An embedded Finite Element framework for the resolution of strongly coupled Fluid–Structure Interaction problems. Application to volumetric and membrane-like structures

A memory-efficient MultiVector Quasi-Newton method for black-box Fluid-Structure Interaction coupling

“…4 and 5 some snapshots of the kvk and p fields, together with the deformed geometry, for one of the IQN MVQN-RZ cases. As it can be observed, the results are in agreement with the expected ones [14,33].…”

“…A mesh conformed by 65.5 k linear triangular elements (Q1P1) 1 is used for the discretization of the fluid domain while 6.4 k linear quadrilateral elements are used in the discretization of the structure domain. The meshes we use for this example are identical to the finest ones used for the mesh convergence study presented in [14].…”

“…Per regards the discretization of the fluid domain, the combination of Arbitrary Lagrangian-Eulerian (ALE) formulations [1][2][3][4] with mesh motion techniques [5][6][7][8] is probably the most popular alternative. However, ALE methods tend to suffer from mesh entanglement problems when the deformations of the domain become important, something that motivated the development of alternatives such as the IBM [9,10], the eXtended Finite Element Method (XFEM) [11,12], the CutFEM [13,14], the purely Lagrangian approaches [15][16][17][18][19][20] or the hybrid alternatives presented in [21,22]. Moreover, recently the field has been enriched by the so called Immersogeometric analysis, which addresses the use of exact geometries in the representation of the structural domain [23,24].…”

A discontinuous Nitsche‐based finite element formulation for the imposition of the Navier‐slip condition over embedded volumeless geometries

“…Finally, it is interesting to point out the further enhancements and future work lines. The first one is to couple the proposed methodology with an structural mechanics solver to build an FSI framework for the analysis of highly flexible membrane and shell structures 50 . Another interesting application is the modeling of the fluid flow around thin biological tissues 3 or cardiac valves 32,66 .…”

“…Instead, we focus on the proposed discontinuous Navier‐slip formulation details as well as on its validation, which we carry out by comparing its performance with the approaches in References 44 and 47. We refer the reader to Reference 50 for the extension of current formulation to FSI problems.…”