AN APPLICATION OF THE CBS SCHEME IN THE FLUID-MEMBRANE INTERACTION

A finite element scheme for the fluid-membrane interaction is proposed. First, governing equations for the incompressible flow and the elastic membrane are presented. Then, the proposed algorithm is discussed in detail. By this method, an improved characteristic-based split (CBS) scheme is combined with the dual-time stepping method and taken as the flow solver, and the Aitken method is applied to accelerate the convergence of the iteration. The governing equation of the structure is discretized by the Galerkin finite element method and the Generalized-α method, and the obtained nonlinear algebraic equations are solved by the Newton-Raphson method. Moreover, the spring analogy method is used for mesh moving, and the flow and structure solvers are loosely coupled. Finally, the proposed method is applied to a benchmark problem, namely, the driven cavity with flexible bottom, and the stability and accuracy of the proposed method are verified. In addition, it is found that the convergence rate of the flow solver can be increased significantly by the Aitken method.