Adaptive quadtree simulation of sediment transport

Morphodynamic change is a key factor in the development of river systems. This paper describes a two-dimensional model of fluvial bed morphodynamics, with the flow hydrodynamics represented by the hyperbolic non-linear shallow water equations and the bed morphodynamics by the bed deformation equation. Bed load transport is estimated using a simple expression. Suspended sediment transport is not considered. The model uses a deviatoric form of the non-linear shallow water equations that mathematically balances the source and flux gradient terms at equilibrium, including the effects of non-uniform bed topography. The governing equations are solved in a decoupled way, using a Godunov-type finite-volume solver for the non-linear shallow water equations and second-order finite differences for the bed deformation equation, both based on adaptive quadtree grids. The evolution of a sandbar in an open channel is tested against generalised approximate analytical solutions. The numerical predictions on adaptive quadtree grids are found to be in excellent agreement with the approximate analytical solutions within the range of validity of the latter. Results are also presented for the evolution of a sand dune and a sandpit. It is demonstrated that the de-coupled shallow flow and bed morphodynamics calculations are computationally efficient and accurate. It is shown that the use of adaptive quadtree grids leads to a much improved computational performance over that on an equivalent fine resolution fixed uniform grid.