Modeling Meandering Channel by Two-Dimensional Shallow Water Equations

Abstract:

This research is to simulate the process of channel meandering using a two-dimensional depth-averaged hydrodynamic model. The multiple interactions between unsteady flow, turbulence, secondary flow, nonequilibrium sediment transport and bank erosion are considered by the model. The governing equations are the 2D depth-averaged Reynolds-averaged Navier-Stokes (2D-RANS) equations and the Exner equation for bed elevation evolution. The Reynolds stresses are calculated by the k-ε turbulence model. The secondary flow, is modeled by the dispersion terms in momentum equations. The spatial lag between the instantaneous flow properties and the rate of sediment transport is simulated by the nonequilibrium sediment transport model. During the process of adaptation, the sediment transport rate gradually develops into the transport capacity of a given flow condition. The evolution of channel bed and bank is modeled by the general Exner equation that accounts for both vertical deformation of bed elevation as well as lateral migration of bank. The system of governing equations is solved by a semi-implicit finite volume method over the Cartesian mesh. The advective fluxes across each cell interface are simultaneously calculated by the extended HLL Riemann solver. At each time step, the diffusion terms in the governing equations are solved by the implicit Euler scheme. The source terms are discretized in a well-balanced way to retain the C-property of the proposed model. Application of the model to different test cases indicates that the model can correctly simulate different phases of meandering channel evolution which include streamwise migration, transverse migration and rotation of channel bends.