Interfaces in Numerical Relativistic hydrodynamics

This thesis investigates numerical techniques for modelling sharp interfaces<br/>between relativistic fluids. The motivation for this work lies in obtaining accurate<br/>models of neutron star interiors for use in multidimensional simulations<br/>in general relativity. The interior structure of a neutron star is believed to<br/>contain several regions, often separated by sharp transition layers. These layers<br/>are too thin to be explicitly incorporated in a numerical simulation of the<br/>entire star. We investigate how techniques can be developed to model these<br/>layers as sharp interfaces, across which the matter model can change, with<br/>the microphysical behaviour of the transition layer described through some<br/>appropriate boundary conditions.<br/><br/>The physical situations in which strong, detectable, gravitational waves are<br/>produced are, by their nature, violent events. As a result, we expect that large<br/>non-linear features, such as shock waves, will be formed. Therefore it is essential<br/>that the techniques developed to incorporate these sharp interfaces allow<br/>for their interaction with non-linear features in a stable manner numerically.<br/><br/>The techniques required for modelling sharp interfaces between two fluid<br/>components has not previously been considered in relativity. However, in Newtonian<br/>computational fluid dynamics, the boundary conditions required for<br/>stable, accurate behaviour across a sharp interface between two fluids, modelled<br/>using level set methods, have been developed. These techniques lend<br/>themselves naturally to an extension to the relativistic situations we wish to<br/>consider. In this thesis we start from the Ghost Fluid Method of Fedkiw et al.<br/>We first investigate whether it can be extended to simple relativistic situations,<br/>hence use special relativity in 1+1 dimensions. In order to use this method in<br/>neutron star simulations, however, full general relativity is required. We therefore<br/>extend these initial results to a spherically symmetric self-gravitating body<br/>in 1+1 dimensional general relativity. Finally, since gravitational wave production<br/>requires a fully asymmetric system, we show that our method extends to<br/>multidimensional relativistic situations. To this end, the final chapter presents<br/>results using 2+1 dimensional special relativistic simulations.

Name dc:type.qualificationname

Ph.D.

Level dc:type.qualificationlevel

doctoral

Grantor dc:publisher.institution

University of Southampton

Year dc:date.issued

2010

Author dc:creator

• Millmore, Stephen Timothy

Advisor dc:contributor.advisor

• Hawke, Ian