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solvermodelica

How to set a convergence tolerance to an specific variable using Dymola?

So, I have a model of a tube with pressure loss, where the unknown is the mass flow rate. Normally, and on most models of this problem, the conservation equations are used to calculate the mass flow rate, but such models have lots of convergence issues (because of the blocked flow at the end of the tube which results in an infinite pressure derivative at the end). See figure below for a representation of the problem on the left and the right a graph showing the infinite pressure derivative.

Problem representation

Because of that I'm using a model which is more robust, though it outputs not the mass flow rate but the tube length, which is known. Therefore an iterative loop is needed to determine the mass flow rate. Ok then, I coded a function length that given the tube geometry, mass flow rate and boundary conditions it outputs the calculated tube length and made the equations like so:

    parameter Real L;
    Real m_flow;
...
equation
    L = length(geometry, boundary, m_flow)

It simulates fine, but it takes ages... And it shouldn't because the mass flow rate is rather insensitive to the tube length, e.g. if L=3 I could say that m_flow has converged if the output of length is within L ± 0.1. On the other hand the default convergence tolerance of DASSL in Dymola is 0.0001, which is fine for all other variables, but a major setback to my model here...

That being said, I'd like to know if there's a (hacky) way of setting a specific tolerance L (from annotations or something). I was unable to find any solution online or in Dymola's user manual... So far I managed a workaround by making a second function which uses a Newton-Raphson method to determine the mass flow rate, something like:

function massflowrate
    input geometry, boundary, m_flow_start, tolerance;
    output m_flow;
protected
    Real error, L, dL, dLdm_flow, Delta_m_flow;
algorithm
    error = geometry.L;
    m_flow = m_flow_start;
    while error>tolerance loop
        L = length(geometry, boundary, m_flow);
        error = abs(boundary.L - L);
        dL = length(geometry, boundary, m_flow*1.001);
        dLdm_flow = dL/(0.001*m_flow);
        Delta_m_flow = (geometry.L - L)/dLdm_flow;
        m_flow = m_flow + Delta_m_flow;
    end while;
end massflowrate;

And then I use it in the equations section:

    parameter Real L;
    Real m_flow;
...
equation
    m_flow = massflowrate(geometry, boundary, delay(m_flow,10), tolerance)

Nevertheless, this solutions is not without it's problems, the real equations are very non-linear and depending on the boundary conditions the solver reaches a never-ending loop... =/

PS: I'm sorry for the long post and the lack of a MWE, the real equations are very long and with loads of thermodynamics which I believe not to be of any help, be that as it may, if necessary, I'm able to provide the real model.

Solution

  • Is the length-function smooth? To me that it being non-smooth seems like a likely cause for problems, and the suggestions by @Phil might also be good ideas.

    However, it should also be possible to do what you want as follows:

    Real m_flow(nominal=1e9);

    Explanation: The equations are normally solved to a certain tolerance in unknowns - in this case m_flow.

    The tolerance for each variable is a relative/absolute tolerance taking into the nominal value, and Dymola does not allow you to set different tolerances for different variables.

    Thus the simple way to compute m_flow less accurately is by setting a high nominal value for it, since the error tolerance will be tol*(abs(m_flow)+abs(nominal(m_flow))) or something like that.

    The downside is that it may be too inaccurate, e.g. causing additional events, or that the error is so random that the solver is still slowed down.