This paper presented a two-dimensional hydrodynamic and sediment transport based on the solutions of the variable density shallow water equations (VDSWEs) for sediment-laden flows, and the Exner equation for bed changes. Those equations are solved in a coupled way by the first-order Godunov-type finite volume method. The Harten-Lax-van Leer-Contact (HLLC) Riemann solver is extended to find the local Riemann fluxes in order to maintain the exact balance between the momentum term and the bed slope term. This well-balance property is verified by the analytical solution to a synthetic case. Then, the model is applied to simulate a laboratory experiment, i.e., 2D dam-break flows over mobile beds. Using the well-balanced scheme has advantages over the traditional un-balanced scheme when sediment concentration is discontinuous. Not only the simulation results show excellent matches to the measurements, but also the model is robust and stable. At last, a field case, the 1996 Lake Ha! Ha! flood event (Canada), is simulated. Results of cross sectional geometries and profiles of longitudinal thalweg agree well with measurements. The errors of measured cross sectional changes is less than 50%. The accuracy and simplicity of the numerical model, together with the robust implementation, make the model a good candidate for practical engineering applications.

A Well-balanced Numerical Scheme for Solving the Variable Density Shallow Water Equations

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[Paper Proceedings](https://doi.org/10.1061/9780784483466)

Conference DOI: https://doi.org/10.26226/m.6329c39b68fb0e00131f77d2