A three-dimensional non-hydrostatic mathematical model with mixed triangle and quadrilateral grids

The three-dimensional numerical models based on the hydrostatic pressure hypothesis can't accurately and effectively simulate the cases of estuaries or natural rivers with the presence of short wave flow, stratified gravity flow, sudden change of local topography or flow near underwater buildings. Therefore it is useful to resort to a more accurate model in which the hydrostatic assumption is removed. Based on the mixed grids of triangle and quadrilateral, a three-dimensional non hydrostatic mathematical model is presented. The control equations are discretized by the semi-implicit fractional step method. The pressure is divided into the hydrostatic pressure and non-hydrostatic pressure terms. At each step, the water level is calculated by solving the sparse equations, and then the non-hydrostatic pressure is obtained by the pressure Poisson equation. Three typical examples were adopted to simulate strong three-dimensional flow. As a result, the results show that the model can accurately and effectively simulate strong three-dimensional flow with a few layers.