Adaptive mesh refinement approach to construction of initial data 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.

13 pages, 11 figures

References in corpus (1)

• Initial data for superposed rotating black holes

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