Hi, I am new to Julia. I’m trying to solve a PDE using Method of lines but I am running into a unexpected error. ERROR: type Term has no field lhs. My code as follows:

using DifferentialEquations
using Plots
using MethodOfLines
using ModelingToolkit
using DomainSets
@parameters t,x
@variables u(..)
Dt = Differential(t)
Dx = Differential(x)
Dxx = Differential(x)^2
v = 5.0
Da = 5.0
pe = 100.0
L = 100.0
C0 = 1.0
eq = [Dt(u(t,x)) ~ -v * Dx(u(t,x)) + Da * Dxx(u(t,x))]
domain = [x ∈ Interval(0.0, 100.0), t ∈ Interval(0.0, 10.0)]
ibc = [C0 ~ -Da/v*Dx(u(t,0.0) + u(t,0.0)), Dx(u(t,L) ~ 0.0), u(0.0,x) ~ 0.0]
@named sys = PDESystem(eq, ibc, domain, [t,x], [u(t,x)] )
#sys = structural_simplify(sys)
dx = 1.0
discretization = MOLFiniteDifference([x => dx], t, approx_order = 2)
prob = discretize(sys, discretization)
sol = solve(prob, Tsit5(), saveat = 0.05)

Hi Chris, thanks for pointing out the typo. I managed to amend the boundary condition typos and still ran into the same error.

I did a bit of reading on the MethodOfLines package and found the following under the “Known Limitations”:

That boundary conditions do not contain references to derivatives which are not in the direction of the boundary, except in time

Since I am trying to solve the Danckwerts boundary conditions for PFR Axial Dispersion, I believe these conditions account for back mixing at the inlet layer which is obviously not in the direction of the boundary.

Once I assumed no back mixing at the inlet boundary condition, the code executed perfectly. Pretty cool!

So, if I were to improve the accuracy of the model by assuming back mixing at the inlet (therefore include a negative derivative not in the direction of the boundary) is there a way to still use the MOL and work around this issue? If not, what would you recommend?
Thanks for the help!