An immersed boundary method coupled non-hydrostatic model for free surface flow

Abstract

An efficient numerical model has been developed for the study of three-dimensional free surface flow, which combines a non-hydrostatic model with the immersed boundary method (IBM). The model utilizes the transformed σ coordinate in the vertical direction, which has been found to be highly effective in accurately capturing the free surface and uneven bottom. In addition, IBM is implemented by introducing a virtual boundary force into the momentum equations to emulate the natural boundary conditions. This implementation enhances the ability of the model in simulating the interactions of wave and solid structures. A robust boundary recognition method is used to identify the location of IB cells neighboring the virtual boundary. Furthermore, a water elevation correction method has been proposed to handle the integral discontinuity in the vertical direction caused by the submerged solid bodies. By adding the virtual boundary forces to the IB cells, the no-slip velocity condition at the solid boundary is effectively enforced. To validate the performance of the model, the numerical results have been compared with experimental data. The benchmark tests focused on the free surface evolution, velocity distributions and the dynamic pressures verified the performance of the numerical model and the robust strategy of the IBM.