This paper presents a novel GPU-parallelized meshless method for solving Reynolds-averaged Navier–Stokes equations with the Spalart–Allmaras turbulence model. Least-square curve fit is utilized to discretize the spatial derivatives of the equations, and a Roe-type upwind scheme is used for computing the flux terms. The compute unified device architecture (CUDA) Fortran programming model is employed to port the meshless method from CPU to GPU in a way of achieving efficiency. For the extracted GPU parallel tasks, a particular two-dimensional thread hierarchy is designed to construct the corresponding computational kernels. Then, a modified strategy, multi-layered point reordering, and a proposed strategy, shared memory access tuning, are used to manage the GPU memory access. A series of typical two- and three-dimensional test cases, including transonic flows over an aerofoil, a wing or a CRM wing-body combination, were carried out to verify the developed method. The computed results agreed well with experimental data and other numerical solutions reported in literature. Impressive speedups, over 40$\times$ and up to 79$\times$ with respect to a single threaded CPU implementation, are successfully achieved for the benchmark tests.

本文提出了一种新颖的GPU并行无网格方法，该方法可利用Spalart-Allmaras湍流模型求解雷诺平均Navier-Stokes方程。利用最小二乘曲线拟合来离散方程的空间导数，并使用Roe型逆风方案来计算通量项。采用计算统一设备架构（CUDA）Fortran编程模型将无网格方法从CPU移植到GPU，以实现效率。对于提取的GPU并行任务，设计了特定的二维线程层次结构来构造相应的计算内核。然后，使用修改后的策略（多层点重新排序）和建议的策略（共享内存访问调整）来管理GPU内存访问。一系列典型的二维和三维测试用例，包括跨翼型，机翼或CRM机体组合的跨音速流进行了验证。计算结果与文献报道的实验数据和其他数值解非常吻合。令人印象深刻的加速，超过40$\times$ 高达79$\times$ 关于单线程CPU实施，已成功完成基准测试。