A novel GPU-parallelized meshless method for solving compressible turbulent flows

Abstract

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× and up to 79× with respect to a single threaded CPU implementation, are successfully achieved for the benchmark tests.