A hybrid hydrostatic and non-hydrostatic numerical model for shallow flow simulations. (31st May 2018) - Zhang, Jingxin; Liang, Dongfang; Liu, Hua
Abstract: Hydrodynamics of geophysical flows in oceanic shelves, estuaries, and rivers, are often studied by solving shallow water model equations. Although hydrostatic models are accurate and cost efficient for many natural flows, there are situations where the hydrostatic assumption is invalid, whereby a fully hydrodynamic model is necessary to increase simulation accuracy. There is a growing concern about the decrease of the computational cost of non-hydrostatic pressure models to improve the range of their applications in large-scale flows with complex geometries. This study describes a hybrid hydrostatic and non-hydrostatic model to increase the efficiency of simulating shallow water flows. The basic numerical model is a three-dimensional hydrostatic model solved by the finite volume method (FVM) applied to unstructured grids. Herein, a second-order total variation diminishing (TVD) scheme is adopted. Using a predictor–corrector method to calculate the non-hydrostatic pressure, we extended the hydrostatic model to a fully hydrodynamic model. By localising the computational domain in the corrector step for non-hydrostatic pressure calculations, a hybrid model was developed. There was no prior special treatment on mode switching, and the developed numerical codes were highly efficient and robust. The hybrid model is applicable to the simulation of shallow flows when non-hydrostatic pressure is predominant only in the local domain. Beyond the non-hydrostatic domain, the hydrostatic model is still accurate. The applicability of the hybrid method was validated using several study cases. Highlights: The paper "A hybrid hydrostatic and non-hydrostatic numerical model for shallow flows" focuses on the numerical approach to reduce the computational cost of the non-hydrostatic model. The main highlights are as follows: Decomposing the computational domain into hydrostatic zone and non-hydrostatic zone. Reducing the computational cost of the non-hydrostatic numerical model. Improving the accuracy of the flow simulation in estuaries or coasts compared to shallow water equation. Promoting the practical application of the non-hydrostatic numerical model to large scale flow simulation in estuaries or coasts.