An Immersed-Boundary Finite-Volume Method for Simulations of Flow in Complex Geometries

A new immersed-boundary method for simulating flows over or inside complex geometries is developed by introducing a mass source/sink as well as a momentum forcing. The present method is based on a finite-volume approach on a staggered mesh together with a fractional-step method. Both momentum forcing and mass source are applied on the body surface or inside the body to satisfy the no-slip boundary condition on the immersed boundary and also to satisfy the continuity for the cell containing the immersed boundary. In the immersed-boundary method, the choice of an accurate interpolation scheme satisfying the no-slip condition on the immersed boundary is important because the grid lines generally do not coincide with the immersed boundary. Therefore, a stable second-order interpolation scheme for evaluating the momentum forcing on the body surface or inside the body is proposed. Three different flow problems (decaying vortices and flows over a cylinder and a sphere) are simulated using the immersed-boundary method proposed in this study and the results agree very well with previous numerical and experimental results, verifying the accuracy of the present method.