An improved ALE and CBS-based finite element algorithm for analyzing flows around forced oscillating bodies

A finite element algorithm based on characteristic based split (CBS) scheme, in combination with arbitrary Lagrangian–Eulerian (ALE) framework, is presented to deal with numerical oscillation and mesh moving, and the complicated flow patterns are given, as studying the flow around oscillating circular cylinders, which are the typical fluid–structure interaction and encountered frequently in the engineering. Following this method, the two-dimensional incompressible Navier–Stokes equations (NSEs) are derived under the ALE reference frame, and consequently the CBS scheme in ALE configuration is given to approach the NSEs in some details. After such transformation, the convective terms can be removed from the original NSEs and the resulting equations become simple diffusion equations, which can be efficiently approached by the standard finite element method. Then, the finite element method is applied to the governing equations obtained, with the aid of an improved moving mesh technique implemented by the modified spring analogy to deal with the coupling between fluid and structure surfaces. Finally, some numerical examples related to flows around stationary and oscillating circular cylinders are simulated with the presented method, in comparison with existing numerical and experimental results. Additionally, the flow patterns of the oscillating cylinder wake are analyzed tentatively to study the evolution of unsteady vortices, which can induce the oscillation of the structures. The results show that the presented algorithm is feasible and efficient for flow around moving bodies, which includes two main typical problems, namely, the numerical oscillation and mesh moving.