A Mixed Acoustic Fluid Finite Element in Boundary Representation for Fluid‐Structure Interaction

Abstract

AbstractThis contribution focuses on a mixed finite element formulation for an acoustic fluid in boundary representation to model fluid‐structure interaction problems. In fact, acoustic fluids are characterized by their lack of dynamic viscosity and undergo displacements through a pure pressure wave propagation. Since many fluids, for instance water, show nearly‐incompressible behavior, volumetric locking occurs in the classical finite element formulation. This drawback is herein evaded by a two‐field, or mixed, finite element formulation. To facilitate the contact condition at the fluid‐structure interface, the acoustic fluid is expressed by structural field variables, which are nodal displacements and internal pressures. Both the displacements and internal pressures are parameterized by a Scaled‐Boundary (SB) approach, in which an interpolation in the scaling direction is employed. From this parametrization, the element mass and stiffness matrices of the fluid can be formulated. Due to the special parametrization of the element boundary, pressure continuity is required between scaled sections in the element interior, although pressure continuity may be interrupted between neighboring Scaled‐Boundary elements. Since the lack of shear viscosity leads to unwanted zero‐energy modes concerned with the fluid's vorticity, this vorticity is penalized on a sectional level. As a result, these modes do not show up in the frequency spectrum of the dynamic eigenvalue problem any longer. The natural frequencies and mode shapes in this spectrum deliver accurate results, even for very coarse meshes.