Multiple-GPU accelerated high-order gas-kinetic scheme for direct numerical simulation of compressible turbulence

High-order gas-kinetic scheme (HGKS) has become a workable tool for the direct numerical simulation (DNS) of turbulence. In this paper, to accelerate computation, HGKS is implemented with graphical processing unit (GPU) using compute unified device architecture (CUDA). To conduct much large-scale DNS turbulence, also be further upgraded multiple GPUs message passing interface (MPI) and CUDA architecture. The benchmark cases compressible including Taylor-Green vortex turbulent channel flows, are presented assess performance Nvidia TITAN RTX Tesla V100 GPUs. For single-GPU compared parallel central (CPU) code running on Intel Core i7-9700 open multi-processing (OpenMP) directives, 7x speedup achieved by 16x V100. multiple-GPU computational time CPU 1024 Xeon E5-2692 cores MPI approximately 3 times longer than that GPU 8 CUDA. Numerical results confirm excellent accelerated in compiled FP32 precision evaluate effect number formats precision. Reasonably, computation FP64 precision, efficiency improved memory cost reduced difference long-time statistical quantities acceptable between solutions. While obvious discrepancy instantaneous can observed, which shows not safe choice should depended requirement accuracy available resources.