Massively parallel direction splitting algorithms for complex flow

目前高性能计算机(HPC)的发展趋势是创建具有大量核心的分布式集群(下一代HPC预计将具有大约一百万个核心)。因此，科学计算模拟算法最重要的特点之一就是在大型并行集群上实现时的性能。传统的偏微分方程组离散化算法并不总是适合于这样的任务。最近，我们针对不可压缩流动和所谓的变密度不可压缩流动发展了一种非常快速且可并行化的方向分裂算法。它使我们能够进行涉及数十亿个未知数的模拟，并使我们处于大规模并行计算流体力学的前沿。 本项目的目标是： (I)将该算法推广和分析到含有刚性颗粒的流动，并对这种流动进行超大规模的模拟。数以百万计的粒子之间的流体动力相互作用当然在这些方法的范围内。然后，我们将使用代码来研究工程应用程序中感兴趣的几个流。 (Ii)发展流固耦合问题的计算方法，用于模拟各种需要很大自由度的生理流动。 (3)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的长期目标的初步阶段。由于该方法非常快速且可并行化，我们相信它将使我们能够在整个地球尺度上进行大气和海洋耦合流动的模拟。

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.