卢志伟, 张皓茹, 万筠钱,等.基于矢通量分裂的绕后台阶流场并行计算及优化[J].河南理工大学学报（自然科学版）,2026,45(3):69-76.

LU Z W, ZHANG H R, WAN Y Q, et al.GPU parallel computing and optimization of backward-facing step flow field based on flux vector splitting[J].Journal of Henan Polytechnic University(Natural Science) ,2026,45(3):69-76.

基于矢通量分裂的绕后台阶流场并行计算及优化

卢志伟, 张皓茹, 万筠钱, 王亚东, 张卓凯, 刘锡尧, 张君安

西安工业大学 机电工程学院，陕西 西安 710032

摘要:目的 为深入挖掘矢通量分裂方法在提升计算效率方面的优势，设计一种基于该方法的GPU （graphics processing unit，GPU）并行算法。  方法 该算法充分利用GPU的强大并行处理能力，对矢通量分裂方法的各个步骤进行并行化处理。通过并行规约优化最值求解过程，结合绕后台阶的物理模型，采用有限差分对二维可压缩N-S方程进行离散和数值求解。为验证算法的准确性和有效性，将其计算结果与经典数值计算方法MacCormack的结果进行对比分析并探究其流场特性。  结果 结果表明：在网格数量相同的情况下，矢通量分裂方法和MacCormack方法计算结果呈一致的趋势，表明矢通量分裂方法和MacCormack方法均可准确模拟流场结果；矢通量分裂数值计算方法的加速比在网格数为128×128时达到8.72，MacCormack方法加速比为5.51，随着网格数量增加，矢通量分裂方法相较于MacCormack方法在加速比方面的优势变得更加显著，这表明矢通量分裂方法在处理大规模计算任务时具有更高的效率和更好的扩展性，能够更高效地将计算任务分配到多个CUDA核心上，充分利用GPU的大规模并行处理能力。  结论 本研究不仅验证了矢通量分裂格式在高性能计算中的优越性，还为未来基于GPU的科学计算提供了重要的算法选择依据，展示了如何利用现代硬件架构提高复杂流体力学问题的求解速度，这对于需要快速、精确模拟的应用场合具有重要意义。

关键词:矢通量分裂;并行计算;复杂流场;数值模拟;性能优化

doi:10.16186/j.cnki.1673-9787.2024120025

基金项目:国家自然科学基金资助项目（52301101）；陕西省“两链”融合重点专项（2025ZG-JBGS-007）；西安市科技计划项目（25GXKJRC00025）

收稿日期:2024/12/11

修回日期:2025/06/23

出版日期:2026/04/28

GPU parallel computing and optimization of backward-facing step flow field based on flux vector splitting

Lu Zhiwei, Zhang Haoru, Wan Yunqian, Wang Yadong, Zhang Zhuokai, Liu Xiyao, Zhang Jun’an

School of Mechatronic Engineering， Xi’an Technological University， Xi’an 710032， Shaanxi， China

Abstract: Objectives To further explore the advantages of the flux vector splitting method in improving computational efficiency，a GPU （graphics processing unit） parallel algorithm based on this method was designed.  Methods The algorithm fully utilized the powerful parallel processing capabilities of the GPU to parallelize each step of the flux vector splitting method.The process of finding the maximum and minimum values was optimized through parallel reduction. Combined with the physical model of a backward-facing step，the two-dimensional compressible Navier-Stokes equations were discretized and numerically solved using the finite difference method. To verify the accuracy and effectiveness of the algorithm， its calculation results were compared with the classic numerical calculation method，MacCormack，and the flow field characteristics were explored.  Results The results showed that under the condition of the same number of grids，the calculation results obtained by the flux vector splitting method and the MacCormack method exhibited a consistent trend，indicating that both methods could accurately simulate the flow field. The speedup ratio of the flux vector splitting  method reached 8.72 when the grid number was 128×128，while that of MacCormack method was 5.51. As the grid number increased，the advantage of the flux vector splitting method in terms of speedup ratio over the MacCormack method became more significant， indicating that the flux vector splitting method exhibits higher efficiency and better scalability when handling large-scale computing tasks，allowing computing tasks to  be allocated more efficiently to multiple CUDA cores and fully utilizing the large-scale parallel processing capabilities of the GPU.  Conclusions This study not only verified the superiority of the flux vector splitting scheme in high-performance computing but also provided an important basis for algorithm selection for future GPU-based scientific computing. It also demonstrated how to use modern hardware architectures to improve the solution speed of complex fluid mechanics problems，which is of great significance for applications requiring rapid and accurate simulations.

Key words:flux vector splitting;parallel computing;complex flow field;numerical simulation;performance optimization