Abstract: Alternating Direction Implicit (ADI) scheme is a typical discretization scheme for solving partial differential equations. However, there are few researches on the implementations and optimizations of ADI scheme on GPUs for practical Computational Fluid Dynamics (CFD) applications. In this paper, through analysis of the characteristics and calculation processes of ADI solver in a practical CFD application, the authors implemented fine-grained GPU parallelization algorithm for the ADI solver based on grid points and grid lines by a Compute Unified Device Architecture (CUDA) model. Some performance optimization methods were discussed. The experimental results on the TianHe-1A supercomputer show that the proposed GPU-enabled ADI solver can achieve overall speedup of 17.3 compared to single CPU core when simulating a 128×128×128 grid. The speedups for inviscid flux calculation, viscous flux calculation and ADI iteration are 100.1, 40.1 and 10.3 respectively.

Key words: Alternating Direction Implicit (ADI), Computational Fluid Dynamics (CFD) solver, structured grid, GPU parallelization

摘要： 交替方向隐格式(ADI)是常见的偏微分方程离散格式之一，目前对ADI格式在计算流体力学（CFD）实际应用中的GPU并行工作开展较少。从一个有限体积CFD应用出发，通过分析ADI解法器的特点和计算流程，基于统一计算架构(CUDA)编程模型设计了基于网格点与网格线的两类细粒度GPU并行算法，讨论了若干性能优化方法。在天河-1A系统上，采用128×128×128网格规模的单区结构网格算例，无粘项、粘性项及ADI迭代计算的GPU并行性能相对于单CPU核，分别取得了100.1、40.1和10.3倍的加速比，整体ADI CFD解法器的GPU并行加速比为17.3

关键词: 交替方向隐式, 计算流体力学解法器, 结构网格, GPU并行