Massively parallel direction splitting algorithms for complex flow

高性能计算机（HPC）的当前发展趋势是创建具有非常大数量的核的分布式集群（下一代HPC预计具有大约一百万个核）。 因此，科学计算的仿真算法的最重要的特征之一是它们在大型并行集群上实现时的性能。 偏微分方程离散化的经典算法并不总是很好地适用于这样的任务。 最近，我们已经开发了一个非常快速和并行化的方向分裂算法的不可压缩和所谓的变密度不可压缩流。 它使我们能够执行涉及数十亿未知数的模拟，并使我们处于大规模并行计算流体动力学的最前沿。 本项目的目标是： (i)将该算法推广到含刚性颗粒的流动，并进行大规模的模拟。 数百万个粒子的流体动力学相互作用当然在这些方法的范围之内。 然后我们将使用代码来研究几个在工程应用中感兴趣的流程。 (ii)发展流体-结构相互作用问题的方法，并将其用于模拟需要大量自由度的各种生理流动。 (iii)开始开发和分析球体上的方向分裂方法。 该项目的这一部分是开发大气和海洋流动模拟工具这一长期目标的初始阶段。 由于该方法是非常快速和并行，我们相信，它将使我们能够进行模拟的规模上的整个地球仪的耦合大气和海洋流动。

The current trend in the development of High Performance Computers (HPC) is to create distributed clusters of very large number of cores (the next generation of HPC are expected to have of the order of one million cores). Therefore, one of the most important features of simulation algorithms for scientific computing is their performance when implemented on large parallel clusters. The classical algorithms for discretization of Partial Differential Equations (PDEs) are not always well suited for such a task. Recently we have developed a very fast and parallelizable direction-splitting algorithm for incompressible and the so-called variable density incompressible flows. It enabled us to perform simulations involving billions of unknowns and placed us at the forefront of large scale parallel computational fluid dynamics. The goals of the present project are: (i) To extend and analyze the algorithm to flows with rigid particles and perform a very large scale simulation of such flows. The hydrodynamic interaction of millions of particles is certainly within the reach of these methods. Then we will use the code to study several flows of interest in engineering applications. (ii) Develop the method for fluid-structure interaction problems and use it for simulation of various physiological flows which require a very large number of degrees of freedom. (iii) Start work on the development and analysis of direction splitting methods on the sphere. This part of the project is the initial stage of a longer-term goal to develop a simulation tool for atmospheric and oceanic flows. Since the method is extremely fast and parallelizable, we believe that it will allow us to perform simulations on the scale of the entire globe of the coupled atmospheric and ocean flow.