Depth-integrated, non-hydrostatic model using a new alternating direction implicit scheme

The hydrostatic pressure assumption has been widely applied in simulating rivers, lakes and reservoirs, but it has been found inappropriate in various cases where the vertical acceleration is significant. This paper presents a depth-integrated, non-hydrostatic model using a new alternating direction implicit scheme. Using the proposed scheme, each step is split into two half steps. In the first half step, the dynamic pressure and the x-direction velocity in the continuity equation and the momentum equations in the x-direction and z-direction are expressed implicitly, and the others explicitly; in the second half step, the dynamic pressure and the y-direction velocity in the continuity equation and the momentum equations in the y-direction and z-direction are discretized implicitly, and the others explicitly. The Thomas algorithm is applied to solve the tri-diagonal linear system at each half step. The model is developed and validated with several analytical solutions and laboratory experiments. The results show that the model can provide comparable results at very low computational cost.