Simulation of large scale dynamic systems—I. Modular integration methods

Abstract

Modular simulation of dynamic systems offers the possibility of computational speed through parallel processing of individual subsystems and through the use of the best integration algorithms for each subsystem. Such simulation needs coordination algorithms to keep the various subsystems in time synchronization and to compute the interconnections between the subsystems. A mathematical description of the coordination problem leads to the development of several new algorithms. These new algorithms are shown to have desirable convergence and stability properties. In particular a new Newton type algorithm is A-stable in a sense similar to that defined for ordinary integration algorithms. Numerical tests with several small example problems and with the simulation of the dynamics of an atmospheric crude unit consisting of 5 interacting columns are used to evaluate the various coordination algorithms. The crude unit simulation was carried out using a prototype modular simulator for distillation systems. The simulator description and the results of applying it to a crude unit are given in Part II. Scope—A formal mathematical definition of the problem of simulating the dynamics of large integrated systems using independent simulations of its subsystems (the coordination problem) yields a framework in which to analyse the behavior of modular integration methods. Analysis shows that most common existing technique, constant extrapolation, has several practical and theoretical defects which are overcome with new Newton type methods. Several examples illustrate and amplify theoretical results. Significance—The modular integration methods presented in this work provide viable alternatives to simulating large systems by integrating a single huge set of equations. They offer the possibility of simulating the dynamics of very large scale process systems using parallel (micro) processors.