Summary
Here, we report our current effort to apply adaptive mesh refinement techniques to the simulations of black hole spacetimes and gravitational waves. We solve Einstein’s equations written in the first-order in time and second-order in space form. We demonstrate that using quadratic-order guardcell filling along with “refluxing” of first order derivatives of the variables as interface conditions at the refinement jumps are essential for accurate evolutions of gravitational waves. Some preliminary results for the head-on collisions of binary black holes are also given.
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References
C. Misner, K. Thorne, and J. Wheeler, Gravitation (W. H. Freeman, New York, 1973)
M. Shibata and T. Nakamura, Evolution of three-dimensional gravitational waves: Harmonic slicing case, Phys. Rev. D52, 5428 (1995).
T. Baumgarte and S. Shapiro, Numerical integration of Einstein’s field equations, Phys. Rev. D59, 024007 (1998).
S. Teukolsky, On the stability of the iterated Crank-Nicholson method in numerical relativity, Phys. Rev. D61, 087501 (2000).
P. MacNeice, K. Olson, C. Mobarry, R. de Fainchtein, and C. Packer, PARAMESH: A parallel adaptive mesh refinement community toolkit, Computer Physics Comm. 126, 330 (2000).
D. DeZeeuw and K. Powell, An Adaptively Refined Cartesian Mesh Solver for the Euler Equations, J. Computat. Phys. 104, 56 (1993).
D. Choi, D. Brown et al, Interface Conditions for Wave Propagation Through Mesh Refinement Boundaries. To appear in Journal of Computational Physics (2003).
K. New, D. Choi et al, Three-dimensional adaptive evolution of gravitational waves in numerical relativity. Phys. Rev. D62 084039 (2000).
S. Teukolsky, Linearized quadrupole waves in general relativity and the motion of test particles Equation using Adaptive Mesh Refinement, Phys. Rev. D26, 745 (1982).
S. Brandt and B. Brügmann, Phys. Rev. Lett. 78, 3606 (1999).
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© 2005 Springer-Verlag Berlin Heidelberg
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Choi, DI.D. (2005). Mesh Refinement Calculations of Gravitational Waves and Black Holes in 3-Dimensions. In: Plewa, T., Linde, T., Gregory Weirs, V. (eds) Adaptive Mesh Refinement - Theory and Applications. Lecture Notes in Computational Science and Engineering, vol 41. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-27039-6_34
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DOI: https://doi.org/10.1007/3-540-27039-6_34
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-21147-1
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