WHAT IS SIMULATION?

Simulation is the representation of the operations or features of one process or system through the use of another. Typically, physical, technical, biological, psychological or economic processes are represented by mathematical or physical models.

This definition implies opposed interpretations: On the one hand, simulation is the imitation of existing complex systems, but on the other hand, it also can give a prediction on the processes of yet inexistent systems. This is one of the principal reasons why simulation technologies have become highly relevant in research and development: With the aid of simulation, procedures in complex systems become understandable and it is predictable, how these systems would react to a modification of the parameters (boundary conditions et. al.).
By narrow definition, (computer) simulation means the numerical solution of physical equations (e.g. the Navier- Stokes equation in fluid dynamics or the Maxwell- equations in electrodynamics). Such simulation technologies share the reduction of infinite degrees of freedom of a continuum (partial ODE) to a finite number of points in space (discrete equations). Using adequate mathematical methods and algorithms, the result is a matrix equation, which can be solved computer-aided with a reasonable amount of effort.
Generally, the reduction to a finite number of elements is based upon the gathering of (physical) information around one point and target it at this point. For this purpose, Finite-Element-Method (FEM) and Finite-Volume-Method (FVM) are firmly established.