215: 2D Nonlinear Poisson with boundary reaction
module Example215_NonlinearPoisson2D_BoundaryReaction
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)
eps=1.0e-2
k=1.0
physics=VoronoiFVM.Physics(
num_species=2,
breaction=function(f,u,node)
if node.region==2
f[1]=k*(u[1]-u[2])
f[2]=k*(u[2]-u[1])
else
f[1]=0
f[2]=0
end
end,
flux=function(f,u0,edge)
u=unknowns(edge,u0)
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])
inival=unknowns(sys)
U=unknowns(sys)
inival.=0.0
control=VoronoiFVM.NewtonControl()
control.verbose=verbose
control.tol_linear=1.0e-5
control.max_lureuse=0
tstep=0.01
time=0.0
istep=0
u25=0
while time<1
time=time+tstep
solve!(U,inival,sys,control=control,tstep=tstep)
inival.=U
for i in eachindex(U) inival[i]=U[i] end
if verbose
@printf("time=%g\n",time)
end
tstep*=1.0
istep=istep+1
u25=U[25]
if isplots(Plotter)
p1=Plotter.contourf(X,Y,reshape(U[1,:],length(X),length(Y)),levels=collect(0:0.125:0.75),clim=(0,0.75),colorbar=:right,color=:viridis,title=@sprintf("max1=%g max2=%g\n",maximum(U[1,:]),maximum(U[2,:])))
p2=Plotter.contourf(X,Y,reshape(U[2,:],length(X),length(Y)),levels=collect(0:0.0025:0.02),clim=(0,0.02), colorbar=:right,color=:viridis)
p=Plotter.plot(p1,p2,layout=(2,1) )
Plotter.gui(p)
end
end
return u25
end
function test()
main(unknown_storage=:sparse) ≈ 0.008761335823958986 &&
main(unknown_storage=:dense) ≈ 0.008761335823958986
end
end
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