Three-Dimensional Simulation of Fluid–Structure Interaction Problems Using Monolithic Semi-Implicit Algorithm

Abstract

A monolithic semi-implicit method is presented for three-dimensional simulation of fluid–structure interaction problems. The updated Lagrangian framework is used for the structure modeled by linear elasticity equation and, for the fluid governed by the Navier–Stokes equations, we employ the Arbitrary Lagrangian Eulerian method. We use a global mesh for the fluid–structure domain where the fluid–structure interface is an interior boundary. The continuity of velocity at the interface is automatically satisfied by using globally continuous finite element for the velocity in the fluid–structure mesh. The method is fast because we solve only a linear system at each time step. Three-dimensional numerical tests are presented.

Stable Semi-Implicit Monolithic Scheme for Interaction Between Incompressible Neo-hookean Structure and Navier-Stokes Fluid

“…The results presented in this paper, including the stability analysis, hold for different 2D geometrical configurations, for example the flow in a channel with elastic wall, [16]. For 3D configurations, for example blood flow in artery [19], the stability result for the structure remains true but the stabilization term added in the fluid scheme has to be adapted accordingly.…”

“…In [11,16,[18][19][20]24] one global mesh for fluid-structure domain which fits to the interface is used. In [11,20], an Eulerian formulation derived from Cayley-Hamilton theorem is used for the incompressible Mooney-Rivlin structure.…”

A Monolithic Eulerian Formulation for non-Classical Fluid-Structure Interaction (nCFSI): Modeling and Simulation

“…In this section, we present the discretization scheme used to approximate the CFSI problem in equations (25)(26)(27). We use a semi-implicit scheme for time discretization and Galerkin discretization finite element method for space.…”

“…Among the formulations used for solving fluid-structure interactions FSI problems some are based on monolithic approach, which finds origin in (Hron and Turek 2006) solve the FSI problems as a single variational equation for the whole system (Dunne 2006;Heil et al 2008), or more recently (Pironneau 2016; Hecht and Pironneau 2017; Chiang et al 2017;Pironneau 2018;Murea 2019). A monolithic Eulerian approach (Pironneau 2016;Hecht and Pironneau 2017) is similar to the fully Eulerian formulation (Dunne and Rannacher 2006;Dunne 2006), presents the governing equations of FSI in terms of displacement, velocity and pressure as usual but in an Eulerian framework.…”

Recent Numerical Advances in Fluid Mechanics

“…Murea [1] presented an efficient semi-implicit monolithic method to simulate fluid-structure interaction problems within the Arbitrary Lagrangian Eulerian framework. The paper by Mohebbi et al [2] exploits an accurate implementation of Kutta conditions for the airfoils with both finite angle and cusp trailing edges.…”