Floating grid characteristics method for unsteady flow over a mobile bed

In this paper, we present a new application of the method of characteristics (MOC) for the 1D simulation of unsteady flow over a mobile bed. The method is based on the floating grid-of-characteristics approach, which here is amended to take account of the more complex structure of the field of characteristics inherent in the morphodynamics (compared to those for hydro- or gas dynamics). Due to the relative simplicity of the algorithm the technique is particularly well suited to waves moving into a downstream reach that is initially dry. As with all MOC schemes the approach is also attractive because it reveals the underlying (morpho)dynamics as the solution progresses. The mathematical model considered here is based on the depth averaged non-linear shallow water equations directly coupled to a bed update (Exner) equation. Closure is obtained using a simple sediment flux relation. The technique described allows the study of fully coupled sediment transport problems and the associated hydro- and morphodynamic evolution. Numerical results are presented for the evolution of a sand dune in a tidal flow as well as the wet-dry dam-break problem on both a fixed and mobile bed. Results compare extremely well with the analytical or quasi-analytical solutions for the problems presented.