A partitioned scheme for fluid–composite structure interaction problems

Abstract

We present a benchmark problem and a loosely-coupled partitioned scheme for fluidstructure interaction with composite structures. The benchmark problem consists of an incompressible, viscous fluid interacting with a structure composed of two layers: a thin elastic layer with mass which is in contact with the fluid and modeled by the Koiter membrane/shell equations, and a thick elastic layer with mass modeled by the equations of linear elasticity. An efficient, modular, partitioned operator-splitting scheme is proposed to simulate solutions to the coupled, nonlinear FSI problem, without the need for subiterations at every time-step. An energy estimate associated with unconditional stability is derived for the fully nonlinear FSI problem defined on moving domains. Two instructive numerical benchmark problems are presented to test the performance of numerical FSI schemes involving composite structures. It is shown numerically that the proposed scheme is at least first-order accurate both in time and space. This work reveals a new physical property of FSI problems involving thin interfaces with mass: the inertia of the thin fluidstructure interface regularizes solutions to the full FSI problem.

Multi-component model of intramural hematoma

“…This is consistent with the experimental measurements of the aortic diameters reported by Wolak et al (2008) and O’Rourke and Nichols (2005). The blood density is taken to be ρ f = 1 g/cm 3 and viscosity μ f = 0.035 g/cm s. We impose symmetry boundary conditions at the fluid bottom boundary ${\mathrm{normal\Gamma }}_b^f$ (see Figure 1) (Khanafer and Berguer (2009), Bukač et al (2015)). …”

“…To circumvent the issues related to the motion of the fluid domain due to the fluid-structure interaction, we use the Navier-Stokes equations in the ALE form (Donea (1983), Duarte et al (2004), Bukač et al (2015)). …”

“…The deformation of the media/adventitia complex is modeled using the 2D equations of linear elasticity (Quaini (2009), Bukač et al (2015)): $${\rho }_{ma}{\partial }_{tt}{\mathrm{bold-italic\eta }}^{ma}=\nabla ·{\mathrm{bold-italic\sigma }}^s,$$ where η ma is the structure displacement and ρ ma is the density. One of the common simplifying assumptions in models of blood flow interaction with the vessel wall is treatment of the biomechanical material properties of the vessel as linearly elastic, homogeneous material (Thubrikar et al (2001), Hua and Mower (2001), Scotti et al (2005), Giannoglou et al (2006)).…”

“…The submodel for the aorta with IMH is coupled with the submodel for blood flow in the lumen. The coupling between blood flow and a 2-layer structure model was previously considered by Bukač et al (2015), but without the presence of the poroelastic material. Furthermore, the coupling between the fluid, a single layer, thin elastic structure and poroelastic material was previously considered by Bukač (2016), but in a different configuration.…”

Adjoint Optimal Control Problems for Fluid-Structure Interaction Systems

“…Examples of this type of systems are quite common in engineering, like floating structures, wind turbines, man-made drones and in the study of biological systems such as artery or heart valves. In literature these topics are investigated deeply and the interested reader can see [9,10,11,12,13,14]. Many attempts to use optimization techniques can be found, for example in [15], where the authors propose a solution method for the problem of optimizing a non-linear aeroelasticity system in a steady-state flow by using a sensitivity method.…”