Bochum, Univ., Diss., 2004. / Computerdatei im Fernzugriff.

Bochum, University, Diss., 2004.

Zugl.: Göttingen, Univ., Diss., 2008

Zugl.: Berlin, Techn. Universiẗat, Diss., 2009.

University, Diss., 2003--Freiburg (Breisgau).

In this thesis, we are interested in numerically preserving stationary solutions of balance laws. We start by developing finite volume well-balanced schemes for the system of Euler equations and the system of MHD equations with gravitational source term. Since fluid models and kinetic models are related, this leads us to investigate AP schemes for kinetic equations and their ability to preserve stationary solutions. Kinetic models typically have a stiff term, thus AP schemes are needed to capture good solutions of the model. For such kinetic models, equilibrium solutions are reached after large time. Thus we need a new technique to numerically preserve stationary solutions for AP schemes. We find a criterion for SP schemes for kinetic equations which states, that AP schemes under a particular discretization are also SP. In an attempt to mimic our result for kinetic equations in the context of fluid models, for the isentropic Euler equations we developed an AP scheme in the limit of the Mach number going to zero. Our AP scheme is proven to have a SP property under the condition that the pressure is a function of the density and the latter is obtained as a solution of an elliptic equation. The properties of the schemes we developed and its criteria are validated numerically by various test cases from the literature. / In dieser Arbeit interessieren wir uns für numerisch erhaltende stationäre Lösungen von Erhaltungsgleichungen. Wir beginnen mit der Entwicklung von well-balanced Finite-Volumen Verfahren für das System der Euler-Gleichungen und das System der MHD-Gleichungen mit Gravitationsquell term. Da Strömungsmodelle und kinetische Modelle miteinander verwandt sind, untersuchen wir asymptotisch erhaltende (AP) Verfahren für kinetische Gleichungen und ihre Fähigkeit, stationäre Lösungen zu erhalten. Kinetische Modelle haben typischerweise einen steifen Term, so dass AP Verfahren erforderlich sind, um gute Lösungen des Modells zu erhalten. Bei solchen kinetischen Modellen werden Gleichgewichtslösungen erst nach langer Zeit erreicht. Daher benötigen wir eine neue Technik, um stationäre Lösungen für AP Verfahren numerisch zu erhalten. Wir finden ein Kriterium für stationär-erhaltende (SP) Verfahren für kinetische Gleichungen, das besagt, dass AP Verfahren unter einer bestimmten Diskretisierung auch SP sind. In dem Versuch unser Ergebnis für kinetische Gleichungen im Kontext von Strömungsmodellen nachzuahmen, haben wir für die isentropen Euler-Gleichungen ein AP Verfahren für den Grenzwert der Mach-Zahl gegen Null, entwickelt. Unser AP Verfahren hat nachweislich eine SP Eigenschaft unter der Bedingung, dass der Druck eine Funktion der Dichte ist und letztere als Lösung einer elliptischen Gleichung erhalten wird. Die Eigenschaften des von uns entwickelten und seine Kriterien werden anhand verschiedener Testfälle aus der Literatur numerisch validiert. / In this thesis, we are interested in numerically preserving stationary solutions of balance laws. We start by developing finite volume well-balanced schemes for the system of Euler equations and the system of Magnetohydrodynamics (MHD) equations with gravitational source term. Since fluid models and kinetic models are related, this leads us to investigate Asymptotic Preserving (AP) schemes for kinetic equations and their ability to preserve stationary solutions. In an attempt to mimic our result for kinetic equations in the context of fluid models, for the isentropic Euler equations we developed an AP scheme in the limit of the Mach number going to zero. The properties of the schemes we developed and its criteria are validated numerically by various test cases from the literature.

No description available.

Magnetohydrodynamic instabilities are responsible for geo- and astrophysical phenomena such as reversals of the geomagnetic field, sunspots, solar flares, and accretion disk dynamics. Two particular types of these instabilities were experimentally investigated in rotating spherical and cylindrical apparatus using the eutectic alloy GaInSn as a working fluid. The spherical apparatus, Hydromagnetic Experiment with Differentially Gyrating sphEres HOlding GaInSn (HEDGEHOG), was used to investigate the magnetised spherical Couette (MSC) flow for a range of the imposed axial magnetic field corresponding to Hartmann numbers of 0 to 40 and for a Reynolds number of 1000. A wave with an azimuthal wavenumber of 2 was observed at a Hartmann number of 0, which changed its azimuthal wavenumber to 3 at Hartmann numbers of 5 and 10. For Hartmann numbers between 10 and 22.5, the experimental flow displayed no temporal dependence, since the MSC flow was in its base state. In the remainder of the investigated range of Hartmann numbers, rotating waves with azimuthal wavenumbers of 2, 3, and 4 manifested, with some dependence on whether the Hartmann numbers were fixed or continuously varied. For the magnetised Taylor-Couette (MTC) flow investigated using the Potsdam ROssendorf Magnetic InStability Experiment (PROMISE), thermal convection was found to influence the azimuthal magnetorotational instability (AMRI) in two major ways. Firstly, it reduced the critical Hartmann number required for the onset of AMRI. Secondly, it broke the symmetry of the AMRI travelling waves so that they either travelled upwards or downwards depending on the direction of the radial heat flux.