\r\nwater flows with mass exchange and an erodible bed is developed.

\r\nThis enables the user to solve a number of complex sediment-based

\r\nproblems including (but not limited to), dam-break over an erodible

\r\nbed, recirculation currents and bed evolution as well as levy and

\r\ndyke failure. This research develops methodologies crucial to the

\r\nunder-standing of multi-sediment fluvial mechanics and waterway

\r\ndesign. In this model mass exchange between the layers is allowed

\r\nand, in contrast to previous models, sediment and fluid are able

\r\nto transfer between layers. In the current study we use a two-step

\r\nfinite volume method to avoid the solution of the Riemann problem.

\r\nEntrainment and deposition rates are calculated for the first time in

\r\na model of this nature. In the first step the governing equations are

\r\nrewritten in a non-conservative form and the intermediate solutions

\r\nare calculated using the method of characteristics. In the second stage,

\r\nthe numerical fluxes are reconstructed in conservative form and are

\r\nused to calculate a solution that satisfies the conservation property.

\r\nThis method is found to be considerably faster than other comparative

\r\nfinite volume methods, it also exhibits good shock capturing. For most

\r\nentrainment and deposition equations a bed level concentration factor

\r\nis used. This leads to inaccuracies in both near bed level concentration

\r\nand total scour. To account for diffusion, as no vertical velocities

\r\nare calculated, a capacity limited diffusion coefficient is used. The

\r\nadditional advantage of this multilayer approach is that there is a

\r\nvariation (from single layer models) in bottom layer fluid velocity:

\r\nthis dramatically reduces erosion, which is often overestimated in

\r\nsimulations of this nature using single layer flows. The model is

\r\nused to simulate a standard dam break. In the dam break simulation,

\r\nas expected, the number of fluid layers utilised creates variation in

\r\nthe resultant bed profile, with more layers offering a higher deviation

\r\nin fluid velocity . These results showed a marked variation in erosion

\r\nprofiles from standard models. The overall the model provides new

\r\ninsight into the problems presented at minimal computational cost.","references":null,"publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 130, 2017"}