论文标题
交错网格多级不完整的LU，可稳定不可压缩流
A staggered-grid multilevel incomplete LU for steady incompressible flows
论文作者
论文摘要
用于研究不可压缩流中的过渡和不稳定性的算法通常需要使用完整的Jacobian矩阵的线性系统解决方案。其他流行的方法，例如基于梯度的设计优化和完全隐式的时间集成，也需要这种类型的线性系统非常强大的求解器。我们为在结构化网格上的3D固定不可压缩的Navier-Stokes方程提供了一个平行的完全耦合的多级不完整分解预处理。该算法和软件基于Wub和Thies开发的强大的两级方法。在本文中，我们确定了两级方案的一些弱点，并提出了诸如该方法的不同领域分配和递归应用之类的补救措施。我们将该方法应用于众所周知的3D盖驱动腔基准问题，并通过与隔离的简单型预处理相比，证明了其出色的鲁棒性。
Algorithms for studying transitions and instabilities in incompressible flows typically require the solution of linear systems with the full Jacobian matrix. Other popular approaches, like gradient-based design optimization and fully implicit time integration, also require very robust solvers for this type of linear system. We present a parallel fully coupled multilevel incomplete factorization preconditioner for the 3D stationary incompressible Navier-Stokes equations on a structured grid. The algorithm and software are based on the robust two-level method developed by Wubs and Thies. In this paper, we identify some of the weak spots of the two-level scheme and propose remedies such as a different domain partitioning and recursive application of the method. We apply the method to the well-known 3D lid-driven cavity benchmark problem, and demonstrate its superior robustness by comparing with a segregated SIMPLE-type preconditioner.
