# Computer simulation

Physically correct simulation of a viscous liquid
Computer simulation of waves from wake
Wave animation of the tsunami in Asia December 2004

Under computer simulation and computer simulation is meant to carry out a simulation using a computer, or rather a computer program . This program describes or defines the simulation model .

The first computer simulations include a simulation of a two-dimensional hard-ball model using the Metropolis algorithm and the Fermi-Pasta-Ulam experiment .

## Types of simulation

### Static simulation

In the static simulation, time is irrelevant. The model is static, i.e. In other words, it only looks at a point in time, so it is more or less a snapshot.

### Monte Carlo simulation

If the simulation is based on random numbers and / or stochastics (probability mathematics ), one speaks of Monte Carlo simulation because of the conceptual proximity to gambling . This method has found important applications , especially in physics , and two books by the physicist Kurt Binder are among the most cited publications in this branch of science.

### Dynamic simulation

Time always plays an essential role for the models of dynamic simulation. The dynamic simulation considers processes or procedures.

#### Continuous simulation

With continuous simulation, continuous processes are mapped. This type of simulation uses differential equations to represent the physical or biological laws on which the process to be simulated is based.

#### Discrete simulation

The discrete simulation uses the time to generate certain events according to statistically or randomly measured time intervals, which in turn determine the (next) system state.

Also known as process simulation or event-driven simulation, discrete simulation is mainly used in the production and logistics area. The vast majority of the practical problems lie in this area. In contrast to the continuous models, the models of this simulation can be represented well with standardized elements (e.g. random numbers , queues , probability distributions , etc.). Another powerful approach to developing discrete, event-driven models is the Petri net theory.

The strength of the discrete simulation lies in the fact that it includes the chance or the probability in the model and provides a statement about the probability of the different system states to be expected if the calculation is carried out sufficiently frequently. The field of application for this type of simulation is accordingly large:

• Workflows in production (all automobile manufacturers are big simulation users)
• Logistics processes (supply chains, container handling, etc.)
• Processes with large numbers of people or goods (airports, large train stations, but also motorway toll stations, public transport systems, post distribution centers, marshalling stations, etc.)

#### Hybrid simulation

Of hybrid simulation is called when the model both properties having continuous and discrete simulation. Such models can be found, for example, in medical simulations - especially for training purposes - in which the biology to be simulated is not sufficiently known to be able to create a sufficiently detailed, continuous model.

### System Dynamics

The simulation is under system dynamics

• more complex,
• discrete time,
• not linear,
• more dynamic and
• fed back

Understand systems. Essentially, such simulators are used

• the feedback behavior of socio-economic systems ("Industrial Dynamics"),
• the development of metropolitan areas ("Urban Dynamics") and
• World models, such as B. for the Club of Rome ("World Dynamics")

subsumed. The working methods and tools correspond almost entirely to those of control engineering or cybernetics .

### Multi-agent simulation

The multi-agent simulation , which can be seen as a special case of the discrete simulation, allows emergent phenomena and dynamic interactions to be modeled.

## Simulation languages

Although a simulation program (simulator) can in principle work with any general programming language - in simple cases even with standard tools such as B. a spreadsheet - can be created, special simulation languages ​​have been developed since the 1960s - after the first availability of sufficiently fast computers.

Initially, these languages ​​were limited to the purely mathematical or numerical determination and representation of the simulation processes and results. With the advent of more and more powerful PCs in the 1980s, however, graphic representation and, more recently, animation came more and more .

In discrete simulation, efforts are currently being made to implement optimizing methods, such as B. Artificial neural networks , genetic algorithms or fuzzy logic . These components should add the characteristic of the independent search for optimal solutions to the classic simulators, which in themselves do not have an optimizing effect.

Under the term " digital factory ", large companies - especially those in vehicle and aircraft construction - try to combine the (predominantly animated) process simulation with procedures for costing, for the automated creation of technical documentation and planning systems for production sites and plants, in order to reduce development times and costs as well as to minimize quality inspection and maintenance costs.