GPS-X Technical Reference

Miscellaneous 424
STEADY-STATE SOLVER
The steady-state solver used in GPS-X is a robust routine based on a direct search algorithm (that
is, no gradients are used). Sometimes, the steady-state convergence appears slow or diverges due
to a problem in the way that the model is set up. For example, if the underflow rate from a settler
is too low, that settler will begin to fill up with solids. Since the concentration ranges of solids in
the ten layers become large, the changes in these layers between loops of the steady-state solver
also become large which may cause slow convergence or divergence.
In all cases of poor convergence, the user should closely examine all the unit processes for proper
specification. The easiest way to do this is to examine the dsum# variable associated with each
unit process where # represents the overflow stream label. You can do this by issuing the display
command in the Command line of the Simulation Control window. The sum of the individual
dsum values equals the dsum value displayed in the Log window. Having done that, there are a
number of parameters associated with the steady-state solver that can be fine-tuned.
The forms shown in Figure 15-9 and Figure 15-10 are accessed by selecting
General Data > System > Parameters > Steady-State. The parameters in these forms are
described below.
The first menu item, number of retries on iteration indicates the number of times the steadystate
solver will try to reach convergence if it fails.
The error limit on individual variables is a tolerance below which the steady-state ignores a
variable. If the steady-state solver is making changes to a state variable that become smaller than
this tolerance, the solver will ignore the variable, assuming it is at steady-state.
When the solver achieves a sum of state variable derivatives below the iteration termination
criteria, a steady-state convergence is triggered. The default value is 10.0, but in some systems it
may need to be increased when in single precision.
The contract constant and expand constant refer to the step size made by the steady-state solver
between iterations. A larger step is taken if an improvement is found, while a smaller step is taken
if no improvement is found. The performance of the steady-state solver can be greatly affected by
these parameters. The expansion factor is limited to the maximum step size in one iteration.
This maximum step size is dampened as the steady-state solution is reached. The damping factor
on final approach will control the damping effect. A zero value means no damping; while a
value of 1.0 means that the maximum step size is limited to one tenth of the maximum step size.
The initial step size that the steady-state solver takes is governed by the initial perturbation
parameter. This number is normally set smaller than the maximum step size to prevent a poor
initial guess by the solver.
GPS-X Technical Reference