NSSC/Exercise_04/run.jl

94 lines
2.6 KiB
Julia

include("./fem.jl")
include("./Parameters.jl")
include("./print_HTP.jl")
using .FEM
using GLMakie
using Makie.GeometryBasics
@enum Variation BASIC V1 V2 V3 V4_div V4_mul
function solve(name::String, variation::Variation)
div = 9
H = zeros(Float64,(div+1)^2, (div+1)^2)
(nodes, elements) = tri_tiles(Parameters.L, div, variation==V1, variation==V2, variation==V3)
for (index, el) in enumerate(elements)
Hₑ = stiffness(el)
if variation == V4_div && index in Parameters.elₘ
Hₑ /= Parameters.c
elseif variation == V4_mul && index in Parameters.elₘ
Hₑ *= Parameters.c
end
for i in 1:3
for j in 1:3
H[el.nodes[i].index, el.nodes[j].index] += Hₑ[i,j]
end
end
end
P = zeros(Float64, 90)
# impose neumann conditions on top edge
# adapted from https://mathoverflow.net/questions/5085/how-to-apply-neuman-boundary-condition-to-finite-element-method-problems
# maybe check if this actually makes sense
nᵧ = -Parameters.q / Parameters.k
# skip=2 since only every second element has a edge along the bottom: ◺◹
for ∂_el in elements[1:2:18]
n1 = ∂_el.nodes[1]
n2 = ∂_el.nodes[2]
l = abs(n2.x - n1.x)
P[n1.index] += nᵧ*l/2
P[n2.index] += nᵧ*l/2
end
rhs = P - H[1:90,91:100]*fill(Parameters.T, 10,1)
T = vec(H[1:90,1:90]\rhs)
append!(T, fill(Parameters.T, 10))
reaction_forces = H[91:100,:]*T
centers = center.(elements)
gradients = map(el -> gradient(el, T), elements)
flux = gradients .* -1
norm = maximum(map(g-> sqrt(g[1]^2 + g[2]^2), gradients))/(Parameters.L/div)*2.5
gradients ./= norm
flux ./= norm
set_theme!(theme_black())
f = Figure(resolution = (1536, 1024))
tris = map(e->Polygon([p(e.nodes[1]), p(e.nodes[2]), p(e.nodes[3])]), elements)
poly(f[1, 1], tris, color=:transparent, linestyle=:solid, strokewidth=0.8, strokecolor=:white, transparency=true)
xs = map(n->n.x, nodes)
ys = map(n->n.y, nodes)
xs = reshape(xs, (div+1, div+1))
ys = reshape(ys, (div+1, div+1))
Ts = reshape(T, (div+1, div+1))
surface(f[2, 1], xs, ys, Ts, colormap=:matter, axis=(type=Axis3,))
contour(f[1:2,2:3], map(n->n.x,nodes), map(n->n.y,nodes), T, levels=16, colormap=:matter)
arrows!(f[1:2,2:3], centers, gradients, arrowcolor=:red, linecolor=:red)
arrows!(f[1:2,2:3], centers, flux, arrowcolor=:blue, linecolor=:blue)
save("plots/$name.png", current_figure())
print_HTP(H, T, P, "txt/htp_$name.txt")
end
solve("baseline", BASIC)
solve("variation1", V1)
solve("variation2", V2)
solve("variation3", V3)
solve("variation4_div", V4_div)
solve("variation4_mul", V4_mul)