Modelling of bedload sediment transport for weak and strong regimes. (English) Zbl 1481.76251
Greiner, David (ed.) et al., Numerical simulation in physics and engineering: trends and applications. Lecture notes of the XVIII ‘Jacques-Louis Lions’ Spanish-French school, Las Palmas de Gran Canaria, Spain, June 25–29, 2018. Cham: Springer. SEMA SIMAI Springer Ser. 24, 179-189 (2021).
Summary: 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 [the second author et al., ESAIM, Math. Model. Numer. Anal. 51, No. 1, 115–145 (2017; Zbl 1360.35176)]. 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 [the third author et al., J. Sci. Comput. 48, No. 1–3, 258–273 (2011; Zbl 1426.76408)]. 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.
For the entire collection see [Zbl 1471.65004].
For the entire collection see [Zbl 1471.65004].
MSC:
| 76T20 | Suspensions |
| 76B70 | Stratification effects in inviscid fluids |
| 76-10 | Mathematical modeling or simulation for problems pertaining to fluid mechanics |
| 86A05 | Hydrology, hydrography, oceanography |
Keywords:
two-layer bedload model; Saint-Venant-Exner model; sediment friction law; gravitational effectReferences:
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