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The treatment of radiative transfer with multiple radiation sources is a critical challenge in simulations of star formation and the interstellar medium. In this paper we present the novel TreeRay method for solving general radiative transfer problems, based on reverse ray tracing combined with tree-based accelerated integration. We implement TreeRay in the adaptive mesh refinement code FLASH, as a module of the tree solver developed by Wunsch et al. However, the method itself is independent of the host code and can be implemented in any grid based or particle based hydrodynamics code. A key advantage of TreeRay is that its computational cost is independent of the number of sources, making it suitable for simulations with many point sources (e.g. massive star clusters) as well as simulations where diffuse emission is important. A very efficient communication and tree-walk strategy enables TreeRay to achieve almost ideal parallel scalings. TreeRay can easily be extended with sub-modules to treat radiative transfer at different wavelengths and to implement related physical processes. Here, we focus on ionising (EUV) radiation and use the On-the-Spot approximation to test the method and its parameters. The ability to set the tree solver time step independently enables the speedy calculation of radiative transfer in a multi-phase interstellar medium, where the hydrodynamic time step is typically limited by the sound speed of the hot gas produced in stellar wind bubbles or supernova remnants. We show that complicated simulations of star clusters with feedback from multiple massive stars become feasible with TreeRay.
This paper describes the open-source code Enzo, which uses block-structured adaptive mesh refinement to provide high spatial and temporal resolution for modeling astrophysical fluid flows. The code is Cartesian, can be run in 1, 2, and 3 dimensions, and supports a wide variety of physics including hydrodynamics, ideal and non-ideal magnetohydrodynamics, N-body dynamics (and, more broadly, self-gravity of fluids and particles), primordial gas chemistry, optically-thin radiative cooling of primordial and metal-enriched plasmas (as well as some optically-thick cooling models), radiation transport, cosmological expansion, and models for star formation and feedback in a cosmological context. In addition to explaining the algorithms implemented, we present solutions for a wide range of test problems, demonstrate the codes parallel performance, and discuss the Enzo collaborations code development methodology.
The design and implementation of a new framework for adaptive mesh refinement (AMR) calculations is described. It is intended primarily for applications in astrophysical fluid dynamics, but its flexible and modular design enables its use for a wide variety of physics. The framework works with both uniform and nonuniform grids in Cartesian and curvilinear coordinate systems. It adopts a dynamic execution model based on a simple design called a task list that improves parallel performance by overlapping communication and computation, simplifies the inclusion of a diverse range of physics, and even enables multiphysics models involving different physics in different regions of the calculation. We describe physics modules implemented in this framework for both non-relativistic and relativistic magnetohydrodynamics (MHD). These modules adopt mature and robust algorithms originally developed for the Athena MHD code and incorporate new extensions: support for curvilinear coordinates, higher-order time integrators, more realistic physics such as a general equation of state, and diffusion terms that can be integrated with super-time-stepping algorithms. The modules show excellent performance and scaling, with well over 80% parallel efficiency on over half a million threads. The source code has been made publicly available.
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 have developed a simulation code with the techniques which enhance both spatial and time resolution of the PM method for which the spatial resolution is restricted by the spacing of structured mesh. The adaptive mesh refinement (AMR) technique subdivides the cells which satisfy the refinement criterion recursively. The hierarchical meshes are maintained by the special data structure and are modified in accordance with the change of particle distribution. In general, as the resolution of the simulation increases, its time step must be shortened and more computational time is required to complete the simulation. Since the AMR enhances the spatial resolution locally, we reduce the time step locally also, instead of shortening it globally. For this purpose we used a technique of hierarchical time steps (HTS) which changes the time step, from particle to particle, depending on the size of the cell in which particles reside. Some test calculations show that our implementation of AMR and HTS is successful. We have performed cosmological simulation runs based on our code and found that many of halo objects have density profiles which are well fitted to the universal profile proposed by Navarro, Frenk, & White (1996) over the entire range of their radius.
Aims. The importance of radiation to the physical structure of protoplanetary disks cannot be understated. However, protoplanetary disks evolve with time, and so to understand disk evolution and by association, disk structure, one should solve the combined and time-dependent equations of radiation hydrodynamics. Methods. We implement a new implicit radiation solver in the AZEuS adaptive mesh refinement magnetohydrodynamics fluid code. Based on a hybrid approach that combines frequency-dependent ray-tracing for stellar irradiation with non-equilibrium flux limited diffusion, we solve the equations of radiation hydrodynamics while preserving the directionality of the stellar irradiation. The implementation permits simulations in Cartesian, cylindrical, and spherical coordinates, on both uniform and adaptive grids. Results. We present several hydrostatic and hydrodynamic radiation tests which validate our implementation on uniform and adaptive grids as appropriate, including benchmarks specifically designed for protoplanetary disks. Our results demonstrate that the combination of a hybrid radiation algorithm with AZEuS is an effective tool for radiation hydrodynamics studies, and produces results which are competitive with other astrophysical radiation hydrodynamics codes.