What Do We Model? What Results Do We Get? An Anatomy of Modelling Systems Foundations

Abstract

The chapter is a reminder, a follow-up of the road-map that leads from observation of natural situation to colourful presentation of results of modelling that are supplied to the user and decision makers. It is unfortunate matter of fact that too many people involved in modelling do not know how the very heart of the software they use was conceived and on what physical and mathematical hypotheses it is based. Most of the users do not realise what are the limitations in the validity of the results that may be traced back to the limitations of the stages of this road-map. Using as the departure point and an example 1D modelling, the chapter describes and, up to a point, lists the chain of intellectual activities that can be summarised as follows: observation of the nature (flow); hypotheses concerning main physical phenomena; formulation of physical laws (e.g. conservation laws) for isolated systems where only these phenomena exist; mathematical formulation of these laws (differential, integral, etc., equations); parameterisation of phenomena not described by equations; impossibility to solve the equations; numerical algorithms solutions of which converge to those of equations; interpretation of parameters and approximate solutions obtained from algorithms; interpretation of results. The purpose is to let the users of commercial software to understand how the very heart of the modelling system they use was conceived and why the validity of the results obtained in the end is limited by the hypotheses of the original concept. In conclusions, the following question is put to the reader: can a modeller who is not sufficiently knowledgeable about all the links of this chain tell his “client” what are possible doubts or deviations between what was just simulated and the reality?