Acceleration Methods
The default method for recycle convergence in PRO/II is Direct-substitution, i.e., the last computed values for the tear streams are used for the next trial solution of the recycle loop. This method is generally stable, but can sometimes be computationally slow and approach convergence asymptotically. In such cases an acceleration method can be used for more rapid solution of recycle loops.
The following two types of acceleration methods are available in PRO/II:
Wegstein acceleration technique
This method provides rapid solution of recycles using an acceleration factor based on the convergence characteristics shown by previous iterations. A negative acceleration factor results in acceleration, with acceleration increasing as the value becomes more negative. But high acceleration values usually result in an unstable convergence path. Damping of oscillating models is also possible, by forcing the acceleration factor to be between 0.0 and 1.0. Note that this method does not work well when multiple recycle streams are interacting, i.e., affecting one another's values.
Broyden acceleration
This is based on the "Householder" method, which allows for rapid, stable solution of recycle loops.
You can specify the recycle streams to be accelerated, the recycle iteration after which acceleration is to be applied, and the number of recycle iterations between application of the acceleration techniques.
Complete technical details may be found in topics under Flowsheet Solution Algorithms in the PRO/II Reference Manual.
Related Topics
Recycle Loops - Technical Information