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SummaryAn OpenACC directive‐based graphics processing unit (GPU) parallel scheme is presented for solving the compressible Navier–Stokes equations on 3D hybrid unstructured grids with a third‐order reconstructed discontinuous Galerkin method. The developed scheme requires the minimum code intrusion and algorithm alteration for upgrading a legacy solver with the GPU computing capability at very little extra effort in programming, which leads to a unified and portable code development strategy. A face coloring algorithm is adopted to eliminate the memory contention because of the threading of internal and boundary face integrals. A number of flow problems are presented to verify the implementation of the developed scheme. Timing measurements were obtained by running the resulting GPU code on one Nvidia Tesla K20c GPU card (Nvidia Corporation, Santa Clara, CA, USA) and compared with those obtained by running the equivalent Message Passing Interface (MPI) parallel CPU code on a compute node (consisting of two AMD Opteron 6128 eight‐core CPUs (Advanced Micro Devices, Inc., Sunnyvale, CA, USA)). Speedup factors of up to 24× and 1.6× for the GPU code were achieved with respect to one and 16 CPU cores, respectively. The numerical results indicate that this OpenACC‐based parallel scheme is an effective and extensible approach to port unstructured high‐order CFD solvers to GPU computing. Copyright © 2015 John Wiley & Sons, Ltd.

A GPU-accelerated discontinuous Galerkin (DG) method is presented for the solution of compressible flows on 3-D unstructured grids. The present work has employed two of the most attractive features in a new programming standard of parallel computing -OpenACC: 1) multi-platform/compiler support and 2) descriptive directive interface to upgrade a legacy CFD solver with the capacity of GPU computing, without significant extra cost in recoding, resulting in a highly portable and extensible GPU-accelerated code. In addition, a face renumbering/grouping scheme is proposed to overcome the "race condition" in facebased flux calculations that occurs on GPU vectorization. Performance of the developed double-precision solver is assessed for both simple and complex geometries. Speedup factors up to but not limited to 24× and 1.6× were achieved by comparing the measured computing time of the OpenACC program running on an NVIDIA Tesla K20c GPU to that of the equivalent MPI program running on one single core and full sixteen cores of an AMD Opteron-6128 CPU respectively, indicating a great potential to port more features of the underlying DG solver into the OpenACC framework.

New entropy stable spectral collocations schemes of arbitrary order of accuracy are developed for the unsteady 3-D Euler and Navier-Stokes equations on dynamic unstructured grids. To take into account the grid motion and deformation, we use an arbitrary Lagrangian-Eulerian (ALE) formulation. As a result, moving and deforming hexahedral grid elements are individually mapped onto a cube in the fixed reference system of coordinates. The proposed scheme is constructed by using the skew-symmetric form of the Navier-Stokes equations, which are discretized by using summation-by-parts spectral collocation operators that preserve the conservation properties of the original governing equations. Furthermore, the metric coefficients are approximated such that the geometric conservation laws (GCL) are satisfied exactly on both static and dynamic grids. To make the scheme entropy stable, a new entropy conservative flux is derived for the 3-D Euler and Navier-Stokes equations on dynamic unstructured grids. The new flux preserves the design order of accuracy of the original spectral collocation scheme and guarantees the entropy conservation on moving and deforming grids. We present numerical results demonstrating design order of accuracy and freestream preservation properties of the new schemes for both the Euler and Navier-Stokes equations on moving and deforming unstructured grids.