面向GPU的可压缩流直接数值模拟大规模并行杂交型间断伽略金求解器
A Massively Parallel Hybridizable Discontinuous Galerkin Solver for Direct Numerical Simulation of Compressible Flows on GPUs
浏览论文内容
中文总结 AI 辅助
本文提出面向GPU的大规模并行HDG求解器，结合高阶离散化、DIRK时间积分等技术，在三类可压缩流基准问题上验证其可解析多种流态的能力，实现高效DNS计算。
中文摘要 AI 辅助
可压缩转捩流与湍流的直接数值模拟（DNS）需要兼具高阶精度、鲁棒性与计算效率的数值方法，以解析宽范围的空间与时间尺度。本文提出一种面向GPU加速高性能计算系统的、用于求解可压缩纳维-斯托克斯方程DNS的大规模并行杂交型间断伽略金（HDG）求解器。该求解器将高阶HDG离散化、鲁棒激波捕捉、对角隐式龙格-库塔（DIRK）时间积分，以及由加性施瓦茨预处理与降阶近似加速的高效牛顿-GMRES求解策略相结合。基于GPU感知MPI、Kokkos及CUDA/HIP库实现的分布式方法，可在异构计算平台上实现可扩展执行。该求解器在三个覆盖宽马赫数流态的经典基准问题上得到验证：Eppler 387翼型的亚音速转捩流、超音速泰勒-格林涡，以及高超声速边界层转捩。数值结果与现有实验测量及已发表的DNS数据对比，在不同流态下均表现出良好一致性，证明该求解器具备解析层流-湍流转捩、强可压缩效应、激波相关流结构及全三维湍流动力学的能力。
英文摘要
Direct numerical simulation (DNS) of compressible transitional and turbulent flows requires numerical methods that combine high-order accuracy, robustness, and computational efficiency to resolve a broad range of spatial and temporal scales. This paper presents a massively parallel hybridizable discontinuous Galerkin (HDG) solver for DNS of the compressible Navier-Stokes equations on GPU-accelerated high-performance computing systems. The proposed solver combines high-order HDG discretization with robust shock capturing, diagonally implicit Runge-Kutta (DIRK) time integration, and an efficient Newton-GMRES solution strategy accelerated by additive Schwarz preconditioning and reduced-basis approximation. A distributed implementation of these methods based on GPU-aware MPI, Kokkos, and CUDA/HIP libraries enables scalable execution on heterogeneous computing platforms. The solver is demonstrated on three canonical benchmark problems covering a wide range of Mach-number flow regimes: subsonic transitional flow over the Eppler 387 airfoil, the supersonic Taylor-Green vortex, and hypersonic boundary-layer transition. Numerical results are compared with available experimental measurements and published DNS data, showing good agreement across distinct flow regimes. The results demonstrate the ability of the proposed solver to resolve laminar-turbulent transition, strong compressibility effects, shock-associated flow structures, and fully three-dimensional turbulent dynamics.
