Extended ALE Method for fluid-structure interaction problems with large structural displacements

Standard Arbitrary Lagrangian-Eulerian (ALE) methods for the simulation of fluid-structure interaction (FSI) problems fail due to excessive mesh deformations when the structural displacement is large. We propose a method that successfully deals with this problem, keeping the same mesh connectivity while enforcing mesh alignment with the structure. The proposed Extended ALE Method relies on a variational mesh optimization technique, where mesh alignment with the structure is achieved via a constraint. This gives rise to a constrained optimization problem for mesh optimization, which is solved whenever the mesh quality deteriorates. The performance of the proposed Extended ALE Method is demonstrated on a series of numerical examples involving 2D FSI problems with large displacements. Two way coupling between the fluid and structure is considered in all the examples. The FSI problems are solved using either a Dirichlet-Neumann algorithm, or a Robin-Neumann algorithm. The Dirichlet-Neumann algorithm is enhanced by an adaptive relaxation procedure based on Aitken's acceleration. We show that the proposed method has excellent performance in problems with large displacements, and that it agrees well with a standard ALE method in problems with mild displacement. Suggested Reviewers: Thomas Wick [email protected] Petr Svacek [email protected] Joan Baiges [email protected] Significance and Novelty 1. A novel extended ALE method is proposed for fluid-structure interaction (FSI) problems with large structural displacements. 2. An optimal mesh is constructed based on a variational mesh optimization technique, combined with an additional constraint imposed to enforce the alignment of the fluid mesh with the structure, without changing connectivity. 3. The main features of the method include: * High solution accuracy near the interface (i.e., due to the mesh alignment, pressure discontinuity along an immersed interface is captured with high accuracy). * non-trivial boundary conditions (e.g. Robin boundary conditions) can be easily implemented, allowing for stable and efficient Domain Decomposition methods. 4. Several numerical examples involving 2D FSI problems with large displacement. *Significance and Novelty of this paper