An adaptive mesh, GPU-accelerated, and error minimized special relativistic hydrodynamics code

Abstract

We present a new special relativistic hydrodynamics (SRHD) code capable of handling coexisting ultra-relativistically hot and non-relativistically cold gases. We achieve this by designing a new algorithm for conversion between primitive and conserved variables in the SRHD solver, which incorporates a realistic ideal-gas equation of state covering both the relativistic and non-relativistic regimes. The code can handle problems involving a Lorentz factor as high as 106 and optimally avoid the catastrophic cancellation. In addition, we have integrated this new SRHD solver into the code gamer (https://github.com/gamer-project/gamer) to support adaptive mesh refinement and hybrid OpenMP/MPI/GPU parallelization. It achieves a peak performance of 7 × 107 cell updates per second on a single Tesla P100 GPU and scales well to 2048 GPUs. We apply this code to two interesting astrophysical applications: (a) an asymmetric explosion source on the relativistic blast wave and (b) the flow acceleration and limb-brightening of relativistic jets.

Hydrodynamic Simulations of a Relativistic Jet Interacting with the Intracluster Medium: Application to Cygnus A

“…where is the specific thermal energy. Note that although the GAMER code [16] that we use for our simulation runs carries out calculations in units where c = 1, we include the factors of c here for completeness. This set of equations is closed by an equation of state (EOS) h(ρ, p); the EOS that we employ in this work is the Taub-Mathews (TM) EOS [17][18][19], which is an approximation to the Synge model, the exact EOS for an ideal, non-degenerate gas composed of a single particle species [20].…”

“…The use of the TM EOS enables the relativistic and non-relativistic gas phases to be combined in a single, realistic simulation, which cannot be achieved with a standard polytropic EOS with a single value for the ratio of specific heats Γ. For the TM EOS, Γ → 5/3 for a non-relativistic fluid and Γ → 4/3 for a relativistic fluid, and the transition between the phases occurs near k B T ∼ mc 2 (see Figure 1 of [16]).…”

“…To perform our simulation runs we use GAMER [21], an adaptive-mesh refinement (AMR) astrophysical hydrodynamic code which has a module for special relativistic hydrodynamics (SRHD) [16]. Since we are operating in a regime where both relativistic and non-relativistic gases are present in the same simulation, there is the risk of catastrophic cancellation in a number of expressions when evolving the numerical versions of Equations 1-3.…”

“…GAMER avoids these cancellations by evolving the equation for the reduced energy density separately and computing Lorentz factors using the four-velocity U ν rather than the three-velocity v i . For more details about the SRHD solver in GAMER, we refer the reader to Section 2 of [16]. In our simulations, we use the Harten-Lax-van Leer with Contact (HLLC) solver [22] to solve the Riemann problem and employ the Piecewise Parabolic Method (PPM) [23] for state estimation.…”

“…The simulations were run on the Pleiades supercomputer at NASA/Ames Research Center. Software packages used in this work include: GAMER 1 [16,21,28]; AstroPy 2 [29]; Matplotlib 3 [30]; NumPy 4 [31]; yt 5 [32] Conflicts of Interest: The authors declare no conflict of interest.…”