WIP: deprecate VoronoiFVM.Physics callbacks without data argument

This patch implements a warning that is triggered if the user constructs
a VoronoiFVM.Physics object with a callback function that uses only three or
two arguments, respectively.

All examples were overhauled to comply with the new interface.
Hereby, the data=nothing default has to be set to allow calls with
and without the data argument. This needs to be done to preserve the
current checks for isdata() and hasdata().
The default can be removed once the deprecated code is removed.

examples/Example001_Solvers.jl

@@ -28,25 +28,25 @@ function main(; n = 10, Plotter = nothing, assembly = :edgwwise, kwargs...)
 
     eps = 1.0e-2
 
-    function reaction(f, u, node)
+    function reaction(f, u, node, data=nothing)
         f[1] = u[1]^2
     end
 
-    function flux(f, u, edge)
+    function flux(f, u, edge, data=nothing)
         f[1] = eps * (u[1, 1]^2 - u[1, 2]^2)
     end
 
-    function source(f, node)
+    function source(f, node, data=nothing)
         x1 = node[1] - 0.5
         x2 = node[2] - 0.5
         f[1] = exp(-20.0 * (x1^2 + x2^2))
     end
 
-    function storage(f, u, node)
+    function storage(f, u, node, data=nothing)
         f[1] = u[1]
     end
 
-    function bcondition(f, u, node)
+    function bcondition(f, u, node, data=nothing)
         boundary_dirichlet!(f,
                             u,
                             node;

examples/Example002_EdgeReaction.jl

@@ -46,18 +46,18 @@ function main(; nref = 0, dim = 2, Plotter = nothing, verbose = "and", case = :c
         i1 = 6
     end
 
-    function storage!(y, u, node)
+    function storage!(y, u, node, data=nothing)
         y[1] = u[1]
     end
 
-    function flux!(y, u, edge)
+    function flux!(y, u, edge, data=nothing)
         y[1] = u[1, 1] - u[1, 2]
     end
 
     # Three ways to give a constant reaction term. As a consequence,
     # these need to yield the same solution.
     # 1: classical node reaction, multiplied  by control volume size
-    function reaction!(y, u, node)
+    function reaction!(y, u, node, data=nothing)
         y[1] = -1
     end
 
@@ -76,7 +76,7 @@ function main(; nref = 0, dim = 2, Plotter = nothing, verbose = "and", case = :c
     #
     #  τ=1/h    v= s*h/2d = σ*h^2/2d 
     #                
-    function edgereaction!(y, u, edge)
+    function edgereaction!(y, u, edge, data=nothing)
         h = meas(edge)
         y[1] = -1 * h^2 / (2 * dim)
     end
@@ -88,14 +88,14 @@ function main(; nref = 0, dim = 2, Plotter = nothing, verbose = "and", case = :c
     # we had before
     ϕ = grid[Coordinates][1, :]
 
-    function edgereaction2!(y, u, edge)
+    function edgereaction2!(y, u, edge, data=nothing)
         ϕK = ϕ[edge.node[1]]
         ϕL = ϕ[edge.node[2]]
         y[1] = -(ϕK - ϕL) * (ϕK - ϕL) / 2
     end
 
     if case == :compare_max
-        function bcondition!(y, u, node)
+        function bcondition!(y, u, node, data=nothing)
             boundary_dirichlet!(y, u, node; species = 1, region = 1, value = 0)
             boundary_dirichlet!(y, u, node; species = 1, region = 2, value = 0)
             boundary_dirichlet!(y, u, node; species = 1, region = 3, value = 0)
@@ -130,7 +130,7 @@ function main(; nref = 0, dim = 2, Plotter = nothing, verbose = "and", case = :c
     end
 
     if case == :compare_flux
-        function bcondition2!(y, u, node)
+        function bcondition2!(y, u, node, data=nothing)
             boundary_dirichlet!(y, u, node; species = 1, region = i1, value = 0)
         end
 

examples/Example101_Laplace1D.jl

@@ -96,7 +96,7 @@ function main()
 
     ## Flux function which describes the flux
     ## between neighboring control volumes
-    function flux!(f, u, edge)
+    function flux!(f, u, edge, data=nothing)
         f[1] = u[1, 1] - u[1, 2]
     end
 

examples/Example105_NonlinearPoisson1D.jl

@@ -38,12 +38,12 @@ function main(; n = 10, Plotter = nothing, verbose = false, unknown_storage = :s
 
     ## Flux function which describes the flux
     ## between neighboring control volumes
-    function flux!(f, u, edge)
+    function flux!(f, u, edge, data=nothing)
         f[1] = ϵ * (u[1, 1] - u[1, 2])
     end
 
     ## Source term
-    function source!(f, node)
+    function source!(f, node, data=nothing)
         if node[1] <= 0.5
             f[1] = 1
         else
@@ -52,7 +52,7 @@ function main(; n = 10, Plotter = nothing, verbose = false, unknown_storage = :s
     end
 
     ## Reaction term
-    function reaction!(f, u, node)
+    function reaction!(f, u, node, data=nothing)
         f[1] = exp(u[1]) - exp(-u[1])
     end
 

examples/Example106_NonlinearDiffusion1D.jl

@@ -44,12 +44,12 @@ function main(; n = 20, m = 2, Plotter = nothing, verbose = false,
 
     ## Flux function which describes the flux
     ## between neighboring control volumes
-    function flux!(f, u, edge)
+    function flux!(f, u, edge, data=nothing)
         f[1] = u[1, 1]^m - u[1, 2]^m
     end
 
     ## Storage term
-    function storage!(f, u, node)
+    function storage!(f, u, node, data=nothing)
         f[1] = u[1]
     end
 

examples/Example107_NonlinearStorage1D.jl

@@ -40,7 +40,7 @@ function main(; n = 20, m = 2.0, Plotter = nothing, verbose = false,
 
     ## Flux function which describes the flux
     ## between neighboring control volumes
-    function flux!(f, u, edge)
+    function flux!(f, u, edge, data=nothing)
         f[1] = u[1, 1] - u[1, 2]
     end
 
@@ -49,7 +49,7 @@ function main(; n = 20, m = 2.0, Plotter = nothing, verbose = false,
     ## Storage term
     ## This needs to be regularized as its derivative
     ## at 0 is infinity
-    function storage!(f, u, node)
+    function storage!(f, u, node, data=nothing)
         f[1] = (ϵ + u[1])^(1.0 / m)
     end
 

examples/Example108_OrdinaryDiffEq1D.jl

@@ -44,12 +44,12 @@ function main(; n = 20, m = 2, Plotter = nothing, verbose = false,
 
     ## Flux function which describes the flux
     ## between neighboring control volumes
-    function flux!(f, u, edge)
+    function flux!(f, u, edg, data=nothing)
         f[1] = u[1, 1]^m - u[1, 2]^m
     end
 
     ## Storage term
-    function storage!(f, u, node)
+    function storage!(f, u, node, data=nothing)
         f[1] = u[1]
     end
 

examples/Example110_ReactionDiffusion1D_TwoSpecies.jl

@@ -29,20 +29,20 @@ function main(; n = 100, Plotter = nothing, verbose = false, unknown_storage = :
     eps::Vector{Float64} = [1.0, 1.0]
 
     physics = VoronoiFVM.Physics(
-                                 ; reaction = function (f, u, node)
+                                 ; reaction = function (f, u, node, data=nothing)
                                      f[1] = u[1] * u[2]
                                      f[2] = -u[1] * u[2]
                                  end,
-                                 flux = function (f, u, edge)
+                                 flux = function (f, u, edge, data=nothing)
                                      nspecies = 2
                                      f[1] = eps[1] * (u[1, 1] - u[1, 2]) *
                                             (0.01 + u[2, 1] + u[2, 2])
                                      f[2] = eps[2] * (u[2, 1] - u[2, 2]) *
                                             (0.01 + u[1, 1] + u[1, 2])
-                                 end, source = function (f, node)
+                                 end, source = function (f, node, data=nothing)
                                      f[1] = 1.0e-4 * (0.01 + node[1])
                                      f[2] = 1.0e-4 * (0.01 + 1.0 - node[1])
-                                 end, storage = function (f, u, node)
+                                 end, storage = function (f, u, node, data=nothing)
                                      f[1] = u[1]
                                      f[2] = u[2]
                                  end)

examples/Example115_HeterogeneousCatalysis1D.jl

@@ -77,19 +77,19 @@ function main(; n = 10, Plotter = nothing, verbose = false, tend = 1,
     ## Diffusion flux for species A and B
     D_A = 1.0
     D_B = 1.0e-2
-    function flux!(f, u, edge)
+    function flux!(f, u, edge, data=nothing)
         f[iA] = D_A * (u[iA, 1] - u[iA, 2])
         f[iB] = D_B * (u[iB, 1] - u[iB, 2])
     end
 
     ## Storage term of species A and B
-    function storage!(f, u, node)
+    function storage!(f, u, node, data=nothing)
         f[iA] = u[iA]
         f[iB] = u[iB]
     end
 
     ## Source term for species a around 0.5
-    function source!(f, node)
+    function source!(f, node, data=nothing)
         x1 = node[1] - 0.5
         f[iA] = exp(-100 * x1^2)
     end
@@ -110,7 +110,7 @@ function main(; n = 10, Plotter = nothing, verbose = false, tend = 1,
     R_AC(u_A, u_C) = kp_AC * u_A * (1 - u_C) - km_AC * u_C
     R_BC(u_B, u_C) = kp_BC * u_B * (1 - u_C) - km_BC * u_C
 
-    function breaction!(f, u, node)
+    function breaction!(f, u, node, data=nothing)
         if node.region == 1
             f[iA] = S * R_AC(u[iA], u[iC])
             f[iB] = S * R_BC(u[iB], u[iC])
@@ -119,7 +119,7 @@ function main(; n = 10, Plotter = nothing, verbose = false, tend = 1,
     end
 
     ## This is for the term \partial_t u_C at the boundary
-    function bstorage!(f, u, node)
+    function bstorage!(f, u, node, data=nothing)
         if node.region == 1
             f[iC] = u[iC]
         end

examples/Example120_ThreeRegions1D.jl

@@ -31,7 +31,7 @@ function main(; n = 30, Plotter = nothing, plot_grid = false, verbose = false,
     eps = [1, 1, 1]
     k = [1, 1, 1]
 
-    function reaction(f, u, node)
+    function reaction(f, u, node, data=nothing)
         if node.region == 1
             f[1] = k[1] * u[1]
             f[2] = -k[1] * u[1]
@@ -43,7 +43,7 @@ function main(; n = 30, Plotter = nothing, plot_grid = false, verbose = false,
         end
     end
 
-    function source(f, node)
+    function source(f, node, data=nothing)
         if node.region == 1
             f[1] = 1.0e-4 * (3.0 - node[1])
         end
@@ -54,20 +54,20 @@ function main(; n = 30, Plotter = nothing, plot_grid = false, verbose = false,
         ## write into the result also where
         ## the corresponding species has not been enabled
         ## Species information is used to prevent the assembly.
-        flux = function (f, u, edge)
+        flux = function (f, u, edge, data=nothing)
             for i = 1:3
                 f[i] = eps[i] * (u[i, 1] - u[i, 2])
             end
         end
 
-        storage = function (f, u, node)
+        storage = function (f, u, node, data=nothing)
             f .= u
         end
     else
         ## This is the "old" way:
         ## Write into result only where
         ## the corresponding species has been enabled
-        flux = function (f, u, edge)
+        flux = function (f, u, edge, data=nothing)
             if edge.region == 1
                 f[1] = eps[1] * (u[1, 1] - u[1, 2])
                 f[2] = eps[2] * (u[2, 1] - u[2, 2])
@@ -79,7 +79,7 @@ function main(; n = 30, Plotter = nothing, plot_grid = false, verbose = false,
             end
         end
 
-        storage = function (f, u, node)
+        storage = function (f, u, node, data=nothing)
             if node.region == 1
                 f[1] = u[1]
                 f[2] = u[2]

examples/Example121_PoissonPointCharge1D.jl

@@ -40,16 +40,16 @@ function main(; nref = 0, Plotter = nothing, verbose = false, unknown_storage =
 
     Q::Float64 = 0.0
 
-    function flux!(f, u, edge)
+    function flux!(f, u, edge, data=nothing)
         f[1] = u[1, 1] - u[1, 2]
     end
-    function storage!(f, u, node)
+    function storage!(f, u, node, data=nothing)
         f[1] = u[1]
     end
 
     ## Define boundary reaction defining charge
     ## Note that the term  is written on  the left hand side, therefore the - sign
-    function breaction!(f, u, node)
+    function breaction!(f, u, node, data=nothing)
         if node.region == 3
             f[1] = -Q
         end

examples/Example125_TestFunctions1D.jl

@@ -19,13 +19,13 @@ function main(; n = 100, Plotter = nothing, verbose = false, unknown_storage = :
     eps::Vector{Float64} = [1, 1.0e-1]
 
     physics = VoronoiFVM.Physics(
-                                 ; reaction = function (f, u, node)
+                                 ; reaction = function (f, u, node, data=nothing)
                                      f[1] = 10 * (u[1] - u[2])
                                      f[2] = 10 * (u[2] - u[1])
-                                 end, flux = function (f, u, edge)
+                                 end, flux = function (f, u, edge, data=nothing)
                                      f[1] = eps[1] * (u[1, 1] - u[1, 2])
                                      f[2] = eps[2] * (u[2, 1] - u[2, 2])
-                                 end, storage = function (f, u, node)
+                                 end, storage = function (f, u, node, data=nothing)
                                      f[1] = u[1]
                                      f[2] = u[2]
                                  end)

examples/Example201_Laplace2D.jl

@@ -14,7 +14,7 @@ import Metis
 
 ## Flux function which describes the flux
 ## between neighboring control volumes
-function g!(f, u, edge)
+function g!(f, u, edge, data=nothing)
     f[1] = u[1, 1] - u[1, 2]
 end