Multiple-Gpu Accelerated High-Order Gas-Kinetic Scheme for Direct Numerical Simulation of Compressible Turbulence

作     者：Wang, Yuhang Cao, Guiyu Pan, Liang 

作者机构：Laboratory of Mathematics and Complex Systems School of Mathematical Sciences Beijing Normal University Beijing China Academy for Advanced Interdisciplinary Studies Southern University of Science and Technology Shenzhen China 

出 版 物：《SSRN》 

年 卷 期：2022年

核心收录：

主　　题：Direct numerical simulation 

摘      要：High-order gas-kinetic scheme (HGKS) has become a workable tool for the direct numerical simulation (DNS) of turbulence. In this paper, to accelerate the computation, HGKS is implemented with the graphical processing unit (GPU) using the compute unified device architecture (CUDA). Due to the limited available memory size, thecomputational scale is constrained by single GPU. To conduct the much large-scale DNS of turbulence, HGKS also be further upgraded with multiple GPUs using message passing interface (MPI) and CUDA architecture. The benchmark cases for compressible turbulence, including Taylor-Green vortex and turbulent channel flows, are presented to assess the numerical performance of HGKS with Nvidia TITAN RTX and Tesla V100 GPUs. For single-GPU computation, compared with the parallel central processing unit (CPU) code running on theIntel Core i7-9700 with open multi-processing (OpenMP) directives, 7x speedup is achieved by TITAN RTX and 16x speedup is achieved by Tesla V100. For multiple-GPU computation, multiple-GPU accelerated HGKS code scales properly with the increasing number of GPU. The computational time of parallel CPU code running on $1024$ Intel Xeon E5-2692 cores with MPI is approximately $3$ times longer than that of GPU code using $8$ Tesla V100 GPUs with MPI and CUDA. Numerical results confirm the excellent performance of multiple-GPUaccelerated HGKS for large-scale DNS of turbulence. Alongside the footprint in reduction of loading and writing pressure of GPU memory, HGKS in GPU is also compiled with FP32 precision to evaluate the effect of number formats precision. Reasonably, compared to the computation with FP64 precision, the efficiency is improved and the memory cost is reduced with FP32 precision. Meanwhile, the differences in accuracy for statistical turbulent quantities appear. For turbulent channel flows, difference in long-time statistical turbulent quantities is acceptable between FP32 and FP64 precision solutions. While the obvious d