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Numerical simulations of 3D free surface flows by a multilayer Saint-Venant model. (English) Zbl 1139.76036
Summary: We present a multilayer Saint-Venant system for the simulation of 3D free surface flows with friction and viscosity effects. A vertical discretization of Navier-Stokes system deduced from a precise analysis of the shallow water assumption leads to a set of coupled Saint-Venant-type systems. The idea is to obtain an accurate description of vertical profile of horizontal velocity while preserving the robustness and computational efficiency of usual Saint-Venant system. For each time-dependent layer, a Saint-Venant-type system is solved on the same 2D mesh by a kinetic solver using a finite volume framework. The free surface is directly deduced from the sum of layers water depth. We validate the model with some numerical academic and realistic examples. We present comparisons with simulations computed with the hydrostatic Navier-Stokes solver of Telemac-3D code developed by Electricité de France.

76M12 Finite volume methods applied to problems in fluid mechanics
76D33 Waves for incompressible viscous fluids
Full Text: DOI
[1] Audusse, Discrete and Continuous Dynamical Systems, Series B 5 pp 189– (2005) · Zbl 1075.35030
[2] Ferrari, M2AN 38 pp 211– (2004)
[3] Gerbeau, Discrete and Continuous Dynamical Systems, Series B 1 pp 89– (2001)
[4] Approssimazione numerica di modelli multistrato per fluidi a superficia libera (in Italian). Tesi di Laurea, Universita degli studi di Milano, Milan, 2002, http://mox.polimi.it/it/progetti/pubblicazioni
[5] Castro, Journal of Computational Physics 195 pp 202– (2004)
[6] Hydrodynamique des écoulements à surface libre; Modélisation numérique avec la méthode des éléments finis. Presses des Ponts et Chaussées: Paris, 2003 (in French).
[7] Modèle hydrostatique pour les écoulements à surface libre tridimensionnels et schémas numériques. Thèse, Université Pierre et Marie Curie, Paris, 2006.
[8] Theoretical and numerical study of shallow water models. Applications to nearshore hydrodynamics. Thesis, Université Bordeaux 1, Bordeaux, 2005.
[9] Dal Maso, Journal de Mathematiques Pures et Appliquees 74 pp 483– (1995)
[10] Audusse, Journal of Computational Physics 206 pp 311– (2005)
[11] Audusse, International Journal of Applied Mathematics and Computer Science
[12] Audusse, SIAM Journal on Scientific Computing 25 pp 2050– (2004)
[13] . Boundary conditions for the shallow water equations solved by kinetic schemes. INRIA Report 4282, 2001, http://www.inria.fr/RRRT/RR-4282.html
[14] Hervouet, Hydrological Processes 14 pp 2211– (2000)
[15] Hervouet, Revue Européenne des Éléments Finis 12 pp 143– (2003)
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