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The purpose of this paper is to present a fully conservative numerical algorithm for solving the coupled shallow water hydro-sediment-morphodynamic equations governing fluvial processes, and also to clarify the performance of a conventional algorithm, which redistributes the variable water-sediment mixture density to the source terms of the governing equations and accordingly the hyperbolic operator is rendered similar to that of the conventional shallow water equations for clear water flows.

The coupled shallow water hydro-sediment-morphodynamic equations governing fluvial processes are arranged in full conservation form, and solved by a well-balanced weighted surface depth-gradient method along with a slope-limited centred scheme. The present algorithm is verified for a spectrum of test cases, which involve complex flows with shock waves and sediment transport processes with contact discontinuities over irregular topographies. The computational results of the conventional algorithm are compared with those of the present algorithm and evaluated by available referenced data.

The fully conservative numerical algorithm performs satisfactorily over the spectrum of test cases, and the conventional algorithm is confirmed to work similarly well.

A fully conservative numerical algorithm, without redistributing the water-sediment mixture density, is proposed for solving the coupled shallow water hydro-sediment-morphodynamic equations. It is clarified that the conventional algorithm, involving redistribution of the water-sediment mixture density, performs similarly well. Both algorithms are equally applicable to problems encountered in computational river modelling.