An energy stable one-field monolithic arbitrary Lagrangian–Eulerian formulation for fluid–structure interaction. (October 2020)

• Record Type: Journal Article
• Authors: Wang, Yongxing; Jimack, Peter K.; Walkley, Mark A.; Pironneau, Olivier
• Is Part Of: Journal of fluids and structures. Volume 98(2020)
• Publication Date: 2020-10
• Subjects: Fluid structure interaction -- Finite element -- One field -- Monolithic scheme -- Arbitrary Lagrangian–Eulerian -- Energy stable; Fluid-structure interaction -- Periodicals; Fluid mechanics -- Periodicals; Structural dynamics -- Periodicals; Structural analysis (Engineering) -- Periodicals; 620.106
• DOI: 10.1016/j.jfluidstructs.2020.103117
• Languages: English
• ISSNs: 0889-9746

Abstract

Abstract: In this article we present a one-field monolithic finite element method in the Arbitrary Lagrangian–Eulerian (ALE) formulation for Fluid–Structure Interaction (FSI) problems. The method only solves for one velocity field in the whole FSI domain, and it solves in a monolithic manner so that the fluid solid interface conditions are satisfied automatically. We prove that the proposed scheme is unconditionally stable, through energy analysis, by utilising a conservative formulation and an exact quadrature rule. We implement the algorithm using both F -scheme and d -scheme, and demonstrate that the former has the same formulation in two and three dimensions. Finally several numerical examples are presented to validate this methodology, including combination with remesh techniques to handle the case of very large solid displacement.