Combined interface boundary condition method for fluid–rigid body interaction

This research is motivated by the recent work which has presented a new loosely-coupled partitioned algorithm for fluid–structure interaction (FSI) [R. Jaiman, P. Geubelle, E. Loth, X. Jiao, Combined interface boundary condition method for unsteady fluid–structure interaction, Comput. Methods Appl. Mech. Engrg. 200 (2011) 27–39]. The loosely-coupled partitioned algorithm is intrinsically exposed to the notorious time lag effect whose remedy promotes the combined interface boundary condition (CIBC) method. In this method, correction terms for velocity and traction are introduced at two sequential time steps with a coupling parameter ω that plays an important part in the stability and accuracy of the coupled system. The structural traction ratio that appears explicitly in the traction correction is estimated based on the solution of the structural subsystem. This handling asks for the structural traction before it is corrected by the CIBC method. In this paper, a new formulation for the CIBC method is developed to repair the aforementioned inconvenience. After simple manipulation, the structural traction ratio is removed in constructing the traction correction. Therefore the structural traction is no more needed in CIBC correction terms. Meantime the ratio ω/Δt is employed to tune the interfacial corrections instead of the coupling parameter ω. An arbitrary Lagrangian–Eulerian finite element method is used to analyze FSI. The characteristic-based split (CBS) scheme is employed to solve incompressible Navier–Stokes equations while the equation for rigid-body dynamics is solved by Newmark-β method. A numerical technique called moving submesh approach is performed for the mesh deformation. For respecting geometric conservation law, a mass source term is implanted into the CBS scheme on the moving mesh. Several numerical examples are tested to validate the proposed methodology for fluid–rigid body interaction. The obtained results are in agreement with the existing data and some famous features of flow phenomena have been detected successfully.