Immersed Boundary Method
The idea with the immersed boundary methods (IBM) is to use a regular non fitting mesh to simulate the fluid flow around an object, and then use a Lagrangian representation of the boundary of the body (immersed boundary) to simulate the moving body. The coupling between the fluid and the surface of the body can be implemented and modeled through various approaches. We have developed the implicit second order accurate in-stationary mirroring immersed boundary (IMIB) method, which due to its implicit formulation can be solved fully coupled with the Navier-Stokes equations. The method is three dimensional and the immersed boundaries of an arbitrary shaped body can de dealt with by triangulation.
In the method a second order accurate immersed boundary condition (IBC) mirrors the velocity field along the normal of the local triangulated surface of the body (immersed boundary), such that the fluid exactly follows the immersed boundary. The IBC generates a reversed velocity field inside the immersed boundary and special treatment is adopted to solve this fictitious velocity field such that the mass is conserved in the cells containing the immersed boundary. The immersed bodies are moved and rotated at each time-step as the result of the calculated fluid, collision and gravity forces.