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In this paper a Godunov-type finite volume method is used for the solution of bedload sediment transport dynamics. The utilised equations for this modelling comprise the shallow water equations used for the hydrodynamic phase and also the Exner equation applied for the morphodynamic variations. These set of equations are then solved using a weakly-coupled scheme based on an augmented Riemann solver. In this approach the morphodynamic equation is first solved and the updated bedload changes with the same Riemann structure are used as a source term within the shallow water equations. The proposed numerical model is first used for the simulation of the parabolic sediment layer and the obtained numerical results are validated with the exact solution. Then, a bedload hump propagation with an initial subcritical condition which is able to create both mild and strong sediment and free-surface interactions is considered and the computed results are compared with the reference solution. These numerical results indicate that the defined weakly coupled method developed based on an augmented Riemann technique is able to be used for modelling bedload sediment transport for all flow regimes and exhibits a very good agreement with analytical or reference solutions for the given test cases.

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Various numerical methods have been developed for solving morphodynamic systems, among which the finite-volume method has been widely employed in recent years. This paper presents an efficient finite volume technique for simulation of bedload sediment transport near dry interfaces. The equations governing sediment transport in channels and rivers comprise the shallow water equations and Exner equation. By considering a novel velocity for Riemann waves, shallow water and Exner equations are solved using a weakly-coupled scheme based on an augmented Riemann solver. In this approach the morphodynamic equation is first solved and the updated bedload changes with the same Riemann structure are used as a source term within the shallow water equations. Augmented Riemann solver is based on a decomposition of an augmented vector—the depth, momentum as well as momentum flux and bottom surface. The proposed numerical model is first used for the simulation dam break flow over a mobile bed. Then, dam failure due to over-topping flow is considered and the computed results are compared with the experimental data.These numerical results indicate that the defined weakly coupled method developed based on an augmented Riemann technique is able to be used for modelling bedload sediment transport near dry interfaces with highly accurate and exhibits a very good agreement with the experimental data for test cases.