Adaptive mesh refinement approach to construction of initial data for black hole collisions
arXiv:gr-qc/9905079 · doi:10.1088/0264-9381/17/2/312
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
Cited by in corpus (18)
- Evolutions in 3D numerical relativity using fixed mesh refinement
- A single-domain spectral method for black hole puncture data
- A 3+1 perspective on null hypersurfaces and isolated horizons
- Numerical simulation of orbiting black holes
- Numerical Relativity: A review
- Binary black holes in circular orbits. II. Numerical methods and first results
- Binary black holes in circular orbits. I. A global spacetime approach
- Evolving a puncture black hole with fixed mesh refinement
- A double-domain spectral method for black hole excision data
- Adaptive Mesh Refinement for Coupled Elliptic-Hyperbolic Systems
- Multigrid elliptic equation solver with adaptive mesh refinement
- Generic Tracking of Multiple Apparent Horizons with Level Flow
- Numerical Relativity and Inhomogeneous Cosmologies
- Three-dimensional adaptive evolution of gravitational waves in numerical relativity
- Computational Relativistic Astrophysics With Adaptive Mesh Refinement: Testbeds
- The Nonlinear Sigma Model With Distributed Adaptive Mesh Refinement
- The initial value problem in numerical relativity
- Local and global properties of conformally flat initial data for black hole collisions