A coupled two-dimensional numerical model for rapidly varying flow, sediment transport and bed morphology

ABSTRACT

This paper presents a coupled two-dimensional model that can produce a more stable numerical simulation of rapid bed evolution than the conventional decoupled model. To solve the coupled bed-load sediment transport terms using a Godunov-type central-upwind method, a novel scheme to estimate the bed-load fluxes which can produce more accurate results than the previously reported coupled model is proposed using a pair of local wave speeds different from those used for the flow. The two-dimensional shallow water equations are used to solve the flow velocities and water depth. The bed level is solved by an Exner-based equation containing bed-load sediment transport as numerical flux terms and sediment entrainment and deposition as source terms. Analytical formulas to compute the eigenvalues of the Jacobian matrix are developed. The linear reconstruction of variables with a multi-dimensional slope limiter, and the second-order Runge-Kutta scheme are employed to achieve higher accuracy in space and time. For the case of rapid bed-erosion, the accuracy and stability of the proposed coupled model are verified by several numerical tests.

Keywords:

• Bed-load transport
• coupled model
• direct numerical simulation methods
• finite volume method
• shallow flows
• two-dimensional models

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Funding

This publication was made possible by the National Priorities Research Programme (NPRP) [Grant number 4-935-2-354] from the Qatar National Research Fund (a member of the Qatar Foundation). The statements made herein are solely the responsibility of the authors.