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Register a new userAn adaptive mesh, GPU-accelerated, and error minimized special relativistic hydrodynamics code
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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 $10^6$ 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 $7times 10^{7}$ 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.
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We present the newly developed code, GAMER (GPU-accelerated Adaptive MEsh Refinement code), which has adopted a novel approach to improve the performance of adaptive mesh refinement (AMR) astrophysical simulations by a large factor with the use of the graphic processing unit (GPU). The AMR implementation is based on a hierarchy of grid patches with an oct-tree data structure. We adopt a three-dimensional relaxing TVD scheme for the hydrodynamic solver, and a multi-level relaxation scheme for the Poisson solver. Both solvers have been implemented in GPU, by which hundreds of patches can be advanced in parallel. The computational overhead associated with the data transfer between CPU and GPU is carefully reduced by utilizing the capability of asynchronous memory copies in GPU, and the computing time of the ghost-zone values for each patch is made to diminish by overlapping it with the GPU computations. We demonstrate the accuracy of the code by performing several standard test problems in astrophysics. GAMER is a parallel code that can be run in a multi-GPU cluster system. We measure the performance of the code by performing purely-baryonic cosmological simulations in different hardware implementations, in which detailed timing analyses provide comparison between the computations with and without GPU(s) acceleration. Maximum speed-up factors of 12.19 and 10.47 are demonstrated using 1 GPU with 4096^3 effective resolution and 16 GPUs with 8192^3 effective resolution, respectively.
We present GAMER-2, a GPU-accelerated adaptive mesh refinement (AMR) code for astrophysics. It provides a rich set of features, including adaptive time-stepping, several hydrodynamic schemes, magnetohydrodynamics, self-gravity, particles, star formation, chemistry and radiative processes with GRACKLE, data analysis with yt, and memory pool for efficient object allocation. GAMER-2 is fully bitwise reproducible. For the performance optimization, it adopts hybrid OpenMP/MPI/GPU parallelization and utilizes overlapping CPU computation, GPU computation, and CPU-GPU communication. Load balancing is achieved using a Hilbert space-filling curve on a level-by-level basis without the need to duplicate the entire AMR hierarchy on each MPI process. To provide convincing demonstrations of the accuracy and performance of GAMER-2, we directly compare with Enzo on isolated disk galaxy simulations and with FLASH on galaxy cluster merger simulations. We show that the physical results obtained by different codes are in very good agreement, and GAMER-2 outperforms Enzo and FLASH by nearly one and two orders of magnitude, respectively, on the Blue Waters supercomputers using $1-256$ nodes. More importantly, GAMER-2 exhibits similar or even better parallel scalability compared to the other two codes. We also demonstrate good weak and strong scaling using up to 4096 GPUs and 65,536 CPU cores, and achieve a uniform resolution as high as $10{,}240^3$ cells. Furthermore, GAMER-2 can be adopted as an AMR+GPUs framework and has been extensively used for the wave dark matter ($psi$DM) simulations. GAMER-2 is open source (available at https://github.com/gamer-project/gamer) and new contributions are welcome.
General-relativistic magnetohydrodynamic (GRMHD) simulations have revolutionized our understanding of black-hole accretion. Here, we present a GPU-accelerated GRMHD code H-AMR with multi-faceted optimizations that, collectively, accelerate computation by 2-5 orders of magnitude for a wide range of applications. Firstly, it involves a novel implementation of a spherical-polar grid with 3D adaptive mesh refinement that operates in each of the 3 dimensions independently. This allows us to circumvent the Courant condition near the polar singularity, which otherwise cripples high-res computational performance. Secondly, we demonstrate that local adaptive time-stepping (LAT) on a logarithmic spherical-polar grid accelerates computation by a factor of $lesssim10$ compared to traditional hierarchical time-stepping approaches. Jointly, these unique features lead to an effective speed of $sim10^9$ zone-cycles-per-second-per-node on 5,400 NVIDIA V100 GPUs (i.e., 900 nodes of the OLCF Summit supercomputer). We demonstrate its computational performance by presenting the first GRMHD simulation of a tilted thin accretion disk threaded by a toroidal magnetic field around a rapidly spinning black hole. With an effective resolution of $13$,$440times4$,$608times8$,$092$ cells, and a total of $lesssim22$ billion cells and $sim0.65times10^8$ timesteps, it is among the largest astrophysical simulations ever performed. We find that frame-dragging by the black hole tears up the disk into two independently precessing sub-disks. The innermost sub-disk rotation axis intermittently aligns with the black hole spin, demonstrating for the first time that such long-sought alignment is possible in the absence of large-scale poloidal magnetic fields.
This paper develops entropy stable (ES) adaptive moving mesh schemes for the 2D and 3D special relativistic hydrodynamic (RHD) equations. They are built on the ES finite volume approximation of the RHD equations in curvilinear coordinates, the discrete geometric conservation laws, and the mesh adaptation implemented by iteratively solving the Euler-Lagrange equations of the mesh adaption functional in the computational domain with suitably chosen monitor functions. First, a sufficient condition is proved for the two-point entropy conservative (EC) flux, by mimicking the derivation of the continuous entropy identity in curvilinear coordinates and using the discrete geometric conservation laws given by the conservative metrics method. Based on such sufficient condition, the EC fluxes for the RHD equations in curvilinear coordinates are derived and the second-order accurate semi-discrete EC schemes are developed to satisfy the entropy identity for the given convex entropy pair. Next, the semi-discrete ES schemes satisfying the entropy inequality are proposed by adding a suitable dissipation term to the EC scheme and utilizing linear reconstruction with the minmod limiter in the scaled entropy variables in order to suppress the numerical oscillations of the above EC scheme. Then, the semi-discrete ES schemes are integrated in time by using the second-order strong stability preserving explicit Runge-Kutta schemes. Finally, several numerical results show that our 2D and 3D ES adaptive moving mesh schemes effectively capture the localized structures, such as sharp transitions or discontinuities, and are more efficient than their counterparts on uniform mesh.
We report on the development of Mezcal-SRHD, a new adaptive mesh refinement, special relativistic hydrodynamics (SRHD) code, developed with the aim of studying the highly relativistic flows in Gamma-Ray Burst sources. The SRHD equations are solved using finite volume conservative solvers. The correct implementation of the algorithms is verified by one-dimensional (1D) shock tube and multidimensional tests. The code is then applied to study the propagation of 1D spherical impulsive blast waves expanding in a stratified medium with $rho propto r^{-k}$, bridging between the relativistic and Newtonian phases, as well as to a two-dimensional (2D) cylindrically symmetric impulsive jet propagating in a constant density medium. It is shown that the deceleration to non-relativistic speeds in one-dimension occurs on scales significantly larger than the Sedov length. This transition is further delayed with respect to the Sedov length as the degree of stratification of the ambient medium is increased. This result, together with the scaling of position, Lorentz factor and the shock velocity as a function of time and shock radius, is explained here using a simple analytical model based on energy conservation. The method used for calculating the afterglow radiation by post-processing the results of the simulations is described in detail. The light curves computed using the results of 1D numerical simulations during the relativistic stage correctly reproduce those calculated assuming the self-similar Blandford-McKee solution for the evolution of the flow. The jet dynamics from our 2D simulations and the resulting afterglow lightcurves, including the jet break, are in good agreement with those presented in previous works. Finally, we show how the details of the dynamics critically depend on properly resolving the structure of the relativistic flow.
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