MTK: vectors with mixed initial values and guesses

[B-LIE]

Is your feature request related to a problem? Please describe.

I try to make a component with a semi-discretized (Method of Lines) partial differential equation model, which connects to a port with pressure as potential and mass flow rates as Flow. When defining the variables, this includes:

# State variables
 p(t)[1:N], [unit = u"Pa", guess = p_guess_vec]
 md(t)[1:N] = fill(0.0, N), [unit = u"kg/s"]

The problem is that I really would like to specify initial values for p[2:N-1], and guess values for p[1], p[N].

Describe the solution you’d like

See above.

Describe alternatives you’ve considered

I suspect this can be done by adding initialization_eqs? Or is that in fact the way to do it?

Additional context

The way I have done it now, is to provide p[2:N-1] as initial values in the ODEProblem statement, but that puts an extra burden on the user.

[B-LIE]

OK, I think I figured it out:

init_eqs = [p[j] ~ p_guess_vec[j] for j in 2:N-1]

return compose(ODESystem(eqs, t, vars, pars; name = name, initialization_eqs = init_eqs), a, b)

This works fine. (The documentation is not really easy to find right now.)

[baggepinnen]

Here's a way

p(t)[1:N], [unit = u"Pa", guess = p_guess_vec]
p_center(t)[2:N-1] = p_guess_vec[2:end-1]
p_1(t), [guess = p_guess_vec[1]]
p_end(t), [guess = p_guess_vec[end]]

equations = [
    p ~ [p_1; p_center; p_end]
]

[AayushSabharwal]

The destructuring approach is typically the way to do this. initialization_eqs also works, but it requires specifying the dynamics for p_guess_vec separately.

[B-LIE]

Thanks to both. I should perhaps have said: p_guess_vec does not have any dynamics. It is just calculated as the hydrostatic pressure along a sloping pipe, to be used to give reasonable initial guesses/values.

@baggepinnen : in your suggestion, I have to declare extra variables p_center, p_1, p_end, as you do (@variables macros)...

• Is it valid to declare a vector as @variables p_center(t)[2:N-1] ??? No need to start at 1?

• Do I also need to add a dynamics model for p_center, etc. Like D(p_center) ~ 0 ? Similarly for p_1 and p_N ????

• Or, will p_center, etc. "implicitly" assume D(p_center) ~ 0 if I don't provide an equation for this vector, and just let it be given by the initial equation p_center = p_guess_vec[2:N-1]

[baggepinnen]

p_center is given by this equation

p ~ [p_1; p_center; p_end]

so are the other p variables.

if you then add your regular equation for p you have what you need