A partitioned coupling approach for dynamic fluid–structure interaction with applications to biological membranes

Abstract

SUMMARYThis paper presents a fully coupled three-dimensional solver for the analysis of time-dependent fluidstructure interaction. A partitioned time-marching algorithm is employed for the solution to the timedependent coupled discretized problem, thus enabling the use of highly developed, robust and well-tested solvers for each field. Coupling of the fields is achieved through a conservative transfer of information at the fluid-structure interface. An implicit coupling is achieved when the solutions to the fluid and structure subproblems are cycled at each time step until convergence is reached. The three-dimensional unsteady incompressible fluid is solved using a powerful implicit dual time-stepping technique with an explicit multistage Runga-Kutta time stepping in pseudo-time and arbitrary Lagrangian-Eulerian formulation for the moving boundaries. A finite element dynamic analysis of the highly deformable structure is carried out with a numerical strategy combining the implicit Newmark time integration algorithm with a NewtonRaphson second-order optimization method. Various test cases are presented for benchmarking and to demonstrate the potential applications of this method.

Towards a Fluid-Structure Interaction Solver for Problems with Large Deformations Within the Open-Source SU2 Suite

“…The convergence criteria on the interface is set to 1/1000 of the cantilever thickness, which generally requires between 4 to 5 iterations to converge. A staggered approach was found to diverge for a time step ∆t = 0.0075 s. Two subiterations of the BGS method, however, were enough to maintain the stability of the simulation for all the tested cases, which matches the reported by Wood et al 23 The structure is integrated using a Newmark time integration procedure as explained in section III.B.1, incorporating a 2% numerical damping in order to prevent the divergence of the solver due to high frequency structural effects. The solver is started from a slightly perturbed, symmetric fluid state, previously computed with a static beam in order to avoid non-physical transient effects due to the initialization of the fluid solver.…”

“…In order to address the verification and validation of the fluid solver with an ALE formulation, the reader may refer to section V.A.5 in the paper by Palacios et al 20 To investigate the implementation of the FSI problem, we will study the behavior of a flexible beam attached on the downwind side of a rigid square, a problem that has been used extensively as benchmark for Fluid-Structure Interaction applications. 14,18,23,26,39,41,63 …”

“…23 On the one hand, it is possible to adopt a monolithic approach, thus solving simultaneously the fluid and structural equations while imposing the interface conditions. This approach is robust and accurate, and has been proven to be more efficient in some applications in biomechanics.…”

Assessment of the Fluid-Structure Interaction Capabilities for Aeronautical Applications of the Open-Source Solver Su2.

“…No experimental data is available for frequencies higher than 10 Hz. In order to test our native implementation of the FSI solver for deformable solids within SU2, we focus on a well-known benchmark test case first proposed by Wall and Ramm [71] (see, for example, [35,44,[72][73][74][75]). They investigated the dynamics of a flexible cantilever attached to the downwind side of a square cylinder in a low-speed flow, as described in Fig.…”

Special issue on biofluid dynamics

“…The paper by Appanaboyina et al [1] deals with an embedded griding technology for complex problems of blood flow and the article by Gambaruto et al [2] attempts to quantify the uncertainties associated with segmentation and reconstruction of arterial conduits. The articles by Lee et al [3] and Barth et al [4] deal with fluid flow in model geometries, relevant to blood flow and the paper by Wood et al [5] discusses a partitioned method for the interaction of fluid and membranes.…”