Methodology for Comparing Coupling Algorithms for Fluid-Structure Interaction Problems

Abstract

The multi-physics simulation of coupled fluid-structure interaction problems, with disjoint fluid and solid domains, requires one to choose a method for enforcing the fluid-structure coupling at the interface between solid and fluid. While it is common knowledge that the choice of coupling technique can be very problem dependent, there exists no satisfactory coupling comparison methodology that allows for conclusions to be drawn with respect to the comparison of computational cost and solution accuracy for a given scenario. In this work, we develop a computational framework where all aspects of the computation can be held constant, save for the method in which the coupled nature of the fluid-structure equations is enforced. To enable a fair comparison of coupling methods, all simulations presented in this work are implemented within a single numerical framework within the deal.ii [1] finite element library. We have chosen the two-dimensional benchmark test problem of Turek and Hron [2] as an example to examine the relative accuracy of the coupling methods studied; however, the comparison technique is equally applicable to more complex problems. We show that for the specific case considered herein the monolithic approach outperforms partitioned and quasi-direct methods; however, this result is problem dependent and we discuss computational and modeling aspects which may affect other comparison studies.

A hybridizable discontinuous Galerkin method for modeling fluid–structure interaction

“…Michler [48] showed that, for a simple one dimensional FSI problem, "the computational cost of the monolithic procedure is three to four times the one of the partitioned procedure;" however, his monolithic results were far more accurate than his weakly coupled partitioned results. Michler hypothesized that for more complex problems the monolithic approach would be superior in a comparison of computational cost to accuracy, and the author's prior work in [49,50] showed this hypothesis to be true in some circumstances.…”

An automated selection algorithm for nonlinear solvers in MDO

“…4 (wing with 35 • sweep and 1.5 cm spar thickness). To simulate implementations in which the CN approach is more competitive compared to the NLBGS approach (similar to the approaches and problems used in the studies cited in the introduction (Fernández and Moubachir, 2005;Heil et al, 2008;Sheldon et al, 2014;Kenway et al, 2014)), we run the same problem with the NLBGS iterations slowed down by adding pauses to the solver code. Figures 7b and 7c show the results with each NLBGS iteration slowed down by 0.02 and 0.04 seconds, respectively (approximately 5 and 10 times the time for one NLBGS iteration on the computer used).…”

“…There have been various studies in FSI that show the promise of CN approaches (Heil, 2004;Heil et al, 2008;Fernández and Moubachir, 2005;Bazilevs et al, 2006;Sheldon et al, 2014). Fernández and Moubachir (2005) compare NLBGS and CN approaches for the transient flow in a thin elastic vessel that is representative of blood flow in large arteries.…”

“…Additionally, the CN approach is shown to be more robust and efficient for unsteady problems, while the NLBGS approach diverges rapidly unless strong under-relaxation is applied. Sheldon et al (2014) compare NLBGS and CN approaches using an unsteady flow benchmark (Turek and Hron, 2006). Their results show that the NLBGS approach (with Aitken's acceleration) requires over four times more CPU time than the CN approach.…”

A Hybrid Reduced-Order Model for the Aeroelastic Analysis of Flexible Subsonic Wings—A Parametric Assessment

“…Fluid-structure interaction (FSI) [8] models coupling finite element methods (FEM) [9] and computational fluid dynamics (CFD) [10] have increasingly been proposed to enhance accuracy [11,12]. However, these high-fidelity tools are computationally expensive [13,14] and require special care [15,16] to ensure that the correct physics are reproduced in their coupling [17,18], especially at all boundaries and interfaces [19,20]. A large amount of time and efforts is then typically necessary for pre-processing the simulations and post-processing the results, which are key features for a reliable implementation of automated MDO routines [21].…”