Adaptive mesh refinement approach to construction of initial data for black hole collisions

TL;DR

This paper introduces an adaptive mesh refinement method using a fully threaded tree to efficiently generate initial data for black hole collision simulations, significantly reducing computational resources needed.

Contribution

It presents a novel second-order accurate adaptive mesh refinement technique with a fully threaded tree for initial data construction in black hole collision models.

Findings

Convergence of solutions with increased resolution

Reduction in memory and computation time by several orders of magnitude

Feasibility of high-resolution Cartesian mesh simulations for black hole collisions

Abstract

The initial data for black hole collisions is constructed using a conformal-imaging approach and a new adaptive mesh refinement technique, a fully threaded tree (FTT). We developed a second-order accurate approach to the solution of the constraint equations on a non-uniformly refined high resolution Cartesian mesh including second-order accurate treatment of boundary conditions at the black hole throats. Results of test computations show convergence of the solution as the numerical resolution is increased. FTT-based mesh refinement reduces the required memory and computer time by several orders of magnitude compared to a uniform grid. This opens up the possibility of using Cartesian meshes for very high resolution simulations of black hole collisions.