A Cartesian grid-based two-dimensional plus time method for simulating ship bow waves

Numerical modeling of ship bow waves is still hard work, partly due to their multiscale features. Direct three-dimensional (3D) computational fluid dynamics simulation could be an appropriate choice to investigate the problem. However, limited by computational resources, small scale phenomena such as spraying and wave breaking that could be observed during the ship wave generation process are usually simplified or not fully distinguished in a 3D simulation. In order to accurately capture the small scales flow field information with the available computational resource, a new Cartesian grid-based two-dimensional plus time (2D+t) method is developed in this paper, which is suitable for 3D slender ships. With this method, a 3D steady ship wave-making problem is transformed into a 2D unsteady wave-making problem of a deformable body. The boundary velocity of the deformable body is obtained with a novel interpolation algorithm, which is then enforced on the background Cartesian grid by a newly proposed immersed boundary method. The pressure boundary condition on the surface of the deformable body is explicitly considered in the solution of the pressure Poisson equation. Moreover, an extra open boundary condition is applied to the upper boundary of the computational domain to achieve a better conservation. The proposed model is validated with selected cases, showing that the model is capable of simulating both non-wave-breaking and wave-breaking problems.