Interfaces in Numerical Relativistic hydrodynamics

Abstract

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.

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Identifiers

ORCID for Ian Hawke: orcid.org/0000-0003-4805-0309

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