Study On The Cartesian Grid Method Based On The GPU Parallel Computation

Non-body-fitted Cartesian grid has many advantages,such as simple generation process,flexible calculation patterns and easy realization of self-adaption.As a result,it also has a bright application prospect in the field of aerodynamic design which is supported by numerical simulations.Compared with the traditional central processing unit(CPU),graphics processing unit(GPU)has extremely high floating-point computation power,which is really suitable for applications in the field of computational fluid dynamics(CFD)with numerous data-intensive tasks.In order to accelerate the numerical simulation,we combined both of them organically in our work.Firstly,the Cartesian grid computing methods were studied in detail,and then the GPU parallel computing methods were further researched on the basis of them.In order to improve the spatial discretization efficiency of Cartesian grids while considering the parallelism in the calculation process,we first researched the generation principles and methods of the nested and the block-structured Cartesian grids,the judgment of cell type and the value transmission among partitions.Then for the approaches of surface treatment,the ghost cell methods were classified into two categories according to the selection of reference points: one was based on the flow point,and the other was based on the mirror point.At the same time,based on the simplified ghost cell method(SGCM),we proposed a weighted ghost cell method(WGCM),which can eliminate the distortion problem in SGCM and solve the slit problem better.In this paper,a computing program based on the block-structured Cartesian grid was accelerated with a GPU,and the GPU parallel algorithms for explicit time scheme,implicit time scheme,and the judgment and assignment of cell type were deeply studied.For the residual value calculation in explicit and implicit time schemes,the kernels were merged through a redundant computation approach,which can reduce the overhead of the accessing and writing of global memory.Moreover,the approach can avoid the use of auxiliary arrays,and decrease the footprint of device memory.Considering the similarity between the block-structured Cartesian grid and the thread hierarchy of the Compute Unified Device Architecture(CUDA),a parallel block-structured Cartesian grid algorithm based on thread hierarchy of CUDA was put forward in this paper,which could accomplish the merging of multiple kernels and then decline the accessing and writing overhead of global memory.Furthermore,we analyzed the performance of GPU programs through test cases,and obtained the speedup ratios of explicit and implicit methods on different mesh sizes.In addition,we investigated and evaluated the optimization strategies of GPU programs by changing the execution configuration,data layout and using the structure reconstruction technology.Finally,we used the GPU-accelerated computing programs based on the blockstructured Cartesian grid to simulate the two-dimensional supersonic flow problems of a pitching air rudder and the booster separation problems of a hypersonic vehicle.For the former,we probed the influences of Mach number,oscillation frequency,mean angle of attack and amplitude on the hysteresis effect,and for the latter,we researched and analyzed the changes of flow field structure and aerodynamic parameters.