220: 2D Nonlinear Poisson with boundary reaction and boundary species
module Example220_NonlinearPoisson2D_BoundarySpecies
using Printf
using VoronoiFVM
function main(;n=10,Plotter=nothing,verbose=false,unknown_storage=:sparse)
h=1.0/convert(Float64,n)
X=collect(0.0:h:1.0)
Y=collect(0.0:h:1.0)
grid=VoronoiFVM.Grid(X,Y)
k=1.0
eps=1.0
physics=VoronoiFVM.Physics(
num_species=3,
breaction=function(f,u,node)
if node.region==2
f[1]=k*(u[1]-u[3])
f[3]=k*(u[3]-u[1])+ k*(u[3]-u[2])
f[2]=k*(u[2]-u[3])
end
end,
bstorage=function(f,u,node)
if node.region==2
f[3]=u[3]
end
end,
flux=function(f,u,edge)
f[1]=eps*(u[1,1]-u[1,2])
f[2]=eps*(u[2,1]-u[2,2])
end,
source=function(f,node)
x1=node[1]-0.5
x2=node[2]-0.5
f[1]=exp(-20.0*(x1^2+x2^2))
end,
storage=function(f,u,node)
f[1]=u[1]
f[2]=u[2]
end
)
sys=VoronoiFVM.System(grid,physics,unknown_storage=unknown_storage)
enable_species!(sys,1,[1])
enable_species!(sys,2,[1])
enable_boundary_species!(sys,3,[2])
function tran32!(a,b)
a[1]=b[2]
end
bgrid2=subgrid(grid,[2],boundary=true,transform=tran32!)
inival=unknowns(sys)
inival.=0.0
U=unknowns(sys)
eps=1.0e-2
control=VoronoiFVM.NewtonControl()
control.verbose=verbose
control.tol_linear=1.0e-5
control.tol_relative=1.0e-5
control.max_lureuse=0
tstep=0.01
time=0.0
istep=0
u5=0
while time<1
time=time+tstep
solve!(U,inival,sys,control=control,tstep=tstep)
inival.=U
if verbose
@printf("time=%g\n",time)
end
tstep*=1.0
istep=istep+1
U_bound=view(U,bgrid2)
u5=U_bound[3,5]
if isplots(Plotter)
p1=Plotter.contourf(X,Y,reshape(U[1,:],length(X),length(Y)),levels=collect(0:0.1:0.6),clim=(0,0.6),colorbar=:right,color=:viridis,title=@sprintf("max1=%g max2=%g maxb=%g\n",maximum(U[1,:]),maximum(U[2,:]),maximum(U_bound[3,:])))
p2=Plotter.contourf(X,Y,reshape(U[2,:],length(X),length(Y)),levels=collect(0:0.0001:0.002),clim=(0,0.002), colorbar=:right,color=:viridis)
p3=Plotter.plot(grid=true,ylims=(0,0.0025))
VoronoiFVM.plot(Plotter,bgrid2,U[3,:],p=p3,show=false)
p=Plotter.plot(p1,p2,p3,layout=(3,1) )
Plotter.gui(p)
end
end
return u5
end
function test()
main(unknown_storage=:sparse) ≈ 0.0020781361856598
main(unknown_storage=:dense) ≈ 0.0020781361856598
end
end
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