一种具有多网格-里奇逊-施瓦茨预条件的单体ALE牛顿-克雷洛夫求解器用于不可压缩流固耦合
A monolithic ALE Newton-Krylov solver with Multigrid-Richardson-Schwarz preconditioning for incompressible Fluid Structure Interaction
AI总结：
本文提出一种单体牛顿-克雷洛夫求解器，采用多网格预条件和修改的里奇逊平滑器，用于求解不可压缩流固耦合问题，展示了其在处理直接到稳态问题时的鲁棒性。
摘要：
本文研究了一种单体牛顿-克雷洛夫求解器，该求解器具有精确雅可比矩阵，用于求解不可压缩流固耦合问题。本文的主要关注点是使用几何多网格预条件器，其修改的里奇逊平滑器通过附加施瓦茨算法预条件。施瓦茨平滑器的子域定义由流体和固体之间的自然分割驱动。单体方法保证了应力平衡和流体-固体界面的运动条件自动满足。通过使用不稳定的有限元对来处理流体和固体的不可压缩性条件。选择适当的任意拉格朗日-欧拉（ALE）算子以避免在求解大位移的移动流体域时出现网格纠缠。二维和三维基准测试的数值结果表明，我们的完全不可压缩求解器在处理直接到稳态问题时表现出鲁棒性。
英文摘要：
In this paper we study a monolithic Newton-Krylov solver with exact Jacobian for the solution of incompressible FSI problems. A main focus of this work is on the use of geometric multigrid preconditioners with modified Richardson smoothers preconditioned by an additive Schwarz algorithm. The definition of the subdomains in the Schwarz smoother is driven by the natural splitting between fluid and solid. The monolithic approach guarantees the automatic satisfaction of the stress balance and the kinematic conditions across the fluid-solid interface. The enforcement of the incompressibility conditions both for the fluid and for the solid parts is taken care of by using inf-sup stable finite element pairs without stabilization terms. A suitable Arbitrary Lagrangian Eulerian (ALE) operator is chosen in order to avoid mesh entanglement while solving for large displacements of the moving fluid domain. Numerical results of two and three-dimensional benchmark tests with Newtonian fluids and nonlinear hyperelastic solids show a robust performance of our fully incompressible solver especially for the more challenging direct-to-steady-state problems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
