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We present the implementation and performance of a class of directionallyunsplit Riemann-solver-based hydrodynamic schemes on Graphic Processing Units(GPU). These schemes, including the MUSCL-Hancock method, a variant of theMUSCL-Hancock method, and the corner-transport-upwind method, are embedded intothe adaptive-mesh-refinement (AMR) code GAMER. Furthermore, a hybrid MPI/OpenMPmodel is investigated, which enables the full exploitation of the computingpower in a heterogeneous CPU/GPU cluster and significantly improves the overallperformance. Performance benchmarks are conducted on the Dirac GPU cluster atNERSC/LBNL using up to 32 Tesla C2050 GPUs. A single GPU achieves speed-ups of101(25) and 84(22) for uniform-mesh and AMR simulations, respectively, ascompared with the performance using one(four) CPU core(s), and the excellentperformance persists in multi-GPU tests. In addition, we make a directcomparison between GAMER and the widely-adopted CPU code Athena (Stone et al.2008) in adiabatic hydrodynamic tests and demonstrate that, with the sameaccuracy, GAMER is able to achieve two orders of magnitude performancespeed-up.

Directionally Unsplit Hydrodynamic Schemes with Hybrid MPI/OpenMP/GPU Parallelization in AMR