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Scalability study of an implicit solver for coupled fluid-structure interaction problems on unstructured meshes in 3D

机译:隐式求解器在3D非结构网格上耦合流固耦合问题的可伸缩性研究

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Fluid-structure interaction (FSI) problems are computationally very challenging. In this paper we consider the monolithic approach for solving the fully coupled FSI problem. Most existing techniques, such as multigrid methods, do not work well for the coupled system since the system consists of elliptic, parabolic and hyperbolic components all together. Other approaches based on direct solvers do not scale to large numbers of processors. In this paper, we introduce a multilevel unstructured mesh Schwarz preconditioned Newton-Krylov method for the implicitly discretized, fully coupled system of partial differential equations consisting of incompressible Navier-Stokes equations for the fluid flows and the linear elasticity equation for the structure. Several meshes are required to make the solution algorithm scalable. This includes a fine mesh to guarantee the solution accuracy, and a few isogeometric coarse meshes to speed up the convergence. Special attention is paid when constructing and partitioning the preconditioning meshes so that the communication cost is minimized when the number of processor cores is large. We show numerically that the proposed algorithm is highly scalable in terms of the number of iterations and the total compute time on a supercomputer with more than 10,000 processor cores for monolithically coupled three-dimensional FSI problems with hundreds of millions of unknowns.
机译:流固耦合(FSI)问题在计算上非常具有挑战性。在本文中,我们考虑了用于解决完全耦合的FSI问题的整体方法。大多数现有技术(例如多网格方法)对于耦合系统均无法很好地工作,因为该系统由椭圆,抛物线和双曲线组件共同构成。基于直接求解器的其他方法无法扩展到大量处理器。在本文中,我们针对隐式离散,完全耦合的偏微分方程组引入了多级非结构网格Schwarz预处理的Newton-Krylov方法,该系统由不可压缩的Navier-Stokes方程组和流体的线性弹性方程组成。需要多个网格才能使求解算法可扩展。其中包括一个细网格,以确保求解的准确性;几个等几何的粗网格,以加快收敛速度​​。在构造和划分预处理网格时要特别注意,以便在处理器内核数量较大时将通信成本降至最低。我们从数值上显示,在具有10,000个处理器核的超级计算机上,针对具有数亿个未知数的单片耦合三维FSI问题,该算法在迭代次数和总计算时间方面具有高度可扩展性。

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