The Perfectly Matched Layer absorbing boundary for fluid–structure interactions using the Immersed Finite Element Method

Abstract

In this work, a non-reflective boundary condition, the Perfectly Matched Layer (PML) technique, is adapted and implemented in a fluid-structure interaction numerical framework to demonstrate that proper boundary conditions are not only necessary to capture correct wave propagations in a flow field, but also its interacted solid behavior and responses. While most research on the topics of the non-reflective boundary conditions are focused on fluids, little effort has been done in a fluid-structure interaction setting. In this study, the effectiveness of the PML is closely examined in both pure fluid and fluid-structure interaction settings upon incorporating the PML algorithm in a fully-coupled fluid-structure interaction framework, the Immersed Finite Element Method. The performance of the PML boundary condition is evaluated and compared to reference solutions with a variety of benchmark test cases including known and expected solutions of aeroacoustic wave propagation as well as vortex shedding and advection. The application of the PML in numerical simulations of fluid-structure interaction is then investigated to demonstrate the efficacy and necessity of such boundary treatment in order to capture the correct solid deformation and flow field without the requirement of a significantly large computational domain.

Modeling isovolumetric phases in cardiac flows by an Augmented Resistive Immersed Implicit Surface method

“…41 To avoid the need of a complete remeshing of the computational domain, while maintaining a sharp description of the valve surface, different XFEM/cutFEM methods have been proposed, [42][43][44][45][46][47][48] but their use to simulate cardiac flows at the organ scale has been limited by their relatively high computational cost. On the other hand, fully Eulerian approaches, such as the immersed boundary method, [49][50][51][52][53][54][55][56][57] the fictitious domain method [58][59][60][61][62][63][64] or the Resistive Immersed Implicit Surface (RIIS) method, 21,65 hinge upon an implicit representation of the leaflets and do not require mesh conformity between the fluid domain and the valves. This allows to track the fluid-valve interface, possibly moving in time, without requiring the fluid mesh to follow the valve.…”

Constructing artificial boundary condition of dispersive wave systems by deep learning neural network

“…The PML method attaches an attenuation layer to the boundary, and carefully choose the parameters such that no wave reflects at the interface and all waves are absorbed in the additional layer [15]. Jiang et al [16], Dastour et al [17] used PML to solve the second order and fourth order Helmholtz equations respectively; Wildman introduced it to the 2D peri-dynamics [18]; Yang et al solved fluid dynamics and fluid-structure interaction problems with PML boundary [19]; Fang et al employed PML to eliminate the boundary reflection when analyzing seismic wave [20], etc. The Higdon-type ABC often adopts the concatenated form of the Higdon operator [21].…”

Subject-Specific Computational Fluid-Structure Interaction Modeling of Rabbit Vocal Fold Vibration

“…Most of the earlier computational models focused on idealized and generic representations for the laryngeal geometry. These models include structural models utilizing the finite element method and coupled with a one-, two-, or three-dimensional (1D, 2D, or 3D) flow solver to simulate the FSI process [ 6 - 13 ]. Many lessons have been learned from these insightful studies, including the vibratory characteristics of the vocal fold tissue, the pulsatile jet flow behavior, the transfer of momentum and energy from the flow to the solid, and the multi-faceted effects of the geometric and material properties.…”