A Loosely Coupled Scheme for Fictitious Domain Approximations of Fluid-Structure Interaction Problems with Immersed Thin-Walled Structures

Abstract

Fictitious domain approximations of fluid-structure interaction problems are generally discretized in time using strongly coupled schemes. This guarantees unconditional stability but at the price of solving a computationally demanding coupled system at each time-step. The design of loosely coupled schemes (i.e., methods that invoke the fluid and solid solvers only once per time-step) is of fundamental interest, especially for three-dimensional simulations, but the existing approaches are known to suffer from severe stability and/or time accuracy issues. We propose a new approach that overcomes these difficulties in the case of the coupling with immersed thin-walled structures.

An unfitted mesh semi‐implicit coupling scheme for fluid‐structure interaction with immersed solids

“…Now, since the fluid bulk terms of the viscous step (15) are integrated (only) in the physical domain and using (24), it can alternatively writen as…”

“…The second numerical example corresponds to the idealized valve test with contact introduced in 45 . It is an extension of the previous one in which the structure is sufficiently long to get in contact with Γ sym .…”

“…This is a direct consequence of the weak treatment of the kinematic interface coupling. To the best of our knowledge, the sole available approaches are the splitting methods introduced in 5,22,23,24 for the immersed boundary or fictitious domain methods, and in 18,19,25,26 for unfitted Nitsche based methods. The loosely coupled schemes reported in 5,18,19,25,23 are known to enforce severe time-step restrictions for stability/accuracy or to be sensitive to the amount of added-mass effect.…”

“…The loosely coupled schemes reported in 5,18,19,25,23 are known to enforce severe time-step restrictions for stability/accuracy or to be sensitive to the amount of added-mass effect. In the case of the coupling with thin-walled solids, these issues are circumvented by the semi-implicit and loosely coupled schemes reported in 22,19,26 and in 24 , respectively. Nevertheless, the former introduces additional unknowns in the fluid sub-problem (intermediate solid velocity) and the accuracy of the latter relies on a grad-div penalty term (for enhanced mass conservation) which spoils the conditioning of the fluid problem.…”

Machine Learning design of Volume of Fluid schemes for compressible flows

“…and even a non Lipschitz profile to emulate a simple triple point geometry. The new VOF-ML schemes are restricted to the dimension d " 2 on uniform Cartesian grids, however the proposed methodology can be used a priori for the reconstruction of internal boundaries in many fields, like in references [3,5] and references therein.…”