Immersed boundary method for flow around an arbitrarily moving body

For the simulation of flow around an arbitrarily moving body, an immersed boundary method is developed in a non-inertial reference frame that is fixed to the body. The Navier–Stokes equation is formulated in a conservative form such that the force terms due to the rotation and the translational and rotational accelerations are included in the nonlinear term. In order to satisfy the no-slip condition on the body surface, momentum forcing and mass source/sink are applied on the body surface or inside the body. The numerical method is based on a finite volume approach on a staggered mesh together with a fractional-step method. The present numerical method is applied to both the forced motion and fluid–structure interaction problems. In the latter, we solve fully coupled Navier–Stokes and dynamic equations for the moving body without introducing any iteration. Four different flow problems are tested and the results are in excellent agreements with previous numerical and experimental ones.