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.