Computational relativistic astrophysics with adaptive mesh refinement: Testbeds

We have carried out numerical simulations of strongly gravitating systems based on the Einstein equations coupled to the relativistic hydrodynamic equations using adaptive mesh refinement (AMR) techniques. We show AMR simulations of NS binary inspiral and coalescence carried out on a workstation having an accuracy equivalent to that of a ${1025}^3$ regular unigrid simulation, which is, to the best of our knowledge, larger than all previous simulations of similar NS systems on supercomputers. We believe the capability opens new possibilities in general relativistic simulations.

Figure 1

HC violation scaled by $(1/dx)$ for runs with different resolutions. Their overlapping with one another implies first order convergence (as the TVD hydro scheme dictates).

Figure 2

Effect of more levels: the addition of one refinement level lowers the HC violation by a factor of $2$ in the region of extra grid level where the HC violation is significant.

Figure 3

The HC violation of the AMR run coincides with that of the unigrid ${321}^3$ run which has a resolution the same as the finest grid of the AMR run.

Figure 4

The lapse of coalescing NSs at 3 different times, with the grid structure superimposed, and with $1$ to $2$ downsampling (showing every other point). Only the inner part of the computational domain is shown.

Figure 5

The AMR (dashed) and unigrid (daggers) simulations give the same results for coalescing NSs: (a) $g_{xx}$ at $t=122.4M_{\odot }$, (b) HC violations vs time.

Figure 6

Maximum HC violations for inspiraling NSs at two different resolutions, showing first order convergence. The maximum of $16\pi \rho$ (dotted line) is given for comparison.

Figure 7

Density for inspiralling NSs is given in grayscale with 4 levels of grid structure (downsampled by a factor of $4$) superimposed. Only the central part of the $(34R{)}^3$ computational domain is shown. (a) $t=288M_{\odot }$, (b) $t=418M_{\odot }$. $418M_{\odot }$ corresponds to 0.6 orbit. The light crossing time for the grid is $310M_{\odot }$.