A new model of granular flows over general topography with erosion and deposition

A fundamental issue for describing gravity-driven flows over general topography is the search for an "optimal" coordinate. Bouchut and Westdickenberg [1] proposed an arbitrary coordinate system (BW) for general topography. The unified coordinate (UC) system (e.g., [2], [3]), which was developed for computational fluid dynamics, combines the advantages of both Eulerian and Lagrangian systems, so that the coordinates can instantaneously move with some singular surface within the flows. By utilizing the benefit of the BW coordinates and UC system, a new model of gravity-driven flows over general topography is derived, in which the erosion and deposition processes at the bed are considered. The depth-integrated mass and momentum equations are presented in the time-dependent and terrain-following coordinate system, which coincides with the interface distinguishing between the static and flowing layers. A shock-capturing numerical scheme is implemented to solve the derived equation system. Simulation results present the new features of this model and reveal a new physical insight of the erosion/deposition processes.