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Berthon, Christophe; Cordier, Stéphane; Delestre, Olivier; Le, Minh Hoang

An analytical solution of the shallow water system coupled to the Exner equation. (English. French summary) Zbl 1235.35218

C. R., Math., Acad. Sci. Paris 350, No. 3-4, 183-186 (2012).
Summary: An exact smooth solution for the equations modeling the bedload transport of sediment in shallow water is presented. This solution is valid for a large family of sedimentation laws which are widely used in erosion modeling such as the Grass model or those of E. Meyer-Peter and R. Müller [“Formulas for bed-load transport”, in: Proceedings of the 2nd meeting of the International Association for Hydraulic Structures Research, Stockholm, Sweden, 39–64 (1948)]. One of the main interests of this solution is the derivation of numerical benchmarks to validate the approximation methods.

Cited in 6 Documents

MSC:

35Q35 PDEs in connection with fluid mechanics
35C05 Solutions to PDEs in closed form
35Q86 PDEs in connection with geophysics

Keywords:

bedload transport of sediment; numerical benchmarks

Software:

SWASHES
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References:

[1] E. Audusse, C. Chalons, O. Delestre, N. Goutal, M. Jodeau, J. Sainte-Marie, B. Spinewine, Sediment transport modelling: Three layer models and relaxation schemes, CEMRACS Proceedings, 2011, submitted for publication.; E. Audusse, C. Chalons, O. Delestre, N. Goutal, M. Jodeau, J. Sainte-Marie, B. Spinewine, Sediment transport modelling: Three layer models and relaxation schemes, CEMRACS Proceedings, 2011, submitted for publication. · Zbl 1407.86003
[2] Castro Díaz, M. J.; Fernández-Nieto, E. D.; Ferreiro, A. M., Sediment transport models in shallow water equations and numerical approach by high order finite volume methods, Computers & Fluids, 37, 3, 299-316 (March 2008) · Zbl 1237.76082
[3] Cordier, S.; Le, M. H.; de Luna, T. Morales, Bedload transport in shallow water models: Why splitting (may) fail, how hyperbolicity (can) help, Advances in Water Resources, 34, 8, 980-989 (2011)
[4] O. Delestre, C. Lucas, P.-A. Ksinant, F. Darboux, C. Laguerre, T.N.T. Vo, F. James, S. Cordier, SWASHES: a library of shallow water analytic solutions for hydraulic and environmental studies, submitted for publication, http://arxiv.org/abs/1110.0288; O. Delestre, C. Lucas, P.-A. Ksinant, F. Darboux, C. Laguerre, T.N.T. Vo, F. James, S. Cordier, SWASHES: a library of shallow water analytic solutions for hydraulic and environmental studies, submitted for publication, http://arxiv.org/abs/1110.0288
[5] Exner, F., Über die wechselwirkung zwischen wasser und geschiebe in flüssen, Sitzungsber., Akad. Wissenschaften pt. IIa, 134 (1925) · JFM 52.1000.19
[6] A.J. Grass, Sediment transport by waves and currents, SERC London Cent. Mar. Technol. Report No. FL29, 1981.; A.J. Grass, Sediment transport by waves and currents, SERC London Cent. Mar. Technol. Report No. FL29, 1981.
[7] J. Hudson, Numerical technics for morphodynamic modelling, PhD thesis, University of Whiteknights, 2001.; J. Hudson, Numerical technics for morphodynamic modelling, PhD thesis, University of Whiteknights, 2001.
[8] E. Meyer-Peter, R. Müller, Formulas for bed-load transport, in: 2nd meeting IAHSR, Stockholm, Sweden, 1948, pp. 1-26.; E. Meyer-Peter, R. Müller, Formulas for bed-load transport, in: 2nd meeting IAHSR, Stockholm, Sweden, 1948, pp. 1-26.
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