A two-dimensional coastal ocean model based on unstructured C-grid is built, in which the momentum equation is discretized on the faces of each cell, and the continuity equation is discretized on the cell. The model is discretized by semi-implicit finite volume method, in that the free surface is semi-implicit and the bottom friction is implicit, thereby removing stability limitations associated with the surface gravity wave and friction. The remaining terms in the momentum equations are discretized explicitly by integral finite volume method and second-order Adams-Bashforth method. Tidal flow in the polar quadrant with known analytic solution is employed to test the proposed model. Finally, the performance of the present model to simulate tidal flow in a geometrically complex domain is examined by simulation of tidal currents in the Pearl River Estuary.
In this study, porosity was introduced into two-dimensional shallow water equations to reflect the effects of obstructions, leading to the modification of the expressions for the flux and source terms. An extra porosity source term appears in the momentum equation. The numerical model of the shallow water equations with porosity is presented with the finite volume method on unstructured grids and the modified Roe-type approximate Riemann solver. The source terms of the bed slope and porosity are both decomposed in the characteristic direction so that the numerical scheme can exactly satisfy the conservative property. The present model was tested with a dam break with discontinuous porosity and a flash flood in the Toce River Valley. The results show that the model can simulate the influence of obstructions, and the numerical scheme can maintain the flux balance at the interface with high efficiency and resolution.
The spatiotemporal characteristics of bridge deck runoff under a natural rainfall event are explored. The Taizhou Bridge is taken as a study case,and a hydrodynamic model based on the two-dimensional shallow water equations is used to analyze the runoff characteristics. The results indicate that the runoff velocity rate and depth are positively related to rainfall intensity,yet they have different response degrees to it. The inlet’s effect degree on lane water film has a positive relationship with rainfall intensity. A natural logarithm function( R^2= 0.706) can illustrate this relationship. However,the inlet’s effect degree on ponding at the curb shows a negative relationship with the rainfall intensity. A negative exponential function( R^2= 0.824) can reveal this relationship. With the decrease in the longitudinal slope SL,the ponding depth at the curb increases significantly at the bridge approach slab,whereas the lane water film thickness( WFT) is almost unchanged,but the lane WFT increases greatly at the location with the minimum longitudinal slope. It is concluded that the characteristics of the bridge deck runoff present apparent spatiotemporal differences,the inlet ’s effects on bridge deck runoff are quantitatively correlated with rainfall intensity, and the effective drainage measures are necessary for the bridge approach slab.
