Abstract This article presents an assessment of the scheduled relaxation Jacobi (SRJ) method for the solution of large-scale Poisson problems arising in the numerical simulation of large eddy turbulent flow in large complex geometry. The SRJ schemes are used both as standalone solvers and as preconditioners to Krylov subspace solvers. The Navier-Stokes equation is solved using structured Cartesian grids (both uniform as well as nonuniform grids). Geometrical complexities are handled using the immersed boundary method (IBM) method. The performance of SRJ schemes as a standalone solver is first validated with the help of a rectangular channel flow problem whose exact solution is known. Numerical experiments are performed to evaluate the performance of SRJ schemes as preconditioners to two robust and efficient Krylov subspace solvers (PCG and BiCGSTAB), and compared with different preconditioners such as Jacobi (diagonal preconditioner), SOR(k) and multigrid preconditioners. SRJ schemes as standalone solver perform quite similarly as predicted before in literature. However, as preconditioner particularly some SRJ schemes work best among the rest for three-dimensional problems.

中文翻译：

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调度松弛雅可比方法作为 Krylov 子空间技术的预处理器，用于大规模泊松问题

摘要 本文介绍了对在大型复杂几何体中的大涡流湍流进行数值模拟中出现的大规模泊松问题的求解的预定松弛雅可比 (SRJ) 方法的评估。SRJ 方案既用作独立求解器，也用作 Krylov 子空间求解器的预处理器。Navier-Stokes 方程使用结构化笛卡尔网格（均匀和非均匀网格）求解。使用浸入边界法 (IBM) 方法处理几何复杂性。SRJ 方案作为独立求解器的性能首先在矩形通道流问题的帮助下进行验证，该问题的精确解是已知的。进行了数值实验以评估 SRJ 方案作为两个鲁棒且高效的 Krylov 子空间求解器（PCG 和 BiCGSTAB）的预处理器的性能，并与不同的预处理器，如 Jacobi（对角预处理器）、SOR(k) 和多重网格预处理器进行比较。SRJ 方案作为独立求解器的性能与之前文献中预测的非常相似。然而，作为预处理器，特别是一些 SRJ 方案在 3D 问题的其余部分中效果最好。