# simulation

Simulation is defined according to the VDE guideline DIN 3633 and is therefore a procedure for the reproduction - i.e. modeling - of a real or imaginary system with its internal dynamic processes in the form of a model that can be experimented with, in order to obtain knowledge that can be transferred to reality. In the broadest sense, simulation also means the preparation, execution and evaluation of simulation experiments with a simulation model.

With the help of simulation, the temporal sequence behavior of complex systems can only be investigated if the effect structures and effect mechanisms responsible for the system behavior are captured as completely as possible and modeled correctly.

Modeling and simulation is basically a system science and is used for system analysis. It is primarily concerned with providing basic principles and methods for describing the relationships between the structure - the structure of effects - and the behavior of systems.

Modeling and simulation are always used when

- the system cannot be observed or investigated in its real environment without the risk of its destruction (e.g. reactor processes, turbulence on airfoils, ...),
- the processes to be investigated are extremely slow or extremely fast (e.g. time-lapse / slow-motion of evolution or explosion processes),
- the complexity of the system does not allow a closed analytical treatment (e.g. due to limiting preconditions and assumptions) or allows it only approximately (e.g. communication systems, socio-economic systems, system management and logistics, ...),
- analytically approximated knowledge and observations have to be validated and
- it is a matter of being able to train operating personnel of complex systems in a hazard-free manner (e.g. operating process control stations, pilot training in flight simulators, ...).

There is a fundamental riskin transferring simulation results to reality, which tends to be greater the more abstracted or idealized reality is in the modeling process. This leads directly to the necessity of validating simulation models. The goal of validation is to answer the question whether a suitable model was used.

The types of simulation in an overview:

Static simulation: Monte Carlo simulation.

Dynamic simulation: Continuous simulation: deterministic simulation, stochastic simulation.

Discrete simulation: deterministic simulation, stochastic simulationHybrid simulation: continuous simulation, discrete simulation.

Static models do not have any state changes and simulation is used to capture the current moment. If the simulation is based on random numbers, it is also called Monte Carlo simulation. In dynamic models, on the other hand, the model state is a function of time.

If the state variables or their temporal changes can be described by continuous functions, one speaks of continuous (time-continuous) models. In a discrete (time-discrete) simulation model, the values of the state variables change only abruptly at certain points in time that are discretely distributed on the time axis. The state changes of a discrete simulation model occur to a certain extent event-like.

A simulation is called deterministic if its reaction to a certain input is unambiguously fixed in the respective model state under consideration. If, however, the reaction of a model to inputs is of a purely random nature, i.e. if the occurring reactions can only be described by probability distributions, one speaks of a stochastic simulation model.

One speaks of hybrid simulation if its properties are both continuous and discrete in nature.

Simulation tasks are realized with the support of powerful computer systems, for which there is a whole range of software tools. Beside the higher programming languages like the programming language C, BASIC, FORTRAN and others, conventional spreadsheet programs are also suitable for simulation tasks. Furthermore, special simulation languages such as ACSL, Simulink, SIMULA, among others, have been developed, which in turn enable standardized, mathematical modeling of the system to be simulated.