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## Über dieses Buch

Matthäus Jäger examines the simulation of liquid-gas flow in fuel tank systems and its application to sloshing problems. The author focuses at first on the physical model and the assumptions necessary to derive the respective partial differential equations. The second step involves the cell-centered finite volume method and its application to fluid dynamic problems with free surfaces using a volume of fluid approach. Finally, the application of the method for different use cases is presented followed by an introduction to the methodology for the interpretation of the results achieved.

## Inhaltsverzeichnis

### Chapter 1. Introduction

The fuel tank system is a very important part of most vehicles, but it is also one of the last things in the development process of an automobile. The first fact results in high requirements with respect to stability, durability and general performance of the tank. The latter, on the other hand, brings limitations concerning the volume and geometry of the tank, because the available design space for the tank is limited by the already existing components.
Matthäus Jäger

### Chapter 2. Modeling

The term sloshing means any motion of a liquid inside a partially filled container and therefore including a free surface. Usually the sloshing is induced by the motion of the container, which often gets again influenced by the sloshing itself (e.g. damping). Due to the different physics involved, it is an unsteady, highly non-linear phenomenon and difficult to describe in full detail.
Matthäus Jäger

### Chapter 3. Discretization

In this section the solution procedure for the system of equations derived in the last section will be addressed. It starts with a short comment on the existence and uniqueness of a solution for the incompressible Navier-Stokes equations given by the equations (N.-S.). The Finite Volume Method will be presented in several steps. First the discretization of a general transport equation with the FVM will be described.
Matthäus Jäger

### Chapter 4. Validation and Application to Sloshing

The numerical solution procedure described in the previous chapters is finally applied to two different problems. Both are sloshing problems. The first is a simple validation test case and used to find a suitable combination of discretization schemes and parameter settings to achieve an accurate solution.
Matthäus Jäger

### Chapter 5. Conclusion and Prospect

The model presented in Chapters 2 and 3 is able to describe the evolution of a free surface between two incompressible fluids. But by using it one has to keep in mind that there are severe assumptions necessary to get the respective partial differential equations (§2.6). The described discretization with the finite volume method and a volume-of-fluid approach for the interface description is generally found to be suitable for the simulation of fuel tank sloshing.
Matthäus Jäger

### Backmatter

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