In these pictures (and video in the slider) one can see the steady wave pattern calculated around two ships. The calculations are done using a two-phase URANS approach, where both water and air phases are solved and a water volume-fraction transport equations is solved. This is usually called a surface-capturing technique (or sometimes erroneously also called VOF method). In these cases the ship starts from rest and accelerates to the cruise speed, and the wave pattern develops accordingly until reaching a steady-state final solution. In ReFRESCO special compressive time-step independent convection schemes are used for the water/air transport equations, which leads to a better accuracy of the interface sharpness (less diffusion). A comparison between numerical results and experiments performed by IIHR institute can be seen in the picture below. The agreement can be considered very good.