Numerical solutions of the general relativistic equations for black hole fluid dynamics
University of Cambridge
Department of Applied Mathematics and Theoretical Physics
Doctor of Philosophy (PhD)
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Blakely, P. (2010). Numerical solutions of the general relativistic equations for black hole fluid dynamics (Doctoral thesis). https://doi.org/10.17863/CAM.16092
Related data - see record for Numerical Solutions of the General Relativistic Equations for Black Hole Fluid Dynamics at http://www.dspace.cam.ac.uk/handle/1810/226117 containing the data from the DVD referred to in the main text.
The aims of this thesis are to develop and validate a robust and efficient algorithm for the numerical solution of the equations of General Relativistic Hydrodynamics, to implement the algorithm in a computationally efficient manner, and to apply the resulting computer code to the problem of perturbed Bondi-Hoyle-Lyttleton accretion onto a Kerr black hole. The algorithm will also be designed to evolve the space-time metric, and standardised tests will be applied to this aspect of the algorithm. The algorithm will use up-to-date High-Resolution Shock-Capturing numerical schemes that have been developed for the stable and accurate solution of complex systems of equations. It will be built around the Adaptive Mesh Refinement and overlapping, curvilinear grid methodologies in order to extend these schemes to the efficient solution of two and three-dimensional problems. When implementing the algorithm, we will use previously written code libraries, where appropriate, to avoid excessive software development. We will validate the algorithm against standard test-cases for Special and General Relativistic Hydrodynamics, and for Einstein's equations for the evolution of the space-time metric. The methodologies we use will be tested to ensure that they lead to the stable and accurate numerical solution of these problems. Finally, the implemented algorithm will be applied to the problem of Bondi-Hoyle-Lyttleton flow onto a Kerr black hole in three dimensions. It will be validated against existing exact and numerical solutions of the problem, and then be used to perform an extensive parametric study of the problem, varying the spin of the black hole and the incident wind direction, and allowing for the perturbation of the fluid density upstream of the black hole. We will then analyze the results of the study, and present the complete set of results on a DVD accompanying this thesis.
GRHD, Bondi Hoyle Lyttleton accretion, Computational Fluid Dynamics, HRSC schemes, Overlapping grids, AMR
Is supplemented by: https://www.repository.cam.ac.uk/handle/1810/226117
This work was supported by an EPSRC Doctoral Training Grant. Some simulations were performed using the Darwin Supercomputer of the University of Cambridge High Performance Computing Service (http://www.hpc.cam.ac.uk/), provided by Dell Inc. using Strategic Research Infrastructure Funding from the Higher Education Funding Council for England.
This record's DOI: https://doi.org/10.17863/CAM.16092
Copyright Philip Blakely