The numerical simulation of fluids has become an established tool in many engineering applications. Free surface fluids represent a special case that is important for a variety of applications. For a free surface simulation, a two phase system, such as air and water, is described by a single fluid phase with a sharp interface and corresponding boundary conditions. This allows the efficient representation and simulation of complex problems. In this thesis, the main application for free surface flows will be the generation of animations of liquids. Additionally, engineering applications from material science and particle technology are considered. The simulation algorithm of this thesis is based on the lattice Boltzmann method. This method has been chosen due to the overall computational efficiency of the basic lattice Boltzmann algorithm, and its ability to deal with complex geometries and topologies. The basic algorithm is extended to compute the motion of free surfaces in three dimensions while conserving the overall mass. Adaptive time steps and grids, in combination with a turbulence model, allow stable and efficient simulations of detailed fluids. In combination with boundary conditions for moving and deforming objects, the algorithm represents a flexible basis for free surface simulations. Its per- formance on single CPU machines will be evaluated. Likewise, performance results of parallelized versions will be given for shared- and distributed-memory architectures. For fluids in computer generated animations it is important to give animators control of the fluid motion. An approach to perform this fluid control, without disturbing the natural fluid behavior, will be given. Another typical problem is the simulation of large open water surfaces due to the highly differing scales of waves and drops. An explanation of how to perform such simulations using a combination of two-dimensional and three-dimensional techniques will be given, in combination with a particle based drop model. To demonstrate the capabilities of the solver that was developed during the work on this thesis, it has been integrated into an open source 3D application. Finally, areas of future work and possible extensions of the algorithm will be discussed. One of these topics is the inclusion of an accurate and efficient curvature com- putation for surface tension forces. Furthermore, an outlook of possible applications in the fields of metal foams and colloidal dispersions will be discussed.

Numerische Stromungssimulationen sind zu einem wichtigen Hilfsmittel vieler tech nischer Anwendungen geworden. Dabei stellen besonders die Stromungen mit freien Oberflaechen einen Spezialfall dar, der in vielen Bereichen von Bedeutung ist. Diese Arbeit konzentriet sich auf die Simulation eines solches System mit zwei Phasen, z.B. Wasser und Luft. Die freie Oberflaeche wird dabei mittels einer einzelnen Fluidphase und einer scharfen Grenzflaeche mit geeigneten Randbedinungen simuliert. Fokus dieser Arbeit ist die Erstellung von Animationen freier Oberflaechen. Weitere Anwendungen sind jedoch unter anderem (Rechtschreibung checken) die Simulation von Metallschaeumen und von Partikeln (oder Partikelsystemen) in einer Stromung. Der in dieser Arbeit verwendete Simulationsalgorithmus basiert auf der Lattice-Boltzmann Methode. Dieser Simulationsansatz ermoglicht die Simulation von komplexen Geometrien und Topologien mit hoher Effizienz. Der Basisalgorithmus wird im Folgenden um die masseerhaltende Behandlung freier Oberflaechen erweitert. Adaptive Zeitschritte und adaptive Gitter in Kombination mit einem LES- Modell ermoglichen die effiziente Simulation detaillierter Stromungen. Im Zusammenspiel mit Rand- bedingungen fur bewegliche und verformbare Objekte stellt dies eine flexible Basis fur Simulationen von Fluiden mit freien Oberflaechen dar.