A graphics processing unit(GPU)-accelerated discontinuous Galerkin(DG)method is presented for solving two-dimensional laminar flows.The DG method is ported from central processing unit to GPU in a way of achieving GPU...A graphics processing unit(GPU)-accelerated discontinuous Galerkin(DG)method is presented for solving two-dimensional laminar flows.The DG method is ported from central processing unit to GPU in a way of achieving GPU speedup through programming under the compute unified device architecture(CUDA)model.The CUDA kernel subroutines are designed to meet with the requirement of high order computing of DG method.The corresponding data structures are constructed in component-wised manners and the thread hierarchy is manipulated in cell-wised or edge-wised manners associated with related integrals involved in solving laminar Navier-Stokes equations,in which the inviscid and viscous flux terms are computed by the local lax-Friedrichs scheme and the second scheme of Bassi&Rebay,respectively.A strong stability preserving Runge-Kutta scheme is then used for time marching of numerical solutions.The resulting GPU-accelerated DG method is first validated by the traditional Couette flow problems with different mesh sizes associated with different orders of approximation,which shows that the orders of convergence,as expected,can be achieved.The numerical simulations of the typical flows over a circular cylinder or a NACA 0012 airfoil are then carried out,and the results are further compared with the analytical solutions or available experimental and numerical values reported in the literature,as well as with a performance analysis of the developed code in terms of GPU speedups.This shows that the costs of computing time of the presented test cases are significantly reduced without losing accuracy,while impressive speedups up to 69.7 times are achieved by the present method in comparison to its CPU counterpart.展开更多
基金partially supported by the National Natural Science Foundation of China(No.11972189)the Natural Science Foundation of Jiangsu Province(No.BK20190391)+1 种基金the Natural Science Foundation of Anhui Province(No.1908085QF260)the Priority Academic Program Development of Jiangsu Higher Education Institutions。
文摘A graphics processing unit(GPU)-accelerated discontinuous Galerkin(DG)method is presented for solving two-dimensional laminar flows.The DG method is ported from central processing unit to GPU in a way of achieving GPU speedup through programming under the compute unified device architecture(CUDA)model.The CUDA kernel subroutines are designed to meet with the requirement of high order computing of DG method.The corresponding data structures are constructed in component-wised manners and the thread hierarchy is manipulated in cell-wised or edge-wised manners associated with related integrals involved in solving laminar Navier-Stokes equations,in which the inviscid and viscous flux terms are computed by the local lax-Friedrichs scheme and the second scheme of Bassi&Rebay,respectively.A strong stability preserving Runge-Kutta scheme is then used for time marching of numerical solutions.The resulting GPU-accelerated DG method is first validated by the traditional Couette flow problems with different mesh sizes associated with different orders of approximation,which shows that the orders of convergence,as expected,can be achieved.The numerical simulations of the typical flows over a circular cylinder or a NACA 0012 airfoil are then carried out,and the results are further compared with the analytical solutions or available experimental and numerical values reported in the literature,as well as with a performance analysis of the developed code in terms of GPU speedups.This shows that the costs of computing time of the presented test cases are significantly reduced without losing accuracy,while impressive speedups up to 69.7 times are achieved by the present method in comparison to its CPU counterpart.
