A monolithic approach to fluid‐structure interaction based on a hybrid Eulerian‐ALE fluid domain decomposition involving cut elements

Abstract

SummaryA novel method for complex fluid‐structure interaction (FSI) involving large structural deformation and motion is proposed. The new approach is based on a hybrid fluid formulation that combines the advantages of purely Eulerian (fixed‐grid) and arbitrary Lagrangian‐Eulerian (ALE) moving mesh formulations in the context of FSI. The structure, as commonly given in Lagrangian description, is surrounded by a fine resolved layer of fluid elements based on an ALE‐framework. This ALE‐fluid patch, which is embedded in a Eulerian background fluid domain, follows the deformation and motion of the structural interface. This approximation technique is not limited to finite element methods but can also be realized within other frameworks like finite volume or discontinuous Galerkin methods. In this work, the surface coupling between the two disjoint fluid subdomains is imposed weakly using a stabilized Nitsche's technique in a cut finite element method (CutFEM) framework. At the fluid‐solid interface, standard weak coupling of node‐matching or nonmatching finite element approximations can be utilized. As the fluid subdomains can be meshed independently, a sufficient mesh quality in the vicinity of the common fluid‐structure interface can be assured. To our knowledge, the proposed method is the only method (despite some overlapping domain decomposition approaches that suffer from other issues) that allows for capturing boundary layers and flow detachment via appropriate grids around largely moving and deforming bodies. In contrast to other methods, it is possible to do this, eg, without the necessity of costly remeshing procedures. A clear advantage over existing overlapping domain decomposition methods consists in the sharp splitting of the fluid domain, which comes along with improved convergence behavior of the resulting monolithic FSI system. In addition, it might also help to save computational costs as now background grids can be much coarser. Various FSI‐cases of rising complexity conclude the work. For validation purpose, results have been compared to simulations using a classical ALE‐fluid description or purely fixed‐grid CutFEM‐based schemes.