A numerical model for three-dimensional shallow water flows with sharp gradients over mobile topography

作者：Liu Xin^*; Mohammadian Abdolmajid; Sedano Julio Angel Infante

来源：Computers & Fluids, 2017, 154: 1-11.

DOI：10.1016/j.compfluid.2017.05.021

• 3-D shallow water equations
• sigma-coordinates
• Relaxation method
• Bed erosion
• Finite volume method
• Dam-break

This study aims to develop a three-dimensional (3-D) numerical model for shallow water flows over mobile topography, which is capable of simulating morphological evolution under shock waves, e.g. dam break flows. The hydrodynamic model solves the three-dimensional shallow water equations (SWEs) using a finite volume method on prismatic cells in sigma-coordinates. The morphodynamic model solves an Exner equation consisting of bed-load sediment transportation. Using a relaxation approach, a hyperbolic system is built for hydrodynamic system, which allows for using a Godunov-type central-upwind method to capture the shocks and approximate the numerical fluxes. Consequently, the 3D-SWEs-Exner model proposed in the present study can stably and accurately solve the dam-break flows over mobile beds. A spatially and temporally second-order "prismatic" central-upwind method is used to approximate the numerical fluxes through cell interfaces. The Exner equation is solved using an upwind method. Using spatially linear reconstruction and explicit two-stage Runge-Kutta time discretization, second order accuracy is achieved in space and time. The proposed model can preserve the well-balanced property due to the special discretization of bed-slope source terms. The proposed model is validated by several tests with experimental measurements, and is compared with the simulated results using reported two-dimensional (2-D) models.

• 出版日期2017-9-1