Partitioned solution strategies for coupled BEM-FEM acoustic fluid-structure interaction problems

TL;DR

This work develops a partitioned BEM–FEM approach for acoustic fluid–structure interaction, coupling a FEM-structured solid with a BEM-modeled fluid via Mortar or Localized Lagrange Multipliers on non-matching interfaces. It introduces a non-symmetric nsBE-FETI framework solved with a projected Bi-CGSTAB algorithm, achieving scalable performance. The study provides detailed comparisons between Mortar and LLM, showing that LLM yields superior interface displacement accuracy in highly non-conforming meshes, while Mortar can exhibit interpolation-induced artifacts. Numerical results across interior cavities, rectangular ducts, and exterior scattering problems demonstrate robust convergence behavior and moderate sensitivity to interface non-conformity, underscoring the practicality of the proposed method for vibro-acoustic FSI applications.

Abstract

This paper investigates two FEM-BEM coupling formulations for acoustic fluid-structure interaction (FSI) problems, using the Finite Element Method (FEM) to model the structure and the Boundary Element Method (BEM) to represent a linear acoustic fluid. The coupling methods described interconnect fluid and structure using classical or localized Lagrange multipliers, allowing the connection of non-matching interfaces. First coupling technique is the well known mortar method, that uses classical multipliers and is compared with a new formulation of the method of localized Lagrange multipliers (LLM) for FSI applications with non-matching interfaces. The proposed non-overlapping domain decomposition technique uses a classical non-symmetrical acoustic BEM formulation for the fluid, although a symmetric Galerkin BEM formulation could be used as well. A comparison between the localized methodology and the mortar method in highly non conforming interface meshes is presented. Furthermore, the methodology proposes an iterative preconditioned and projected bi-conjugate gradient solver which presents very good scalability properties in the solution of this kind of problems.

Figures (17)

• Figure 1: Differences in the description of mortar (a) and localized (b) interfaces. Classical multipliers are used in (a) with a direct connection of the interfaces. In (b), an independent discretization of the interface is introduced and connected to the solid and fluid boundaries using localized Lagrange multipliers.
• Figure 2: Modified linear ansatz functions used with Mortar method in the presence of Dirichlet boundary conditions for the approximation of interface Lagrange multipliers.
• Figure 3: Coupling with the Mortar method fluid and solid interfaces. Approximation spaces for boundary displacements and multipliers.
• Figure 4: FSI BEM-FEM system with intercalated frame and localized Lagrange multipliers.
• Figure 5: Acoustic cavity with a flexible wall and harmonic excitation. Problem definition (a) and BEM-FEM subdomains coupled using LLM (b).