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.

This paper presents an effort to implement a recently proposed meshless dynamic cloud method [Hong Wang et al. A study of gridless method with dynamic clouds of points for solving unsteady CFD problems in aerodynamics, Int. J. Numer. Meth. Fluids 2010; 64: 98-118] on modern high-performance graphic processing units (GPUs) with the compute unified device architecture (CUDA) programming model. Within the framework of the meshless method, clouds of points used as basic computational stencils are distributed in the whole flow domain. The spatial derivatives of the governing equations are discretised by the moving-least square scheme on every cloud of points. Roe's approximate Riemann solver is adopted to compute the convective flux. A dual-time stepping approach, which iterates in physical and pseudo temporal spaces, is employed to obtain the time-accurate solution. Simulation of steady compressible flows over a fixed aerofoil is firstly carried out to verify the GPU implementation of the method. Then it is extended to compute unsteady flows past oscillatory aerofoils. Numerical outcomes are compared with experimental and/or other reference results to validate the method. Significant performance speedup of more than an order of magnitude is verified by the numerical results. Systematic analysis shows that GPU is more energy efficient than CPU for solving aerodynamic problems. This demonstrates the potential of the proposed method to solve fluid-structure interaction problems.

In this paper, the gridless adaptive method is extended to simulate unsteady flows with moving shocks. In order to capture physical features like moving shocks with local high resolution, a technique of dynamic cloud of points is achieved by adopting clouds refinement and clouds coarsening procedures during the evolution of the unsteady flows. The regions for clouds refinement and clouds coarsening are determined at every time step by an indicator, which is defined as a function of the local pressure gradient. Once the regions of cloud of points to be adjusted are located by the indicator, the clouds refinement is carried out by introducing new points based on the existing structure of cloud of points, and the clouds coarsening procedure is also implemented simultaneously in order to control the size of the points distributed in the whole computational domain. The numerical test cases show that the gridless adaptive method presented can capture moving shocks with high resolution successfully in both inviscid and viscous test cases.