In this paper, adaptive mesh refinement (AMR) is performed to simulate flows 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 fine to coarse grid levels, while a weighted-average formula is used to transfer variables inversely to keep the law of conservation. 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. Three cases are investigated to check the validity of the present method: flows past a stationary circular cylinder at low Reynolds number, a forced oscillating circular cylinder in the transverse direction and a free circular cylinder subjected to vortex-induced vibration in two degrees of freedom. Computational results agree well with literature and the flow fields are smooth around interfaces of different levels of refinement. Study for computational efficiency shows that the AMR approach is helpful to reduce the total grid number and speed up the time integration.

在本文中，执行自适应网格细化（AMR）来模拟围绕固定边界和移动边界的流动。有限差分方法与锋利的界面沉浸边界（IB）方法一起应用。拉格朗日多项式用于简化从细网格到粗网格的插值，而加权平均公式则用于逆向传递变量，以保持守恒定律。为了节省内存，仅在靠近墙边界的局部区域中生成最细的网格，然后根据墙边界的位置动态重建网格。Navier-Stokes方程是通过空间中的二阶中心差分方案和三阶的Runge-Kutta时间积分来数值求解的。研究了三种情况以检查本方法的有效性：流体流过一个低雷诺数的固定圆柱体，一个横向受力振荡的圆柱体以及一个受到两个自由度涡旋振动的自由圆柱体。计算结果与文献吻合得很好，并且流场在不同精炼水平的界面附近是平滑的。对计算效率的研究表明，AMR方法有助于减少总网格数并加快时间整合。