth = linewidth,
markershape = markershape, markersize = markersize)
end

omega_bbmbbm_(k, d0) = sqrt(g * h0) * k / (1 + 1/6*(d0 * k)^2)
omega_bbmbbm_(k, d0) = sqrt(g * h0) * k / (1 + 1 / 6 * (d0 * k)^2)
omega_bbmbbm(k) = omega_bbmbbm_(k, h0)
plot_dispersion_relation(omega_bbmbbm, "BBM-BBM", :cross)


alpha_set1 = -1/3 * c0 * h0^2
alpha_set1 = -1 / 3 * c0 * h0^2
beta_set1 = 0.0 * h0^3
gamma_set1 = 0.0 * c0 * h0^3

Expand All @@ -79,11 +89,11 @@ function fig_2()
gamma_set4 = 0.04034343434343434 * c0 * h0^3

function char_equation(alpha, beta, gamma, k)
a = (1 + beta/h0*k^2)
b = (-alpha - beta*alpha/h0*k^2 - gamma/h0)*k^3
c = -g*h0*k^2 + gamma*alpha/h0*k^6
omega1 = (-b + sqrt(b^2 - 4*a*c))/(2*a)
# omega2 = (-b - sqrt(b^2 - 4*a*c))/(2*a)
a = (1 + beta / h0 * k^2)
b = (-alpha - beta * alpha / h0 * k^2 - gamma / h0) * k^3
c = -g * h0 * k^2 + gamma * alpha / h0 * k^6
omega1 = (-b + sqrt(b^2 - 4 * a * c)) / (2 * a)
# omega2 = (-b - sqrt(b^2 - 4*a*c))/(2*a)
return omega1
end

Expand Down Expand Up @@ -112,24 +122,30 @@ function fig_3()

all_Ns = minimum(initial_Ns) * 2 .^ (0:(maximum(iters) - 1))

plot([], label = :none, xscale = :log2, yscale = :log10, xticks = all_Ns, xlabel = "N", ylabel = L"||\eta - \eta_{ana}||_2 + ||v - v_{ana}||_2")
plot([], label = :none, xscale = :log2, yscale = :log10, xticks = all_Ns, xlabel = "N",
ylabel = L"||\eta - \eta_{ana}||_2 + ||v - v_{ana}||_2")
for i in 1:length(accuracy_orders)
Ns = initial_Ns[i] * 2 .^ (0:(iters[i] - 1))
_, errormatrix = convergence_test("examples/bbm_bbm_1d/bbm_bbm_1d_basic.jl", iters[i]; N = initial_Ns[i], tspan = tspan, accuracy_order = accuracy_orders[i])
_, errormatrix = convergence_test("examples/bbm_bbm_1d/bbm_bbm_1d_basic.jl",
iters[i]; N = initial_Ns[i], tspan = tspan,
accuracy_order = accuracy_orders[i])
# Use sum over all L^2-errors for all variables, i.e. ||η - η_ana||_2 + ||v - v_ana||_2
l2_err = sum(errormatrix[:l2], dims=2)
l2_err = sum(errormatrix[:l2], dims = 2)
eocs = log.(l2_err[2:end] ./ l2_err[1:(end - 1)]) ./ log(0.5)
eoc_mean = round(sum(eocs) / length(eocs), digits = 2)
plot!(Ns, l2_err, style = styles[i], label = "p = $accuracy_order, EOC: $eoc_mean")
end
savefig(joinpath(OUT, "orders.pdf"))

plot([], label = :none, xscale = :log2, yscale = :log10, xticks = all_Ns, xlabel = "N", ylabel = L"||\eta - \eta_{ana}||_2 + ||v - v_{ana}||_2")
plot([], label = :none, xscale = :log2, yscale = :log10, xticks = all_Ns, xlabel = "N",
ylabel = L"||\eta - \eta_{ana}||_2 + ||v - v_{ana}||_2")
for i in 1:length(accuracy_orders)
Ns = initial_Ns[i] * 2 .^ (0:(iters[i] - 1))
_, errormatrix = convergence_test("examples/bbm_bbm_1d/bbm_bbm_1d_relaxation.jl", iters[i]; N = initial_Ns[i], tspan = tspan, accuracy_order = accuracy_orders[i])
_, errormatrix = convergence_test("examples/bbm_bbm_1d/bbm_bbm_1d_relaxation.jl",
iters[i]; N = initial_Ns[i], tspan = tspan,
accuracy_order = accuracy_orders[i])
# Use sum over all L^2-errors for all variables, i.e. ||η - η_ana||_2 + ||v - v_ana||_2
l2_err = sum(errormatrix[:l2], dims=2)
l2_err = sum(errormatrix[:l2], dims = 2)
eocs = log.(l2_err[2:end] ./ l2_err[1:(end - 1)]) ./ log(0.5)
eoc_mean = round(sum(eocs) / length(eocs), digits = 2)
plot!(Ns, l2_err, style = styles[i], label = "p = $accuracy_order, EOC: $eoc_mean")
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142 changes: 71 additions & 71 deletions plot_examples.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -66,38 +66,38 @@ const EXAMPLES_DIR_SVAERD_KALISCH = "svaerd_kalisch_1d"
# Travelling wave solution for one-dimensional BBM-BBM equations with periodic boundary conditions
# using periodic SBP operators
@plot_example(joinpath(EXAMPLES_DIR_BBMBBM, "bbm_bbm_1d_basic.jl"),
ylims_gif=[(-8, 4), :auto], tspan=(0.0, 50.0))
ylims_gif=[(-8, 4), :auto], tspan=(0.0, 50.0))

###############################################################################
# Travelling wave solution for one-dimensional BBM-BBM equations with periodic boundary conditions
# using discontinuously coupled Legendre SBP operators
@plot_example(joinpath(EXAMPLES_DIR_BBMBBM, "bbm_bbm_1d_dg.jl"),
ylims_gif=[(-4, 2), :auto])
ylims_gif=[(-4, 2), :auto])

###############################################################################
# Travelling wave solution for one-dimensional BBM-BBM equations with periodic boundary conditions
# using periodic SBP operators and relaxation, is energy-conservative
@plot_example(joinpath(EXAMPLES_DIR_BBMBBM, "bbm_bbm_1d_relaxation.jl"),
ylims_gif=[(-8, 4), (-10, 30)],
tspan=(0.0, 30.0))
ylims_gif=[(-8, 4), (-10, 30)],
tspan=(0.0, 30.0))

###############################################################################
# Travelling wave solution for one-dimensional BBM-BBM equations with periodic boundary conditions
# using periodic SBP operators. Uses the BBM-BBM equations with variable bathymetry, but sets the bathymetry
# as a constant. Should give the same result as "bbm_bbm_1d_basic.jl"
@plot_example(joinpath(EXAMPLES_DIR_BBMBBM_VARIABLE,
"bbm_bbm_variable_bathymetry_1d_basic.jl"),
ylims_gif=[(-8, 4), :auto],
tspan=(0.0, 50.0))
"bbm_bbm_variable_bathymetry_1d_basic.jl"),
ylims_gif=[(-8, 4), :auto],
tspan=(0.0, 50.0))

###############################################################################
# One-dimensional BBM-BBM equations with a Gaussian bump as initial condition for the water height
# and initially still water. The bathymetry is a sine function. Relaxation is used, so the solution
# is energy-conservative. Uses periodic finite difference SBP operators.
@plot_example(joinpath(EXAMPLES_DIR_BBMBBM_VARIABLE,
"bbm_bbm_variable_bathymetry_1d_relaxation.jl"),
ylims_gif=[(-1.5, 6.0), (-10.0, 10.0)],
tspan=(0.0, 10.0))
"bbm_bbm_variable_bathymetry_1d_relaxation.jl"),
ylims_gif=[(-1.5, 6.0), (-10.0, 10.0)],
tspan=(0.0, 10.0))

###############################################################################
# One-dimensional BBM-BBM equations with a Gaussian bump as initial condition for the water height
Expand All @@ -113,99 +113,99 @@ const EXAMPLES_DIR_SVAERD_KALISCH = "svaerd_kalisch_1d"
# and initially still water. The bathymetry is a sine function. Relaxation is used, so the solution
# is energy-conservative. Uses periodic finite difference discontinuously coupled SBP operators.
@plot_example(joinpath(EXAMPLES_DIR_BBMBBM_VARIABLE,
"bbm_bbm_variable_bathymetry_1d_upwind_relaxation.jl"),
ylims_gif=[(-1.5, 6.0), (-10.0, 10.0)],
tspan=(0.0, 10.0))
"bbm_bbm_variable_bathymetry_1d_upwind_relaxation.jl"),
ylims_gif=[(-1.5, 6.0), (-10.0, 10.0)],
tspan=(0.0, 10.0))

###############################################################################
# One-dimensional BBM-BBM equations with a constant water height
# and initially still water. The bathymetry is discontinuous. Relaxation is used, so the solution
# is energy-conservative. Uses periodic finite difference SBP operators. The solution should be
# (exactly) constant in time.
@plot_example(joinpath(EXAMPLES_DIR_BBMBBM_VARIABLE,
"bbm_bbm_variable_bathymetry_1d_well_balanced.jl"),
ylims_gif=[(2.0 - 1e-3, 2.0 + 1e-3), (-1e-3, 1e-3)],
tspan=(0.0, 10.0))
"bbm_bbm_variable_bathymetry_1d_well_balanced.jl"),
ylims_gif=[(2.0 - 1e-3, 2.0 + 1e-3), (-1e-3, 1e-3)],
tspan=(0.0, 10.0))

###############################################################################
# One-dimensional BBM-BBM equations with initial condition that models
# a wave make. This setup comes from experiments by W. M. Dingemans.
@plot_example(joinpath(EXAMPLES_DIR_BBMBBM_VARIABLE,
"bbm_bbm_variable_bathymetry_1d_dingemans.jl"),
ylims_gif=[(-0.1, 0.9), (-0.3, 0.3)],
ylims_x=[:auto, :auto],
x_values=[3.04, 9.44, 20.04, 26.04, 30.44, 37.04],
tlims=[
(15.0, 45.0),
(19.0, 48.0),
(25.0, 52.0),
(30.0, 60.0),
(33.0, 61.0),
(35.0, 65.0),
],
tspan=(0.0, 70.0))
"bbm_bbm_variable_bathymetry_1d_dingemans.jl"),
ylims_gif=[(-0.1, 0.9), (-0.3, 0.3)],
ylims_x=[:auto, :auto],
x_values=[3.04, 9.44, 20.04, 26.04, 30.44, 37.04],
tlims=[
(15.0, 45.0),
(19.0, 48.0),
(25.0, 52.0),
(30.0, 60.0),
(33.0, 61.0),
(35.0, 65.0),
],
tspan=(0.0, 70.0))

###############################################################################
# One-dimensional equations from Svärd and Kalisch with initial condition that models
# a wave make. This setup comes from experiments by W. M. Dingemans.
@plot_example(joinpath(EXAMPLES_DIR_SVAERD_KALISCH,
"svaerd_kalisch_1d_dingemans.jl"),
ylims_gif=[(-0.1, 0.9), (-0.3, 0.3)],
ylims_x=[:auto, :auto],
x_values=[3.04, 9.44, 20.04, 26.04, 30.44, 37.04],
tlims=[
(15.0, 45.0),
(19.0, 48.0),
(25.0, 52.0),
(30.0, 60.0),
(33.0, 61.0),
(35.0, 65.0),
],
tspan=(0.0, 70.0))
"svaerd_kalisch_1d_dingemans.jl"),
ylims_gif=[(-0.1, 0.9), (-0.3, 0.3)],
ylims_x=[:auto, :auto],
x_values=[3.04, 9.44, 20.04, 26.04, 30.44, 37.04],
tlims=[
(15.0, 45.0),
(19.0, 48.0),
(25.0, 52.0),
(30.0, 60.0),
(33.0, 61.0),
(35.0, 65.0),
],
tspan=(0.0, 70.0))

###############################################################################
# One-dimensional equations from Svärd and Kalisch with initial condition that models
# a wave make. This setup comes from experiments by W. M. Dingemans.
@plot_example(joinpath(EXAMPLES_DIR_SVAERD_KALISCH,
"svaerd_kalisch_1d_dingemans_upwind.jl"),
ylims_gif=[(-0.1, 0.9), (-0.3, 0.3)],
ylims_x=[:auto, :auto],
x_values=[3.04, 9.44, 20.04, 26.04, 30.44, 37.04],
tlims=[
(15.0, 45.0),
(19.0, 48.0),
(25.0, 52.0),
(30.0, 60.0),
(33.0, 61.0),
(35.0, 65.0),
],
tspan=(0.0, 70.0))
"svaerd_kalisch_1d_dingemans_upwind.jl"),
ylims_gif=[(-0.1, 0.9), (-0.3, 0.3)],
ylims_x=[:auto, :auto],
x_values=[3.04, 9.44, 20.04, 26.04, 30.44, 37.04],
tlims=[
(15.0, 45.0),
(19.0, 48.0),
(25.0, 52.0),
(30.0, 60.0),
(33.0, 61.0),
(35.0, 65.0),
],
tspan=(0.0, 70.0))

###############################################################################
# One-dimensional equations from Svärd and Kalisch with initial condition that models
# a wave make. This setup comes from experiments by W. M. Dingemans. Relaxation is used
# to preserve the modified entropy.
@plot_example(joinpath(EXAMPLES_DIR_SVAERD_KALISCH,
"svaerd_kalisch_1d_dingemans_relaxation.jl"),
ylims_gif=[(-0.1, 0.9), (-0.3, 0.3)],
ylims_x=[:auto, :auto],
x_values=[3.04, 9.44, 20.04, 26.04, 30.44, 37.04],
tlims=[
(15.0, 45.0),
(19.0, 48.0),
(25.0, 52.0),
(30.0, 60.0),
(33.0, 61.0),
(35.0, 65.0),
],
tspan=(0.0, 70.0))
"svaerd_kalisch_1d_dingemans_relaxation.jl"),
ylims_gif=[(-0.1, 0.9), (-0.3, 0.3)],
ylims_x=[:auto, :auto],
x_values=[3.04, 9.44, 20.04, 26.04, 30.44, 37.04],
tlims=[
(15.0, 45.0),
(19.0, 48.0),
(25.0, 52.0),
(30.0, 60.0),
(33.0, 61.0),
(35.0, 65.0),
],
tspan=(0.0, 70.0))

###############################################################################
# One-dimensional Svärd-Kalisch equations with a constant water height
# and initially still water. The bathymetry is discontinuous. Relaxation is used, so the solution
# is energy-conservative. Uses periodic finite difference SBP operators. The solution should be
# (exactly) constant in time.
@plot_example(joinpath(EXAMPLES_DIR_SVAERD_KALISCH,
"svaerd_kalisch_1d_well_balanced.jl"),
ylims=[(2.0 - 1e-3, 2.0 + 1e-3), (-1e-3, 1e-3)],
tspan=(0.0, 10.0))
"svaerd_kalisch_1d_well_balanced.jl"),
ylims=[(2.0 - 1e-3, 2.0 + 1e-3), (-1e-3, 1e-3)],
tspan=(0.0, 10.0))
2 changes: 1 addition & 1 deletion src/util.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -193,7 +193,7 @@ function analyze_convergence(errors, iterations,
# For the following iterations print errors and EOCs
for j in 2:iterations
for k in 1:nvariables
@printf("%-5d", initial_N * 2^(j - 1))
@printf("%-5d", initial_N*2^(j - 1))
@printf("%-10.2e", error[j, k])
@printf("%-10.2f", eocs[kind][j - 1, k])
end
Expand Down

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