We present an immersed boundary projection method for flow-structure interaction problems involving rigid bodies with complex geometries. Dynamics of a rigid body interacting with fluid flow and kinematics of other rigid bodies undergoing prescribed motions are coupled implicitly with the incompressible vorticity equations. In particular, the method is formulated in a frame of reference fixed on the rigid body under flow-structure interaction (the target) so that the coupled system can be solved non-iteratively, accurately, and efficiently. The implicit coupling of the fluid solver and dynamics and kinematics of rigid bodies ensures the method being stable for low solid-to-fluid mass ratios. The influence of fictitious fluid inside the rigid body is considered and the spurious oscillations in surface stresses are filtered to impose physically correct rigid body dynamics. Similar to many predecessors of the immersed boundary projection method, the resulting discrete system is solved efficiently using a block-LU decomposition. We then validate the method with two-dimensional test problems of a neutrally buoyant cylinder migrating in a planar Couette flow and a freely falling or rising cylindrical rigid body.

我们提出了一种浸入式边界投影方法，用于涉及具有复杂几何形状的刚体的流固耦合问题。与流体流动相互作用的刚体的动力学和经历规定运动的其他刚体的运动学与不可压缩的涡度方程式隐式耦合。特别地，该方法在流动-结构相互作用（目标）下固定在刚体上的参考系中制定，从而可以非迭代，精确和有效地求解耦合系统。流体求解器与刚体的动力学和运动学之间的隐式耦合确保了该方法对于低的固液比是稳定的。考虑了虚拟流体在刚体内部的影响，并过滤了表面应力中的虚假振荡，以施加物理上正确的刚体动力学。与沉浸式边界投影方法的许多前辈相似，使用块LU分解可以有效地解决所得离散系统。然后，我们用二维测试问题验证了该方法，该问题是中性浮力圆柱在平面Couette流中迁移以及自由下降或上升的圆柱刚体。