Non-hydrostatic versus hydrostatic modelings of free surface flows

The hydrodynamics of geophysical flows in oceanic shelves, estuaries, and rivers are often studied by solving shallow water equations under either hydrostatic or non-hydrostatic assumptions. Although the hydrostatic models are quite accurate and cost-efficient for many practical applications, there are situations when the fully hydrodynamic models are preferred despite a larger cost for computations. The present numerical model is implemented by the finite volume method (FVM) based on unstructured grids. The model can be efficiently switched between hydrostatic and non-hydrostatic modules. The case study shows that for waves propagating along the bar a criterion with respect to the shallowness alone, the ratio between the depth and the wave length, is insufficient to warrant the performance of shallow flow equations with a hydrostatic approach and the nonlinearity in wave dynamics can be better accounted with a hydrodynamic approach. Besides the prediction of the flows over complex bathymetries, for instance, over asymmetrical dunes, by a hydrodynamic approach is shown to be superior in accuracy to the hydrostatic simulation.