Improved Implicit Immersed Boundary Method via Operator Splitting

We present an implicit immersed boundary method via operator splitting technique for simulating fluid flow over moving solid with complex shape. An additional moving force equation is derived in order to impose the interface velocity condition exactly on the immersed surface. The moving force matrix is formulated to be symmetric and positive definite, thus its calculation is computational inexpensive by using the conjugate gradient method. Moreover, the proposed immersed boundary method is incorporated into the rotational incremental projection method as a plug-in. No numerical boundary layers will be generated towards the velocity and pressure during the calculation. The method is validated through various benchmark tests.