面向上万核环境流体控制问题的全隐式全耦合可扩展算法

Flow control problem, which is a class of important problems in computational fluid dynamics (CFD), has a wide range of applications such as optimal control, the design of large-scale industrial applications, and the research of flow mechanism. But the flow control problem is such a high degree of nonlinear problem and the accuracy requirements, the scalable parallel algorithms and application softwares that can not be based on thousands to ten thousand processors are the bottleneck that impedes the development of this direction. In this project, we focus on the some applications in computational fluid dynamics, and by using the domestic teraflop and petaflop secondary supercomputers we study some key techniques in large-scale iterative algorithms and preconditioners for flow control problems. In the research, we select the representative Navier-Stokes equations in the application areas, combine with Newton-Krylov type iterations and domain decomposition preconditioners, mainly study the numerical simulation of unsteady incompressible flow control problems, and pay attention to the interdisciplinary between computational science and computer science. By the research, we hopefully obtain the framework of the highly scalable iterative algorithms and preconditioners, establish the corresponding convergence theory, and analyse the effectiveness of the proposed methods based on large scale calculations involving tens of millions to nearly billion unknowns obtained on the domestic teraflop and petaflop secondary supercomputers with ten thousand processors.

流体控制问题是计算流体力学(CFD)中的一类重要问题，在最优控制、工业大规模设计计算和流动机理的研究等方面有着广泛的应用，但是该类问题非线性程度高、精度要求高, 面向数千至上万核环境的可扩展并行算法和应用软件是该方向急需突破的瓶颈。在本项目中，我们拟针对计算流体力学中的具体应用，面向国产百万亿次、千万亿次级超级计算机，深入研究流体控制问题的大规模可扩展迭代算法和预条件子关键技术。在研究中，拟在应用领域选取具有代表性的Navier-Stokes方程组，结合Newton-Krylov类迭代法和区域分解的预条件子技术，重点研究非稳态不可压缩流控制问题的数值模拟，注重计算科学和计算机科学的学科交叉。通过研究，形成一套高可扩展迭代算法和预条件子框架，建立相应的收敛性理论，在国产百万亿次、千万亿次级超级计算机上高效实现上万核的可扩展性和数千万、近亿未知量规模以上的数值模拟，分析验证其有效性。

本项目针对计算流体力学中的两类典型应用——流体控制问题和大气输运问题，结合全隐式的并行算法、区域分解算法和全耦合的Newton-Krylov-Schwarz类方法，兼顾并行数值算法的创新和适应异构、众核环境的并行程序设计和优化技术，进行面向千万亿次超级计算机的大规模可扩展算法研究；在以天河等为代表的国产千万亿次超级计算机上，高效实现数千核的可扩展性以及数亿未知数规模以上的大规模数值模拟，为面向千万亿次科学计算的可扩展算法和应用软件实现技术提供思路，努力推动国产超级计算机的应用。相关成果发表在国际SCI期刊Journal of Scientific Computing，Computers and Fluids和Inverse Problems上。