Partitioned formulation of internal and gravity waves interacting with flexible structures

Partitioned vibration analysis of internal fluid‐structure interaction problems

“…Here, N f and N s denote the shape functions of the fluid and structure displacement elements, respectively, evaluated on the discretized interface surface b . In some cases, as in curved geometries, the discretized interface may differ slightly from the original one [35]. The integral evaluations in (60)-(63) are greatly simplified by assuming that N f and N s are Dirac delta functions collocated at the fluid and structure interface nodes, respectively.…”

“…In summary, the proposed finite element approach provides second-order accuracy, thanks to the inclusion of the geometrical stiffness term (35). It was found that resonance and a high value of the steepness parameter Ä s > 0.1 lead to significantly nonlinear behavior.…”

“…After a brief introduction of the problem statement and its variational form of the present partitioned continuum‐based formulation in Sections 2 and 3, a detailed continuum‐based derivation of Lagrangian fluid equations is presented in Section 4. While the present derivation begins with an earlier continuum‐based Lagrangian description of an earlier work , several noteworthy refinements and implementation details are presented. First, the surface traction term on the free surface that is often approximated by the Laplace–Young surface tension formula is removed by invoking the equilibrium condition between the free‐surface pressure and the traction terms from the continuum variational term.…”

“…For treatment of FSI interfaces, various techniques have been proposed. These range from tightly coupled monolithic schemes to loosely coupled partitioned procedures [17,20,21,23,[29][30][31][32][33][34][35][36].In developing a partitioned formulation of FSI analysis and after surveying previous work on internal FSI problems, the present authors identified in an earlier work [35] that a more general and computationally modular approach should possess the following desirable attributes. First, formulations and computer implementation for each of the coupled components (fluid and structure in our case) should be stand-alone, with coupling terms modularly separated from each component.…”

“…For treatment of FSI interfaces, various techniques have been proposed. These range from tightly coupled monolithic schemes to loosely coupled partitioned procedures [17,20,21,23,[29][30][31][32][33][34][35][36].…”