GPU Implementation and Optimization of a High-Order Spectral Difference Method for Aeroacoustic Problems

This study focuses on the implementation of the spectral difference (SD) method on hexahedral elements to NVIDIA graphics processing units (GPUs) using the Compute Unified Device Architecture (CUDA) for aeroacoustic problems. Three problems were addressed in the implementation of this study: thread parallelism strategy optimization within the GPU, data access patterns management, and multi-GPU parallelization implementation. Computational speed testing showed that the three factors significantly affect the efficiency of the code on the GPU. The implemented GPU solver was validated using an inviscid problem and a viscous problem. The numerical results show that the GPU solver achieves the same level of accuracy as the CPU program, with remarkable speed improvements. Specifically, compared with a single CPU core with a turbo boost frequency of 3.2 GHz (Intel Xeon Silver 4210), the inviscid case tested on an RTX 2070 Super GPU achieved acceleration of 122.4x, and the viscous case conducted on an RTX 3090 GPU achieved acceleration of 229.7x. Additionally, the GPU solver exhibits a parallel efficiency exceeding 93% when performing parallel computing on a platform with multiple RTX 3090 GPU cards. Furthermore, the GPU-accelerated computational aeroacoustics solver was applied to compute the noise from a low-speed propeller. The computed results were compared with experimental data, and the excellent agreement demonstrated the effectiveness and feasibility of the GPU implementation of the SD solver.