The Lattice-Boltzmann-model is analyzed with regard to application to numerical solution of flow acoustic problems. In the first part of this study the description of sound wave propagation by common variants of the Lattice-Boltzmann-model is examined by calculation of phase velocity and effective viscosity for sound waves. Schemes with nine velocities in two dimensions and nineteen velocities in three dimensions are considered. For each of these a single relaxation time model (LBGK-model) and a multiple relaxation time model (MRT) is investigated. All schemes exhibit an almost isotropic error in phase speed of sound waves. With a spatial resolution of 10 or 30 grid spacings per wavelength the deviation of phase speed is less than 1 % or 0.1 %, respectively. The dissipation of sound waves is not simulated correctly by LBGK-models since there the bulk viscosity is fixed to the shear viscosity. Apart from that there is only very little numerical dissipation. The dissipation error therefor is negligible in the audible frequency range in air as long as the simulation volumes do not become very large, i.e. much more than some hundred wavelengths. The MRT-models allow to adjust the bulk viscosity by a suitable choice of relaxation parameters. However, if the bulk viscosity is set to a realistic value, stability of the scheme requires free relaxation parameter values which are close to the relaxation parameters that determine the viscosities. Then the gain in stability of MRT-models compared to LBGK-models is lost to some extent. All schemes considered here are able to reproduce the effect of sound wave convection in homogeneous background flows. Although additional numerical errors arise in transport coefficients, the overall errors are of the same order of magnitude as in the case with zero background flow and are not critical in practical applications. In the second part of the work numerical experiments are described which demonstrate the coupling of the flow- and sound field. Three test cases are considered: Sound generation by a single vortex interaction with the leading edge of a semi-infinite flat plate, sound generation by a grazing flow over a partially covered cavity and instationary flow around a half-cylinder with an attached wedge tail. The first test case is simulated in two dimensions with a self-written program. The sound calculated directly is compared to prediction based on an acoustic analogy. The observed amplitudes of the radiated sound agree quantitatively well for all flow and eddy velocities considered here. This implies, that the coupling of the sound and flow field is correct. In the case of the cavity the flow is computed in two dimensions with a self-written program as well as in three dimensions with the commercially available program PowerFLOW. The simulated pressure fluctuations in the cavity are compared to results of a wind tunnel experiment. Good agreement between simulation and wind tunnel experiment is found. The instationary flow around a half cylinder with an attached wedge tail is simulated in three dimensions using PowerFLOW. The radiated sound cannot be captured with PowerFLOW because of insufficient quantization of fluid density. However, pressure fluctuations on the surface of the body exhibit good agreement with the result of a wind tunnel test. Summarizing the results of this work it can concluded, that the Lattice-Boltzmann-model is well suited to numerical solutions of flow acoustic problems.

Gegenstand dieser Arbeit ist die Forschungsdisziplin, welche in der Strukturmechanik als Modellordnungsreduktion bekannt ist. Im Mittelpunkt stehen Kopplungsprozesse von starren und elastischen Mehrkörpersystemen - sowohl in theoretischer Hinsicht als auch bezüglich der praktischen Realisation im Rahmen des Finite-Elemente-Programms ANSYS und des Mehrkörpersimulationsprogramms SIMPACK. Eine Vielfalt von strukturerhaltendenMOR-Methoden wurde zum Zwecke des Überblicks dargestellt. Darüber hinaus findet sich eine Kategorisierungsmethodik in Hinsicht auf den später beschriebenen FEM-MKS-Kopplungsprozess. Die Effizienz der MOR-Methoden wird sowohl hinsichtlich der Qualität der ROM als auch bezogen auf die hierfür benötigte Rechenzeit bemessen. Aus diesem Grunde wurden etliche MOR Schemata dargelegt, mit dem Ziel, den Effizienzfaktor während der Berechnung eines ROMs zu maximieren, das heißt maximale Qualität und minimale Rechenzeit zu erzielen. Die Validierung der dynamischen ROM-Eigenschaften basiert auf der Anwendung der sogenannten Modellkorrelationskriterien. Dies wurde an vier Anwendungsbeispielen aus dem Feld der Strukturmechanik getestet: der 3D-Balkenstruktur, der UIC60-Schiene, dem Pleuel und der Kurbelwelle. Die Anwendung der diagonal perturbation-Methodik verbessert die Kondition der Steifigkeitsmatrix eines Modells, von beiden Arten von Lösungsprozeduren, d.h. direkte und iterative Verfahren, betroffen sind. Die dynamische Bewegung mechanischer MKS wird als ein Index-3-DAE-Systemformuliert und die Information über die elastischen Körper wird in Form der sogenannten Standard Input Datei in einen MKS-Code transferriert. Die Einführung des Back-projection-Ansatzes ermöglicht die weitere Verwendung bestimmter ROM-Typen, derren assoziierten physikalische Eigenschaften unangemessen definiert wurden. Zum Abschluss werden die theoretischen, modellierenden und numerischen Fortschritte der Arbeit resümiert und kombiniert im Sinne der Model Order Reduction Package Toolbox (MORPACK). Die Matlab-basierte MORPACK-Toolbox ermöglicht den FEM-MKS-Kopplungsprozess für die Verwendung von ANSYS und SIMPACK. Hierin sind ein Großteil der zuvor erläuterten Erweiterungen eingeschlossen. Mit Hilfe der zwei integrierten inneren MOR- und SID-Schnittstellen als auch der vier Anwendungsebenen wird der Import von freien oder eingespannten ROM in SIMPACK ermöglicht. / The research discipline referred to as the Model Order Reduction in structural mechanics is the topic of this Thesis. Special emphasis is given to the coupling process of rigid and elastic Multi Body Dynamics in terms of both the theoretical aspects and the practical realization within the environment of the commercial Finite Element and the Multi Body Systems software packages, ANSYS and SIMPACK respectively. In this regard, a variety of structure preserving Model Order Reduction methods is presented and a categorization methodology is provided in view of the later FEM-MBS coupling process. The algorithmic scheme of several of the MOR methods indicates the capability of generating qualitatively better Reduced Order Models than the standardized Guyan and Component Mode Synthesis approaches. The efficiency of a MOR method is measured in terms of both the quality of the ROM and the associated time required for the .computation Based on the application of the, so called, Model Correlation Criteria the efficiency of the MOR schemes is tested on four application examples originating from the area of structural mechanics, i.e. the 3D elastic solid bar structure, the UIC60 elastic rail, the elastic piston rod, and the elastic crankshaft model. Herewith, the superiority of alternative MOR schemes in comparison to Guyan or CMS methods is demonstrated in terms of the ROM?s quality and the computation time by the use of either the one-step or the two-step MOR algorithms. Numerous of the FE discretized structures suffer from the, so called, ill-conditioned properties regarding the associated stiffness matrix. On one hand, the direct solution of a MOR method might produce erroneous ROMs due to the associated truncation phenomenon and on the other hand, any kind of iterative approach suffers from vast computation times. The application of the diagonal perturbation methodology improves the condition properties of the model?s stiffness matrix and thus, both kinds of the aforementioned solution procedures are affected. The back-projection approach is introduced, which projects the ROM belonging to the Non physical subspace reduction-expansion methods category back onto the physical configuration space and thus, enabling its further usage in a MBS code, e.g. SIMPACK. Finally, the theoretical, modelling, and numerical advancements are combined in terms of the Model Order Reduction Package. The Matlab-based MORPACK toolbox enables the FEM-MBS coupling process for the ANSYS-SIMPACK utilization and herewith, several of the aforementioned enhancements are included. With the help of the two integrated inner interfaces, i.e. MOR and SID, as well as four application levels, the import into SIMPACK of alternatively free or fixed ROMs is enabled. The functionality of MORPACK is demonstrated based on two application examples, namely, the 3D elastic solid bar and the UIC60 elastic rail, the dynamic properties of which are validated prior to their import into SIMPACK.