11.6 Finite-difference multi-block orbiting binary black-hole simulations

In [325Jump To The Next Citation Point] orbiting binary black-hole simulations using a high-order FD multi-domain approach were presented. The basic layout of the full domain used is shown in Figures 15View Image and 16View Image, where the centers of the excised black-hole spheres are located along the x axis at x = ±a. The computational domain is based on two types of building blocks, shown in Figure 17View Image, which are essentially variations of cubed spheres. In the simulations of [325] the optimized D8 −4 difference operator described in Section 8.3 was used, the patches were communicated using the penalty technique (see Section 10), and the resulting equations were evolved in time using an embedded fourth- and fifth-order Runge–Kutta stepper (see Section 7.5). The formulations of the equations used, boundary conditions and dual frame technique are exactly those of the spectral evolutions discussed above, only the numerical and domain decomposition approaches differ, which follow building work from [281, 141, 385, 145, 324]. Strong and weak scaling is observed up to at least several thousand processors.
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Figure 15: Equatorial cut of the computational domain used in multi-block simulations of orbiting black-hole binaries (left). Schematic figure showing the direction considered as radial (red arrows) for the cuboidal blocks (right). Reprinted with permission from [326]; copyright by APS.
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Figure 16: Multi-block domain decomposition for a binary black-hole simulation. Reprinted with permission from [326]; copyright by APS.
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Figure 17: Equatorial cross-section of varations of cubed sphere patches. Reprinted with permission from [326]; copyright by APS.

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