A relatively recent development in computational analysis is a coupling between fluid flow and structural dynamics. These fluid-structure interactions may be observed in many physical phenomena including bridge vibrations due to gusts, aerodynamic flow patterns in response to flapping of wings, deformation of blood vessels and heart in reponse to blood flow and vibrations of airway tissues in response to breathing during snoring. From literature, two approaches are common in modelling fluid structure interactions – (i) structural mesh that conforms to the fluid mesh or (ii) structural mesh that do not conform to the fluid mesh [1,2]. In the former (and more common) approach, the fluid domain and boundaries are frequently changed as it follows the deformation of the interfacing structure [3-5]. As a result, an Arbirtrary Lagrangian-Eulerian (ALE) formulation is required for the fluid physics. More significantly, complete remeshing or mesh deformation is needed to be solved for the whole fluid domain, which involves substantial computational effort.
Alternatively, the latter approach where the structural mesh do not conform with the fluid mesh, a fixed fluid grid is employed with an Eulerian formulation for the fluid physics [1,6]. This has the advantage of eliminating the need for repeated mesh update of the fluid domain. Several schemes have been developed that falls within this approach, including an eXtended Finite Element Method (XFEM) that employs Lagrangian multipliers to enforce fluid-structure interactions , a fictitious domain/mortar element method , immersed boundary methods (IBM) that employs smoothed dirac-delta functions to interpolate variables between the fluid and structural domains [9,10] and immersed finite element methods (IFEM), which unlike IBM, uses a repoducing kernel particle method to interpolate interfacing velocities and body forces . However, a major disadvantage of this fixed grid approach is that flow near the moving structures are not resolved accurately [1,6]. The interpolation function which defines the fluid-structure interaction typically smears or blurs the distinction between fluid and structure interface to within the mesh widths of the fluid grids. Furthermore, resolution of boundary layers near the structural surface is difficult to capture without employing boundary layer meshes that are aligned with the structural body.
The aim of this study is to combine the benefits from the ALE grid approach and the the fixed grid approach, by developing an overlapping grid formulation, where a localised ALE grid (which conforms to structural deformation) overlaps a fixed fluid grid in the background. Indeed, continuity and interaction between the fixed fluid grid and ALE fluid grid shall need to be enforced in this overlapping grid formulation. Unlike previous overlapping schemes, for example, XFEM methods that uses Lagrange multipliers [2,7] or Chimera methods [2,12] that require additional iteration between grids, it is hypothesised that a forcing feedback scheme [10,13] may be efficiently employed to model this localised and background grid continuity. It is anticipated that with this overlapping grid formulation, flow resolution surrounding the structural body may be resolved as accurately as possible and the mesh update (or even remeshing) is limited to localised, dynamic fluid grids that surrounds the structure, thus, minimising computational effort.