Research On GPU-Accelerated Numerical Methods And Their Applications For Three-Dimensional Complex Flows

Nowadays,a novel Graphics Processing Unit(GPU)computing technology has been receiving more and more attentions in both academic researches and engineering applications due to its excellent performances of floating-point operations and memory bandwidth.The use of GPU to develop powerful parallel software packages becomes one of the hot topics in modern Computational Fluid Dynamics(CFD)researches.Sticking to this trend,the present work is mainly focused on the development of GPU-parallelized CFD methods for solving the Euler/Navier-Stokes equations in order to accelerate the simulations of three-dimensional complex flows.Firstly,based on the cell vertex scheme and four stage Runge-Kutta iteration scheme,a GPU-parallelized explicit finite volume method(GEFVM)is investigated for solving the Euler/Navier-Stokes equations.Compute unified device architecture(CUDA)is employed to develop the GEFVM code in a way of achieving efficiency,which involves three steps of works including the division of parallel tasks,the implementation of GPU parallel threads and kernel subroutines and the management of data storage structure.The GPU parallel tasks are technically divided in the first step according to the related calculation processes of the time marching procedure and then classified into three types based on their computing locations.Then the corresponding GPU parallel threads and kernel subroutines are carefully constructed in the second step to meet the computation scales of these tasks.The related storage structure of the computing data is also manipulated technically in the last step to meet with the GPU's consolidated memory access pattern.Based on above works,the GEFVM code is developed and then tested with a set of typical flows over airfoils and winds.Numerical results reveal that as expected,significant GPU speedups(8× to 46× times)are achieved by GEFVM.Secondly,the investigation of a GPU-parallelized implicit finite volume method(GIFVM)is carried out for achieving higher computational efficiency.The biggest challenge is to solve the sharp contradiction between the inherent data dependency of implicit methods and the required data independency of GPU computations.Concerning this issue,a multi-color point grouping strategy is proposed in the present work.Every couple of neighbor points are painted with different colors to make sure that the implicit calculations of the points from the same color group are independed with each other.Based on the multi-color point grouping strategy,the standard LU-SGS implicit scheme is successfully modified into a GPU-parallelizable form.The resulting GIFVM code is verified and evaluated with a set of typical inviscid and viscous flow cases,which reveals that the proposed GIFVM can achieve relatively higher GPU speedups as expected,and compared with GEFVM,further enhancements of 2 to 4 times are obtained by GIFVM.Finally,in order to utilize the flexibility of meshless methods for treating complex geometries for real three-dimensional complicated flow problems,GPU-accelerated meshless methods are devised and developed.Since only scattered points are needed in the discretization of computational domains,the meshless methods appear great flexibility for accommodating complex geometries.However,due to their specific structure of point clouds,the GPU parallelization of meshless methods are rarely reported.To fill this gap,a point-based mapping relation is constructed in this paper between the GPU parallel threads and the meshless points to developed the corresponding GPU-parallelized meshless methods.Specifically,a GPU-parallelized explicit meshless method(GEMLM)is firstly developed based on the least-square curve fit approach and the explicit Runge-Kutta iteration scheme,and then a GPU-parallelized implicit meshless method(GIMLM)is developed by using a proposed multi-color grouping strategy of meshless clouds.Two specific techniques,kernel merging and multi-layered point reordering(MLPRO),are also proposed under the frame of the point-based algorithm to further enhance the GPU speedups of both GEMLM and GIMLM.A set of typical inviscid and viscous flows are selected to validate those developed methods.Numerical results reveal that significant speedups of upmost 85 times can be obtained by GEMLM,GIMLM can achieve higher speedups of 2 to 5 times compared with GEMLM,and the proposed techniques of kernel merging and MLPRO reordering can also enhance the GPU speedups.