Abstract
A two-layer shallow water type model is proposed to describe bedload sediment transport for strong and weak interactions between the fluid and the sediment. The key point falls into the definition of the friction law between the two layers, which is a generalization of those introduced in Fernández-Nieto et al. (https://doi.org/10.1051/m2an/2016018). Moreover, we prove formally that the two-layer model converges to a Saint-Venant-Exner system (SVE) including gravitational effects when the ratio between the hydrodynamic and morphodynamic time scales is small. The SVE with gravitational effects is a degenerated nonlinear parabolic system, whose numerical approximation can be very expensive from a computational point of view, see for example T. Morales de Luna et al. (https://doi.org/10.1007/s10915-010-9447-1). In this work, gravitational effects are introduced into the two-layer system without any parabolic term, so the proposed model may be a advantageous solution to solve bedload sediment transport problems.
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Acknowledgements
This research has been partially supported by the Spanish Government and FEDER through the coordinated Research projects MTM 2015-70490-C2-1-R and MTM 2015-70490-C2-2-R. The authors would like to thank M.J. Castro Díaz and R. Maurin for fruitful discussions.
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Escalante, C., Fernández-Nieto, E.D., Luna, T.M.d., Narbona-Reina, G. (2021). Modelling of Bedload Sediment Transport for Weak and Strong Regimes. In: Greiner, D., Asensio, M.I., Montenegro, R. (eds) Numerical Simulation in Physics and Engineering: Trends and Applications. SEMA SIMAI Springer Series, vol 24. Springer, Cham. https://doi.org/10.1007/978-3-030-62543-6_6
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