GPU computing of compressible flow problems by a meshless method with space-filling curves

A graphic processing unit (GPU) implementation of a meshless method for solving compressible flow problems is presented in this paper. Least-square fit is used to discretise the spatial derivatives of Euler equations and an upwind scheme is applied to estimate the flux terms. The compute unified device architecture (CUDA) C programming model is employed to efficiently and flexibly port the meshless solver from CPU to GPU. Considering the data locality of randomly distributed points, space-filling curves are adopted to re-number the points in order to improve the memory performance. Detailed evaluations are firstly carried out to assess the accuracy and conservation property of the underlying numerical method. Then the GPU accelerated flow solver is used to solve external steady flows over aerodynamic configurations. Representative results are validated through extensive comparisons with the experimental, finite volume or other available reference solutions. Performance analysis reveals that the running time cost of simulations is significantly reduced while impressive (more than an order of magnitude) speedups are achieved.