Depth-averaged Two-dimensional Model for Sediment Transport in Unsteady Flow

A depth-averaged two-dimensional turbulent shallow flow model has been developed to simulate sediment transport in unsteady flows over mobile bed. The governing equations are the two-dimensional depth-averaged RANS equations, the K-Epsilon turbulence model, and the Exner equation. The system's domain of hyperbolicity is analyzed and discussed. The eigenstructure (eigenvalues and eigenvectors) of Jacobian matrix for the flux is analytically derived and evaluated. This system of governing equations is solved by the Godunov-type finite volume method. A coupled Roe-type approximate Riemann solver is adopted to calculate the fluxes across the cell interfaces. By solving the system of equations with a coupled scheme, the spurious/unphysical oscillations are avoided. The second-order MUSCL and Runge-Kutta schemes are used in model and lead to a second-order solution in both time and space. The following empirical sediment transport formulae have been tested in this work: Grass (1981), Meyer-Peter and Muller (1948), Van Rijn (1984), Nielsen (1992) and Camenen and Larson (2005). The model is verified against several laboratory and field test cases, including both 1D and 2D situations. The results show good agreements with the laboratory and field measurements.