Parallel running of a modular simulation scheme

Abstract

The idea of modularity in simulation is discussed in relation to parallel processing. A mathematical model for parallel simulation is presented. In this model a possibly nonlinear set of consistency conditions is satisfied in between time steps. Two examples are given which are fundamental to HVAC simulation: (1) heat flow in networks of heat paths and thermal capacitors, and (2) inertialess flow of fluid in networks of pipes and other components. These examples present in abstract from many of the difficulties encountered in thermal simulation of buildings with heating and ventilating plants. The question of convergence of networks of parallel processes is discussed, convergence is proved for the two examples, and a general theorem which implies unconditional convergence is developed. This theorem applies in many cases in which the processes represent physical components, and each process resets some variables to attain local steady state with its neighbors, so the sum of the local distances from steady state is at least not increased by any process.