Numerical simulations of interfaces in relativistic hydrodynamics

TL;DR

This paper develops and tests numerical methods for simulating sharp interfaces in relativistic hydrodynamics, relevant for neutron stars and phase transitions, demonstrating the effectiveness of level set techniques.

Contribution

It introduces and validates level set-based numerical techniques for stable evolution and interaction of interfaces in relativistic hydrodynamics.

Findings

Level set methods extend well to relativistic hydrodynamics.

Techniques allow stable interface evolution and merging.

Effective in special and general relativity contexts.

Abstract

We consider models of relativistic matter containing sharp interfaces across which the matter model changes. These models will be relevant for neutron stars with crusts, phase transitions, or for viscous boundaries where the length scale is too short to be modelled smoothly. In particular we look at numerical techniques that allow us to evolve stable interfaces, for the interfaces to merge, and for strong waves and shocks to interact with the interfaces. We test these techniques for ideal hydrodynamics in special and general relativity for simple equations of state, finding that simple level set-based methods extend well to relativistic hydrodynamics.