Bound error on Discretization when specifying a uniform grid as a vector about methodoflines.jl HOT 5 OPEN

I have seen this one recently, I will look closer soon

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I see the problem, you need to supply bcs for any of your observables that contain derivatives else they are not well specified. This needs a better error though.

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Thanks for looking into it so quickly.

Why do I need to specify additional boundary conditions (bcs) when specifying the same grid by a vector compared to specifying the same grid by a grid spacing? I thought the problem description did not change semantically.
For me its not quite intuitive to specify bcs for observables, such as a local sink decomposition flux, that are not related to transport.

Would it be sensible to assume zero-fluxes by default? Could this be implemented as a standard in the package that is only changed if bcs are explicitly specified for some observables?

For the delta-grid control case, this seems to be already the case. Then, is the advection-observable in the example for the first layer actually taking into account the specified bc for Y(t,0) or does it assume a default no-flux bc? Although the overall solution is correct, the user should be made aware that observables related to transport are not fully corresponding to the solution at the boundary.

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Thinking a bit more about it: its not a zero-flux condition that is applied by default with the delta-grid with the upwind scheme, but the flux at the border is the same as between the adjacent two cells/layers. Hence, the default condition corresponds rather to a zero-gradient in the flux, i.e. a zero second derivative of the amount.

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Based on @xtalax advice, I constructed a modified working vector-grid example with specifying addtional bcs. It does not throw the Boundary error. It skips most of the observed variables.

The MWE works only, if I specify bcs for the non-transport related dec_Y. The actual formulation of the boundary condition should not matter for the solution of the problem, but only for inspecting the observed variables at the borders.

When inspecting the simplified corresponding ODESystem (using symbolic_discretize):

(dec_Y(t))[15] ~ (Y(t))[15]*k_Y   # expected
 (dec_Y(t))[1] ~ 0.0002(12500.000000000002(dec_Y(t))[2] - 10000.000000000004(dec_Y(t))[3] + 2500.0000000000014(dec_Y(t))[4])
 (dec_Y(t))[16] ~ 0.00019999999999999963(2499.9999999999936(dec_Y(t))[13] - 9999.999999999982(dec_Y(t))[14] + 12499.999999999996(dec_Y(t))[15])

I would expect an observed variable: (dec_Y(t))[16] ~ (Y(t))[16]*k_Y

The example demonstrates that equations of observed variables unrelated to transport are currently strange at the borders - should be treated differently, and the user should not be required to specify boundary conditions for them.
Further, a default bc corresponding to the dz-number based discretization for the transport-related observed variables would be really helpful.

discretization_grid = MOLFiniteDifference([z => z_grid], t;
    advection_scheme = UpwindScheme(), approx_order = 2)
∂_zz = Differential(z)^2
eqs2 = [
    ∂_t(Y(t, z)) ~ i_Yz(t, z, i_Y) - dec_Y(t, z) + adv_Yo(t, z), 
    dec_Y(t, z) ~ k_Y * Y(t, z),          # observable of decomposition 
    adv_Yo(t, z) ~ -ω * ∂_z(Y(t, z)),  # observable advective flux of Y
]
bcs2 = [
    Y(0, z) ~ 1/z_m * Y0, 
    ∂_z(Y(t, 0)) ~ (Y(t, 0) - fagr(t,i_Y_agr, i_Y_agr_pulse)/ω) / dzs[1], 
    ∂_zz(Y(t, z_m)) ~ 0.0, 
    ∂_zz(dec_Y(t, 0)) ~ 0.0, 
    ∂_zz(dec_Y(t, z_m)) ~ 0.0, 
    #∂_zz(adv_Yo(t, 0)) ~ 0.0, 
    ∂_z(adv_Yo(t, 0)) ~ (fagr(t,i_Y_agr, i_Y_agr_pulse) - ω * Y(t, 0))/dzs[1], 
    ∂_zz(adv_Yo(t, z_m)) ~ 0.0, 
    ]
state_vars2 = [Y(t, z), dec_Y(t, z), adv_Yo(t,z)]
@named pdesys2 = PDESystem(eqs2, bcs2, domains, [t, z], state_vars2, params)
# Convert the PDE problem into an ODE problem
prob2 = discretize(pdesys2, discretization_grid) 

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