Diagonal Cartesian method for the numerical simulation of flow and suspended sediment transport over complex boundaries

There is increasing demand for simulation tools of flow and suspended sediment transport over complex boundaries in hydraulic engineering. The diagonal Cartesian method, which approximates complex boundaries using both Cartesian grid lines and diagonal lines segments, is presented in the paper to simulate the complex boundaries of two-dimensional shallow-water turbulence equations and nonequilibrium suspended sediment transport equation. The method, which utilizes cell-centered nodes on a nonstaggered grid, uses boundary velocity information at the wall boundary to avoid the specification of water level. An enlarged finite-difference method is introduced for momentum and suspended sediment equations on the complex boundary. This paper describes an application of the diagonal Cartesian method to calculate the tidal current and suspended sediment concentration of Quanzhou Bay in the Fujian province of China. The results show that the method predicts the flow and suspended sediment concentration well, and the calculations agree well with the measurement.