### A Pluto.jl notebook ###
# v0.16.1

using Markdown
using InteractiveUtils

# This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error).
macro bind(def, element)
    quote
        local el = $(esc(element))
        global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : missing
        el
    end
end

# ╔═╡ 60941eaa-1aea-11eb-1277-97b991548781
begin 
    using PlutoUI,GridVisualize,SimplexGridFactory,Triangulate,ExtendableGrids,VoronoiFVM,PlutoVista,PlutoUI,PyPlot
end

# ╔═╡ de468cb9-b34d-4d2e-b911-9b93920caca1
md"""
# Flux reconstruction and visualization for the Laplace operator
"""

# ╔═╡ 928a70c5-4706-40a1-9387-abcb71c09443
"""
Define a "Swiss cheese domain" with punched-out holes, where each hole boundary corresponds to a different boundary condition.
"""
function swiss_cheese_2d()

    function circlehole!(builder, center, radius; n=20)
        points=[point!(builder, center[1]+radius*sin(t),center[2]+radius*cos(t)) for t in range(0,2π,length=n)]
        for i=1:n-1
            facet!(builder,points[i],points[i+1])
        end
        facet!(builder,points[end],points[1])
        holepoint!(builder,center)
    end


    builder=SimplexGridBuilder(Generator=Triangulate)
    cellregion!(builder,1)
    maxvolume!(builder,0.1)
    regionpoint!(builder,0.1,0.1)

    
    p1=point!(builder,0,0)
    p2=point!(builder,10,0)
    p3=point!(builder,10,10)
    p4=point!(builder,0,10)
    
    facetregion!(builder,1)
    facet!(builder,p1,p2)
    facet!(builder,p2,p3)
    facet!(builder,p3,p4)
    facet!(builder,p4,p1)

    holes=[1.0 2.0;
           8.0 9.0;
           2.0 8.0;
  		   8.0 4.0;
           9.0 1.0;
           3.0 4.0;
           4.0 6.0;
           7.0 9.0;
           4.0 7.0;
           7.0 5.0;
           2.0 1.0;
           4.0 1.0;
           4.0 8.0;
           3.0 6.0;
           4.0 9.0;
           6.0 9.0;
           3.0 5.0;
           1.0 4.0]'

    radii=[0.15, 0.15, 0.1, 0.35, 0.2, 0.3, 0.1, 0.4, 0.1, 0.4,  0.2, 0.2, 0.2, 0.35, 0.15, 0.25, 0.15, 0.25]

    for i=1:length(radii)
        facetregion!(builder,i+1)
        circlehole!(builder,holes[:,i], radii[i])
    end

    simplexgrid(builder)
end

# ╔═╡ 49f425a4-455c-40f5-b939-da704032cb88
md"""
Generate & plot grid
"""

# ╔═╡ bc304085-69c3-4974-beb4-6f2b981ac0f1
grid=swiss_cheese_2d()

# ╔═╡ ad0367e6-7308-46bc-a7ff-9c17dcfe470d
gridplot(grid,Plotter=PlutoVista)

# ╔═╡ 236d6cd5-c190-49c7-98fe-021fae224455
"""
Simple flux function for Laplace operator 
"""
flux(y,u,edge)= y[1]=u[1,1]-u[1,2]

# ╔═╡ f4ebe6ad-4e04-4f33-9a66-6bec977adf4d
md"""
Define a finite volume system with Dirichlet boundary conditions at some of the holes
"""

# ╔═╡ 934a98f1-9734-45bc-848e-4d4d8ad80e4e
physics=VoronoiFVM.Physics(flux=flux)

# ╔═╡ f3af20fb-c3cc-41af-9782-d40adf2371f7
system=VoronoiFVM.System(grid,physics)

# ╔═╡ 50ea0a7e-97e0-428d-b4ec-6bd4d7aef31f
enable_species!(system,1,[1])

# ╔═╡ 49d3c96b-f6b4-4581-8600-8aaf50bb07fc
boundary_dirichlet!(system,1,2,10.0)

# ╔═╡ fa5200ff-713e-48fb-b452-c6ee96935cfc
boundary_dirichlet!(system,1,3,0.0)

# ╔═╡ 6b09f75a-521b-40d9-9636-155e62ab0cac
md"""
At hole #11, the value will be bound to a slider defined below
"""

# ╔═╡ d86c43f3-ec2f-4fae-88d2-1068603e7044
md"""
Solve, and trigger solution upon boundary value change
"""

# ╔═╡ 41bd1230-c87c-47b0-8e58-67ad55609fd3
md"""
Reconstruct the node flux. It is a ``d\times n_{spec}\times n_{nodes}`` tensor.
`nf[:,ispec,:]` then is a vector function representing the flux density of species `ispec` in each node of the domain. This readily can be fed into `GridVisualize.vectorplot`.
"""

# ╔═╡ 17be52fb-f55b-4b3d-85e5-33f36134046b
vis=GridVisualizer(Plotter=PlutoVista,dim=2,resolution=(400,400));vis

# ╔═╡ 03f582ec-4e95-4ca4-8482-9c797027810d
md"""
``v_{11}:`` $(@bind  val11 Slider(0:0.1:10,default=5,show_value=true))
"""

# ╔═╡ e8ae2b22-ac60-449b-952f-d2c55852677c
boundary_dirichlet!(system,1,11,val11)

# ╔═╡ 27efdcac-8ee4-47e4-905d-8d8c7313ddd1
val11; sol=solve(unknowns(system,inival=0),system)

# ╔═╡ 41f427c1-b6ad-46d4-9151-1d872b4efeb6
nf=nodeflux(system,sol)

# ╔═╡ c9b9fdb1-5734-430f-949a-6e6126d2f091
"""
Joint plot of solution and nodal flux of the solution
"""
function myplot(vis)
	scalarplot!(vis,grid,sol[1,:],levels=9,colormap=:summer,clear=true)
	vectorplot!(vis,grid,nf[:,1,:],clear=false,spacing=0.5,vscale=1.5)
	reveal(vis)
end

# ╔═╡ 531edb71-6d32-4231-b117-5e36416d2fb1
myplot(vis)

# ╔═╡ e0b92e00-dd0b-448b-baae-5cd4e0a2059a
md"""
Plot with PyPlot: $(@bind use_pyplot CheckBox(default=false))
"""

# ╔═╡ 1495eb67-12ec-4662-b0e7-049ffef569c0
if use_pyplot
	pyvis=GridVisualizer(Plotter=PyPlot,resolution=(400,400))
	myplot(pyvis)
end

# ╔═╡ 00000000-0000-0000-0000-000000000001
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"""

# ╔═╡ 00000000-0000-0000-0000-000000000002
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"""

# ╔═╡ Cell order:
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# ╠═1495eb67-12ec-4662-b0e7-049ffef569c0
# ╟─00000000-0000-0000-0000-000000000001
# ╟─00000000-0000-0000-0000-000000000002
