Adaptive mesh refinement for simulating fluid-structure interaction using a sharp interface immersed boundary method

In this article, adaptive mesh refinement (AMR) is performed to simulate flow around both stationary and moving boundaries. The finite-difference approach is applied along with a sharp interface immersed boundary (IB) method. The Lagrangian polynomial is employed to facilitate the interpolation from a coarse to a fine grid level, while a weighted-average formula is used to transfer variables inversely. To save memory, the finest grid is only generated in the local areas close to the wall boundary, and the mesh is dynamically reconstructed based on the location of the wall boundary. The Navier-Stokes equations are numerically solved through the second-order central difference scheme in space and the third-order Runge-Kutta time integration. Flow around a circular cylinder rotating in a square domain is firstly simulated to examine the accuracy and convergence rate. Then three cases are investigated to test the validity of the present method: flow past a stationary circular cylinder at low Reynolds numbers, flow past a forced oscillating circular cylinder in the transverse direction at various frequencies, and a free circular cylinder subjected to vortex-induced vibration in two degrees of freedom. Computational results agree well with these in the literature and the flow fields are smooth around the interface of different refinement levels. The effect of refinement level has also been evaluated. In addition, a study for the computational efficiency shows that the AMR approach is helpful to reduce the total node number and speed up the time integration, which could prompt the application of the IB method when a great near-wall spatial resolution is required.