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# Simulation

Theo Gilch, winter semester 2015/16

Simulation is the rebuilding of a dynamical process in a system, by using a model in order to acquire knowledge that can be transferred to reality. [1] Simulation can be done with experiments, like a crash test for cars, or computer based by solving differential equations which describe the issue that is to be examined. [2] In this article the focus is put on the computer based techniques.

## Used Methods

The computer based simulation techniques can be split up in two groups:

### Analytical Methods

These methods are usually based on a solution of the closed form of the differential equation. The solution of the equations can be found by using series expansion techniques. [3] [4]

### Numerical Methods

The numerical methods are based on discretization of the model, which enables us to find a solution for the weak form of the differential equation. Discretization means that the examined area is divided into small parts, in order to get a finite number of variables, also called degrees of freedom. Due to this the differential equation changes to a system of algebraic equations, which can be solved numerically. Depending on the problem that has to be solved, there are different methods to find a discretization: [3]

• Finite Element Method (FEM)
• Finite Volume Method (FVM)
• Finite Difference Method (FDM)
• Boundary Element Method (BEM)

## Procedure

In every type of computer based simulation three steps have to be passed to achieve dependable results:

### Preprocessing

In this step a model consisting of information about geometry, material properties and boundary conditions is defined. The more exact this model depicts the real system the more reliable results are gained. The partition of the system is also part of this step which is done by generating a mesh. [5]

### Processing

The computer is now able to create the system of algebraic equations, which contains all information to describe the model. A numerical solver generates the solution for these equations. It is important to keep in mind that this solution is an approximation. The error of the calculation depends on the model quality and on the solving techniques. The more degrees of freedom the system has got the more computing power and time is needed for this step. [5]

### Postprocessing

In this step results can be visualized in tables, plots or animations. Afterwards it is important to check if the results are reliable and if the assumptions made in the model definition are correct. [5]

## Properties

The properties of the computer based simulation techniques is the reason why they are often used in nondestructive testing. A numerical method can be used for every type of differential equation, which means that all physical phenomenon’s can be investigated. It is possible to calculate sound fields, wave propagation and electromagnetic fields which are fundamental for nondestructive testing. [4]

Simulation can be used to prepare for an experiment, for example to find the best sensor position for the task. Simulating before starting the measurement, can often save the time during the experimental research. As a result of this the investigation often gets cheaper.

Simulation is a good tool to understand the archived measurement results. In an experiment it is often not possible to see what happened exactly, because the event occurred to fast or inside the component that is been looked at. With simulation the event can be reconstructed and analyzed. [3] [6]

## Literature

• Simulation. German Wikipedia. Page call: 20.01.2016.
• Simulation in der Materialforschung. Bundesamt für Materialforschung- und prüfung. Page call: 20.01.2016.
• 2 Abaqus Basics. Dassault Systems. Page call: 20.01.2016.
• Blatt 1. VDI 3633. 2015.
• Finite Elemente. Lehrstuhl für numerische Mechanik. Skriptum zur Vorlesung vom WS 2015/16.
• Bungartz, H.-J.; Zimmer, S.; Buchholz, M.; Pflüger, D.: Modellbildung und Simulation - eine anwendungsorientierte Einführung. 2. Auflage. Springer-Verlag. Berlin Heidelberg, 2009, 2013. ISBN 978-3-642-37656-9.

## References

1. Blatt 1. VDI 3633. 2015.
2. Simulation. German Wikipedia. Page call: 20.01.2016.
3. Finite Elemente. Lehrstuhl für numerische Mechanik. Skriptum zur Vorlesung vom WS 2015/16.
4. Simulation in der Materialforschung. Bundesamt für Materialforschung- und prüfung. Page call: 20.01.2016.
5. 2 Abaqus Basics. Dassault Systems. Page call: 20.01.2016.
6. Bungartz, H.-J.; Zimmer, S.; Buchholz, M.; Pflüger, D.: Modellbildung und Simulation - eine anwendungsorientierte Einführung. 2. Auflage. Springer-Verlag. Berlin Heidelberg, 2009, 2013. ISBN 978-3-642-37656-9.