Numerical approaches for 1D morphodynamic modelling

Existing methods for solving 1D morphodynamical systems have been reviewed and new, improved approaches have been identified. Usually the flow equations and the bed-updating equation are solved at separate time steps, using a quasi-steady approach. In this paper we have investigated the simultaneous (or coupled) solution of the equations. The schemes tested are the Lax–Wendroff and the Roe schemes, both with and without flux-limiting methods. Furthermore the discretisation of source terms has been investigated and has shown to be important.