A general method for simulation of fluid flows with moving and compliant boundaries on unstructured grids

In this paper a method for simulating fluid-structure interaction is described. The numerical model is based on a 2D Navier-Stokes incompressible flow solver on unstructured moving grid using the arbitrary Lagrangian Eulerian (ALE) approach. A high-order upwind characteristics-based finite volume scheme and an implicit dual time stepping method are employed for the simulation of unsteady flows and the fluid-structure interaction. Furthermore, a new dynamic mesh method is adopted to handle large deformation of the flow field. With the dynamic mesh method, the efficiency of unsteady flow simulation is significantly improved and more complex fluid-structure interaction problems can be easily tackled. The dynamic mesh method and the solver are validated for an unsteady channel flow with a moving indentation. It is observed that the dynamic mesh method is very robust and able to handle large deformation without excessive distortion of the dense mesh near the wall. In order to study fluid flow in a channel with an elastic membrane wall and their interaction, a new membrane model has been adopted, which can be applied to calculate arbitrary wall movement and variable tension along the membrane. The membrane equation is also solved by the same implicit dual time stepping scheme for improved stability and efficiency. It is shown that the proposed method is able to simulate unsteady flow with self-excited oscillations that develop in a collapsible channel. High-frequency flutter is found in all the cases studied, which is in the form of travelling waves along the membrane. And the flutter is superimposed on lower-frequency large-amplitude oscillation due to the wall inertia and its tension. The travelling waves tend to have larger amplitude and higher frequency with increased inertia and reduced tension.