Combining ODE and PDE (part 2)

[ctessum]

Hello,

Continuing from #83, and starting with this test:

MethodOfLines.jl/test/pde_systems/MOL_1D_Linear_Diffusion.jl

Lines 742 to 789 in 17f4cbf

	@testset "Test 13: one linear diffusion with mixed BCs, one ODE" begin
	# Method of Manufactured Solutions
	u_exact = (x,t) -> exp.(-t) * sin.(x)
	v_exact = (t) -> exp.(-t)
	@parameters t x
	@variables u(..) v(..)
	Dt = Differential(t)
	Dx = Differential(x)
	Dxx = Dx^2
	# 1D PDE and boundary conditions
	eqs = [Dt(u(t,x)) ~ Dxx(u(t,x)),
	Dt(v(t)) ~ -v(t)]
	bcs = [u(0,x) ~ sin(x),
	v(0) ~ 1,
	u(t,0) ~ 0,
	Dx(u(t,1)) ~ exp(-t) * cos(1)]
	# Space and time domains
	domains = [t ∈ Interval(0.0,1.0),
	x ∈ Interval(0.0,1.0)]
	# PDE system
	@named pdesys = PDESystem(eqs,bcs,domains,[t,x],[u(t,x),v(t)])
	# Method of lines discretization
	l = 100
	dx = range(0.0,1.0,length=l)
	dx_ = dx[2]-dx[1]
	order = 2
	discretization = MOLFiniteDifference([x=>dx_],t)
	# Convert the PDE problem into an ODE problem
	prob = discretize(pdesys,discretization)
	# Solve ODE problem
	sol = solve(prob,Tsit5(),saveat=0.1)
	x_sol = dx[2:end-1]
	t_sol = sol.t
	# Test against exact solution
	for i in 1:length(sol)
	@test all(isapprox.(u_exact(x_sol, t_sol[i]), sol.u[i][1:length(x_sol)], atol=0.01))
	@test v_exact(t_sol[i]) ≈ sol.u[i][end] atol=0.01
	end
	end

I change the equation Dt(u(t,x)) ~ Dxx(u(t,x)) to be Dt(u(t,x)) ~ Dxx(u(t,x)) + v(t):

using ModelingToolkit, MethodOfLines, OrdinaryDiffEq, DomainSets

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

# 1D PDE and boundary conditions
eqs = [Dt(u(t,x)) ~ Dxx(u(t,x)) + v(t), # This is the only line that is significantly changed from the test.
        Dt(v(t)) ~ -v(t)]

bcs = [u(0,x) ~ sin(x),
        v(0) ~ 1,
        u(t,0) ~ 0,
        Dx(u(t,1)) ~ exp(-t) * cos(1)]
domains = [t ∈ Interval(0.0,1.0),
            x ∈ Interval(0.0,1.0)]
@named pdesys = PDESystem(eqs,bcs,domains,[t,x],[u(t,x),v(t)])
discretization = MOLFiniteDifference([x=>0.01],t)
prob = discretize(pdesys,discretization)

I was expecting that this would add a value to that equation that varied in t but was constant across all x. Instead, I get the following error: ERROR: ArgumentError: reducing over an empty collection is not allowed.

Is this a bug, or is it the expected behavior? Thanks for your help!

[xtalax]

I know where this error comes from, I expected that this should already be supported. I will take a closer look at fixing this soon.

[ctessum]

Thanks for checking!

[ctessum]

Thanks!