Robin‐Neumann transmission conditions for fluid‐structure coupling: Embedded boundary implementation and parameter analysis

Abstract

Partitioned procedures are appealing for solving complex fluid-structure interaction (FSI) problems, as they allow existing computational fluid dynamics (CFD) and computational structural dynamics algorithms and solvers to be combined and reused. However, for problems involving incompressible flow and strong added-mass effect (eg, heavy fluid and slender structure), partitioned procedures suffer from numerical instability, which typically requires additional subiterations between the fluid and structural solvers, hence significantly increasing the computational cost. This paper investigates the use of Robin-Neumann transmission conditions to mitigate the above instability issue. Firstly, an embedded Robin boundary method is presented in the context of projection-based incompressible CFD and finite element-based computational structural dynamics. The method utilizes operator splitting and a modified ghost fluid method to enforce the Robin transmission condition on fluid-structure interfaces embedded in structured non-body-conforming CFD grids. The method is demonstrated and verified using the Turek and Hron benchmark problem, which involves a slender beam undergoing large transient deformation in an unsteady vortex-dominated channel flow. Secondly, this paper investigates the effect of the combination parameter in the Robin transmission condition, ie, f , on numerical stability and solution accuracy. This paper presents a numerical study using the Turek and Hron benchmark problem and an analytical study using a simplified FSI model featuring an Euler-Bernoulli beam interacting with a two-dimensional incompressible inviscid flow. Both studies reveal a trade-off between stability and accuracy: smaller values of f tend to improve numerical stability, yet deteriorate the accuracy of the partitioned solution. Using the simplified FSI model, the critical value of f that optimizes this trade-off is derived and discussed.KEYWORDS embedded boundary method, fluid-structure interaction, numerical added-mass effect, partitioned procedure, Robin-Neumann transmission conditions 578

A spatially varying robin interface condition for fluid‐structure coupled simulations

“…Remark: A simpler version of this problem, in which the beam has uniform density and is a constant, has been solved both numerically and analytically (e.g., [33,23]). Cao et al [23] have derived the value of that optimizes the trade-off between numerical stability and accuracy, i.e.…”

“…To circumvent this difficulty, we apply the method of manufactured solutions (e.g., [34]). Specifically, we "manufacture" the following closed-form solutions based on a simpler version of the problem with a uniform beam, which can be solved analytically [23].…”

“…Over the past decade, several research teams have investigated the use of a Robin interface condition to mitigate the numerical added mass effect [18,19,5,20,21,22,23,24,25,26,27,28,29,30]. The basic idea is to substitute the kinematic interface condition by its linear combination with the dynamic interface condition.…”

“…Nobile et al [19,5,20] and Fernandez et al [21,22] have introduced the Robin interface condition to different types of partitioned procedures and fluid/structural governing equations, and demonstrated their performance in the context of blood flow -vessel wall interaction. To solve FSI problems involving complex geometry and large deformation, Cao et al [23] have developed an algorithm to enforce the Robin interface condition using an embedded boundary method. We have also shown that when choosing the value of , there is a trade-off: smaller values of tend to improve numerical stability, while larger values give smaller numerical errors.…”

“…Examples include uniform beams and thin-walled tubes with constant thickness, density and elastic moduli. Several authors have suggested that in order to mitigate the numerical added mass effect, the value of Robin combination factor must be determined based on the material and geometry of the specific problem being solved (e.g., [18,26,23]). However, previous discussions have been focused on designing and applying a constant for the entire fluid-structure interface.…”