An immersed boundary method is proposed for the simulation of the interaction of an incompressible flow with rigid bodies. The method is based on a new interpretation of velocity-vorticity formulation and no longer includes the force term which is an essential issue of common immersed boundary methods. The system is considered in an Eulerian frame and retrieving the vorticity in this formulation enforces continuity at the fluid-solid interface and rigid motion of the solid. The method focuses on the mutual kinematic relations between the velocity and vorticity fields and with retrieving the vorticity field and recalculating the velocities yields the solenoidal velocity field. The method is applied to the two dimensional problems and the results show that the solenoidality is satisfied acceptably. The comparisons with 2D test cases are provided to illustrate the capabilities of the proposed method.
