Numerical simulations of interfaces in relativistic hydrodynamics

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.

Discontinuous Galerkin methods for general-relativistic hydrodynamics: Formulation and application to spherically symmetric spacetimes

“…[59][60][61]). The most commonly used approach to treat vacuum regions is to fill them with a low-density fluid, such that if a fluid element is evolved to have a rest-mass density below a certain threshold, it is set to have a floor value and zero coordinate velocity [62,63].…”

The nonlinear development of the relativistic two-stream instability

“…The main technical barrier to incorporating these effects in current simulations is the lack of either a balance law form or a non-conservative form that explicitly controls entropy at discontinuities. Our future work is aimed at overcoming this technical hurdle before combining the multifluid effects with nonlinear relativistic elasticity [17] and appropriate numerical techniques for interfaces [18] to produce such simulations.…”

Revisiting spherically symmetric relativistic hydrodynamics

“…Notice that the term that goes as ∼ p/r is singular at r = 0. However in order to regularize the equations there, it is possible to split the flux balance form of the equations by appropriately splitting the flux vector and avoid the presence of such singular term [8,9]:…”