An improved immersed boundary method with new forcing point searching scheme for simulation of bodies in free surface flows

An improved immersed boundary method is proposed and applied to simulate fluid-structure interactions by combining a level set method for free water surface capturing. An efficient Navier-Stokes equation solver adopting the fractional step method at a staggered Cartesian grid system is used to solve the incompressible fluid motion. A new efficient algorithm to search forcing points near the immersed body boundary is developed. The searching schemes for forcing points located both inside and outside the solid phase with the linear interpolation schemes for the determination of velocities at forcing points are presented and compared via the case of dam break over obstacles. The accuracy and effectiveness of the proposed forcing point searching schemes are further demonstrated by the study of wave propagation over a submerged bar and more challenging cases of wedge with prescribed velocity or falling freely into the water. By the extensive comparison of present numerical results with other experimental and numerical data, it suggests that the present improved immersed boundary method with the new forcing point searching scheme has a better performance and is very promising due to its accuracy, efficiency and ease of implementation. Furthermore, the present numerical results show that the outside forcing scheme is superior over the inside forcing scheme.