An Eulerian-Lagrangian-Lagrangian method for 2D fluid-structure interaction problem with a thin flexible structure immersed in fluids. (February 2020) - Han, Dong; Liu, G.R.; Abdallah, Shaaban
Highlights: ELL overcomes the disability of IFEM to employ a reduced solid model. The ELL approach is extended to solve FSI problems with thin flexible structures. The classical CB beam element is adopted for the first time to solve FSI problem. The velocity boundary condition is explicitly imposed, more physically realistic. The widely used discretized Dirac delta function in IBM is removed. Abstract: In this paper, the Eulerian-Lagrangian-Lagrangian (ELL) method is extended to solve fluid–structure interaction (FSI) problem with a very thin flexible structure immersed in the fluid. Such a new approach overcomes the failure of the immersed finite element method (IFEM) in handling the FSI problem when a reduced solid model is used for the thin structure. In this work, a continuum-based (CB) beam theory is adopted to model the 2D flexible thin structure that undergoes large deformation. In the ELL approach, the solid meshes can always coincide with the Lagrangian fluid meshes in a so-called "composite solid" domain that allows the accurate imposing of the changing interface boundary conditions in the FSI zone. The proposed approach is verified using three benchmarking problems of flow over a flexible vertical beam, flow over a cylinder beam system and 2D flapping flag in the uniform flow. The results are compared with those from the open literature. Other numerical examples are also computed to demonstrate the effectiveness of the ELL method.