What is this book about?

Simulation of real systems

Computer simulations of real systems require a model of that reality. A model consists of both a representation of the system and a set of rules that describe the behavior of the system. For dynamical descriptions one needs in addition a specification of the initial state of the system, and if the response to external influences is required, a specification of the external influences.

Both the model and the method of solution depend on the purpose of the simulation: they should be accurate and efficient. The model should be chosen accordingly. For example, an accurate quantum-mechanical description of the behavior of a many-particle system is not efficient for studying the flow of air around a moving wing; on the other hand, the Navier–Stokes equations – efficient for fluid motion – cannot give an accurate description of the chemical reaction in an explosion motor. Accurate means that the simulation will reliably (within a required accuracy) predict the real behavior of the real system, and efficient means “feasible with the available technical means.” This combination of requirements rules out a number of questions; whether a question is answerable by simulation depends on:

• the state of theoretical development (models and methods of solution);

• the computational capabilities;

• the possibilities to implement the methods of solution in algorithms;

• the possibilities to validate the model.

Validation means the assessment of the accuracy of the model (compared to physical reality) by critical experimental tests.