刚体-流体耦合运动的浸入边界法研究

为避免复杂贴体网格的生成和动、静界面滑移网格技术插值带来的误差，提出采用浸入边界法模拟流体刚体的耦合运动.借助求解不可压缩N-S方程组的分步投影方法的思想，来求解基于浸入边界法的耦合系统方程.其中刚体边界离散点的作用力密度通过强制满足刚体边界的无滑移条件（位移和速度一致）导出，结合刚体定轴旋转的动量矩定理，采用Newmark时间积分方法，实现对刚体运动特性的预测.同时，通过δ光滑函数，将刚体边界离散点的作用力密度转换到流体的欧拉网格点上，实现对流场速度的修正.在空间离散上，对流项采用Quick迎风格式，扩散项采用中心差分格式，采用2阶显式Adams-Bashforth法离散时间项.以雷诺数为300的圆柱绕流为基准数值算例，验证数值计算结果的可靠性. 

Numerical Simulation of Rigid Body and Fluid Coupling Using Immersed Boundary Method

To avoid the deviation produced in the traditional body-fitted numerical methods and the complex interpolation for sliding mesh on the interface between stator and rotor, a new numerical simulation method was presented for studying on free rotation of rigid body about a fixed axis under fluid force. A mathematical model was established to describe the interaction between immersed rigid body and fluid based on the projection step method. In this paper, the moment source was not pre-calculated, but determined implicitly in such a way that velocity at the immersed boundary interpolated from the corrected velocity field accurately satisfied the no slip boundary conditions, also, the displacement and velocity of rigid body was updated according to the theorem of moment of momentum. The Quick upwind scheme and the second central scheme were applied to solve convection and diffusion terms respectively. The second explicit Adams-Bashforth method was used to the time discretization. Taking the flow over one circular cylinder with Reynolds number 300 as the basic numerical example, the present immersed boundary method(IBM) was validated.