GPU Implementation Of Numerical Methods For Compressible Viscous Flow Based On Unstructured Grids

Over the past decade, the performance of a CPU isn't getting much better due to the power consumption and manufacturing processes. At the same time, the GPU is gaining more and more popularity as scientific applications can well benefit from its better arithmetic performance and higher memory bandwidth compared to a contemporary CPU. Reseachers began to accelerate CFD codes by using a GPU and achieved good results.This paper focuses on the GPU implementation of numerical methods for steady and unsteady compressible viscous flow based on unstructured grids. The finite volume method is applied to the RANS equations. A vertex-centered scheme is selected to construct the control volume on unstructured grids. Both Roe and Hllc flux computing methods are employed here. The linear reconstruction method combined with the Venkatakrishnan limiter is used to attain second order spatial accuracy. The explicit Runge-Kutta temporal integration method, as well as the implicit LUSUS method is realized. The Dual Time-Stepping method is introduced to help accelerate the convergence in unsteady simulations which proves to be of second order precision in time. The Spalart-Allmaras turbulence model is introduced as a first-order closure of the RANS equations with a DES option to take advantages of LES method in separation region while keeping using RANS equations within the boundary layer. A scheme based on KD-Tree is employed to solve the nearest neighboring search problem.A complete and efficient kernel design based on double precision variables is set forth after analyzing the detailed software and hardware architecture of a GPU. In view of a vertex-centered scheme on unstructured grids, optimizations of hardware utilizations, memory accesses and instruction executions are applied. New grid reordering methods are put forward to improve the global memory accessing performance. Multiple steady and unsteady test cases are carried out to verify and validate our GPU implementation. The speedup of the Runge-Kutta method and LU-SGS method on GPU is estimated to be 82~116 times and 55~100 times respectively as compared to the CPU serial version. The results indicate GPU has good potential to accelerate CFD solvers.