Author(s): J. Murillo; P. García-Navarro; P. Brufau; J. Burguete

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Keywords: Load transport; erosion/deposition; source term discretization; moving boundaries; large-time steps; debris flow; finite

Abstract: This work describes a finite volume model applied to solve the coupled shallow water/load transport equations, where low concentrations of sediment load are assumed so that the concentration of the solid fraction is assumed not to influence the equations governing the dynamics. The unsteady simulation of erodible bed requires special attention in the discretization of the bed and friction source terms as important instabilities can arise in some situations. The upwind discretization of the time variable bed slope source terms is presented to provide an exact balance of the numerical fluxes and to guarantee steady-state solutions contrary to the pointwise formulation that leads to instabilities destroying the computation. Robust numerical schemes are presented for both moving and fixed boundaries. In the last case a numerical technique is provided to keep the concentration load bounded for values of CFL (Courant–Friedrichs–Lewy) greater than one and therefore decreasing the necessary computational cost.

DOI: https://doi.org/10.1080/00221686.2008.9521847

Year: 2008