Error while simulating tutorial heat equation problem

[SourabhJadhav2]

`using ModelingToolkit, MethodOfLines, OrdinaryDiffEq, DomainSets

@parameters x y t
@variables u(..) v(..)
Dt = Differential(t)
Dx = Differential(x)
Dy = Differential(y)
Dxx = Differential(x)^2
Dyy = Differential(y)^2

∇²(u) = Dxx(u) + Dyy(u)

brusselator_f(x, y, t) = (((x-0.3)^2 + (y-0.6)^2) <= 0.1^2) * (t >= 1.1) * 5.

x_min = y_min = t_min = 0.0
x_max = y_max = 1.0
t_max = 11.5

α = 10.

u0(x,y,t) = 22(y*(1-y))^(3/2)
v0(x,y,t) = 27(x*(1-x))^(3/2)

eq = [Dt(u(x,y,t)) ~ 1. + v(x,y,t)u(x,y,t)^2 - 4.4u(x,y,t) + α∇²(u(x,y,t)) + brusselator_f(x, y, t),
Dt(v(x,y,t)) ~ 3.4u(x,y,t) - v(x,y,t)u(x,y,t)^2 + α∇²(v(x,y,t))]

domains = [x ∈ Interval(x_min, x_max),
y ∈ Interval(y_min, y_max),
t ∈ Interval(t_min, t_max)] `

Periodic BCs

`bcs = [u(x,y,0) ~ u0(x,y,0),
u(0,y,t) ~ u(1,y,t),
u(x,0,t) ~ u(x,1,t),

   v(x,y,0) ~ v0(x,y,0),
   v(0,y,t) ~ v(1,y,t),
   v(x,0,t) ~ v(x,1,t)] 

@nAmed pdesys = PDESystem(eq,bcs,domains,[x,y,t],[u(x,y,t),v(x,y,t)])

N = 32

dx = (x_max-x_min)/N
dy = (y_max-y_min)/N

order = 2

discretization = MOLFiniteDifference([x=>dx, y=>dy], t, approx_order=order, grid_align=center_align)`

Convert the PDE problem into an ODE problem

`println("Discretization:")
@time prob = discretize(pdesys,discretization)

println("Solve:")
@time sol = solve(prob, TRBDF2(), saveat=0.1)`

got following error at this last line

no method matching interp_summary(::Dict{Num, Interpolations.GriddedInterpolation{Float64, 3, Array{Float64, 3}, Gridded{Linear{Throw{OnGrid}}}, Tuple{Vector{Float64}, Vector{Float64}, Vector{Float64}}}})

[bowenszhu]

This is an error with printing sol. For now, you can still retrieve the solution.

[xtalax]

Thank you, I will define a specialised show.

[gkantsidis]

After ignoring the "interp_summary" error, I continue and run the following:
solu = sol[u(t, x, y)]

Then, I get the error: ERROR: Invalid indexing of solution. u(t, x, y) not found in solution.
(although, sol does exist and seems to be right).
I am using MethodOfLines version 0.5.0 and Julia 1.8.2.
Any ideas of what is going wrong?

[bowenszhu]

@named pdesys = PDESystem(eq,bcs,domains,[x,y,t],[u(x,y,t),v(x,y,t)])

The dependent variables you input to PDESystem are [u(x,y,t),v(x,y,t)].
Could you try sol[u(x,y,t)] instead of sol[u(t, x, y)]? The order of arguments matters.

[gkantsidis]

Great, thanks, it works!
You may need to update the source code in:
http://methodoflines.sciml.ai/dev/tutorials/brusselator/
(I had just copied the code from there; maybe, also add an ending semicolon in @time sol = solve(prob, TRBDF2(), saveat=0.1); to avoid the original error)

[ChrisRackauckas]

Updated by @bowenszhu