Lessons for adaptive mesh refinement in numerical relativity

Abstract

We demonstrate the flexibility and utility of the Berger-Rigoutsos Adaptive Mesh Refinement (AMR) algorithm used in the open-source numerical relativity code GRChombo for generating gravitational waveforms from binary black-hole inspirals, and for studying other problems involving non-trivial matter configurations. We show that GRChombo can produce high quality binary black-hole waveforms through a code comparison with the established numerical relativity code \lean. We also discuss some of the technical challenges involved in making use of full AMR (as opposed to, e.g. moving box mesh refinement), including the numerical effects caused by using various refinement criteria when regridding. We suggest several ``rules of thumb'' for when to use different tagging criteria for simulating a variety of physical phenomena. We demonstrate the use of these different criteria through example evolutions of a scalar field theory. Finally, we also review the current status and general capabilities of GRChombo.

Radiation from global topological strings using adaptive mesh refinement: Methodology and massless modes

“…The evolution scheme is fourth-order Runge-Kutta, with fourth-order spatial discretisation. Further specific details about the AMR implementation and wave extraction are discussed in [24]. Production simulations with AMR are carried out using a coarse simulation box size of 256 × 256 × 32 or 256 × 256 × 16 (N 1 × N 2 × N 3 ), with periodic boundary conditions in the z-direction and Sommerfeld (outgoing radiation) boundary conditions in the x-and y-directions.…”

“…This is often added to numerical simulations to ensure stability by damping high frequency modes that can be generated when using finite difference methods [25]. GRChombo uses Kreiss-Oliger damping, defined by adding the following term to the right side of the evolution equations: where F is the relevant evolution variable, i is the index for the grid point and σ is the damping parameter set by the user [24]. The parameter σ must satisfy…”

Black hole merger simulations in wave dark matter environments

“…In the former class, the energy density of the cloud reaches the boundary of our simulated domain, allowing for continued accretion from spatial infinity. (This is imposed using extrapolating boundary conditions as described in [161].) Within this class we study:…”

“…In the second class of initial conditions, the scalar cloud has a sufficiently large radius to cover the BBH, but the energy density goes to zero at the boundaries, reproducing an isolated cloud which has exhausted its dark matter reservoir. (For these cases we use Sommerfeld radiative boundary conditions as described in [161].) Here we study two cases:…”

“…For this we use the CCZ4 formalism [182] with the moving puncture gauge [163,[183][184][185][186]. In both cases we use the open-source numerical relativity code GRCHOMBO [187,188] with adaptive mesh refinement [161].…”