Relaxation approximation to bed-load sediment transportRelaxation approximation to bed-load sediment transport Peer-Reviewed Journal Publication Δημοσίευση σε Περιοδικό με Κριτές 2015-10-252008enIn this work we propose and apply a numerical method based on finite volume relaxation approximation for computing the bed-load sediment transport in shallow water flows, in one and two space dimensions. The water flow is modeled by the well-known nonlinear shallow water equations which are coupled with a bed updating equation. Using a relaxation approximation, the nonlinear set of equations (and for two different formulations) is transformed to a semilinear diagonalizable problem with linear characteristic variables. A second order MUSCL-TVD method is used for the advection stage while an implicit–explicit Runge–Kutta scheme solves the relaxation stage. The main advantages of this approach are that neither Riemann problem solvers nor nonlinear iterations are required during the solution process. For the two different formulations, the applicability and effectiveness of the presented scheme is verified by comparing numerical results obtained for several benchmark test problems.http://creativecommons.org/licenses/by/4.0/Journal of Computational and Applied Mathematics2132521-546 Delis Anargyros Δελης Αναργυρος I. Papoglou Elsevier Finite volume Relaxation methods Bed-load sediment transport Shallow water equations