We deal with efficient numerical solution of the steady incompressible Navier–Stokes equations (NSE) using our in‐house solver based on the isogeometric analysis (IgA) approach. We are interested in the solution of the arising saddle‐point linear systems using preconditioned Krylov subspace methods. Based on our comparison of ideal versions of several state‐of‐the‐art block preconditioners for linear systems arising from the IgA discretization of the incompressible NSE, suitable candidates have been selected. In the present paper, we focus on selecting efficient approximate solvers for solving subsystems within these preconditioning methods. We investigate the impact on the convergence of the outer solver and aim to identify an effective combination. For this purpose, we compare convergence properties of the selected solution approaches for problems with different viscosity values, mesh refinement levels and discretization bases.

中文翻译：

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用于通过等几何分析离散化的不可压缩纳维-斯托克斯问题的块预处理的近似内求解器

我们使用基于等几何分析 (IgA) 方法的内部求解器来处理稳定不可压缩纳维-斯托克斯方程 (NSE) 的有效数值解。我们感兴趣的是使用预处理 Krylov 子空间方法来求解所产生的鞍点线性系统。基于我们对由不可压缩 NSE 的 IgA 离散化产生的线性系统的几种最先进的块预处理器的理想版本的比较，已经选择了合适的候选者。在本文中，我们重点关注选择高效的近似求解器来求解这些预处理方法中的子系统。我们研究了对外部求解器收敛的影响，旨在确定有效的组合。为此，我们针对具有不同粘度值、网格细化水平和离散化基础的问题，比较了所选解决方案的收敛特性。