Extremely High-Order Convergence in Simulations of Relativistic Stars

TL;DR

This paper introduces a high-order numerical method for simulating relativistic stars with unprecedented accuracy, using a novel surface-tracking approach that could enhance gravitational waveform predictions for future detectors.

Contribution

The authors develop a 1+1-dimensional high-order convergence method with a novel surface-tracking technique, enabling more precise simulations of relativistic stars without increased computational resources.

Findings

Achieved up to 7th-order convergence in simulations

Numerical errors are six orders of magnitude smaller than standard methods

No fundamental obstacles to higher-order convergence identified

Abstract

We provide a road towards obtaining gravitational waveforms from inspiraling material binaries with an accuracy viable for third-generation gravitational wave detectors, without necessarily advancing computational hardware or massively-parallel software infrastructure. We demonstrate a proof-of-principle 1+1-dimensional numerical implementation that exhibits up to 7th-order convergence for highly dynamic barotropic stars in curved spacetime, and numerical errors up to 6 orders of magnitude smaller than a standard method. Aside from high-order interpolation errors (Runge's phenomenon), there are no obvious fundamental obstacles to obtaining convergence of even higher order. The implementation uses a novel surface-tracking method, where the surface is evolved and high-order accurate boundary conditions are imposed there. Computational memory does not need to be allocated to fluid variables in the vacuum region of spacetime. We anticipate the application of this new method to full $3\! +\! 1$-dimensional simulations of the inspiral phase of compact binary systems with at least one material body. The additional challenge of a deformable surface must be addressed in multiple spatial dimensions, but it is also an opportunity to input more precise surface tension physics.