Calculation of hydrodynamic forces acting on a submerged moving object using immersed boundary method

General formulae are derived to calculate the hydrodynamic force acting on a solid object, either stationary or in motion, when an immersed boundary (IB) method is used to simulate the flow around the object. These formulae explore the fact that the imposed force term in the IB method contributes to the force applied by the object on the external fluid as well as the unsteady flow inside the virtual domain which is occupied by the object. These formulae are particularly important when the object in unsteady motion is solved in an inertial coordinate system. The formulae are adopted in the present two-dimensional (2D) numerical model, in which a SIMPLEC-type two-step computational scheme is introduced to solve the Navier–Stokes (N–S) equations. Several case studies, including the simulation of the vortex-induced vibration (VIV) of a circular cylinder, are carried out in this work. The agreement of the predicted results with the experimental and numerical data reported by other researchers proves the significance of these formulae.