A semi-implicit three-dimensional numerical model for non-hydrostatic pressure free-surface flows on an unstructured, sigma grid

A semi-implicit 3-D numerical formulation for solving non-hydrostatic pressure free-surface flows on an unstructured, sigma grid is proposed. Pressure-splitting and θ semi-implicit methods are inherited and reformed from Casulli's z-coordinate formulation. The non-orthogonal sigma-coordinate transformation leads to additional terms. The resulting linear system for the non-hydrostatic correction is diagonally dominant but unsymmetric, and it is solved by the BiCGstab method. In contrast with z-coordinate non-hydrostatic models, the new model fits vertical boundaries much better, which is important for the long-time simulation of sediment transport and riverbed deformation. A lock-exchange density flow is computed to determine whether the new scheme is able to simulate non-hydrostatic free-surface flows. The new model is further verified using the field data of a natural river bend of the lower Yangtze River. Good agreement between simulations and earlier research results, field data is obtained, indicating that the new model is applicable to hydraulic projects in real rivers.