Interfaces in numerical relativistic hydrodynamics

• Main Author: Millmore, Stephen Timothy
• Other Authors: Hawke, Ian
• Published: University of Southampton 2010
• Subjects: 518; QA Mathematics
• Online Access: https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.525694

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