Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

Multilayer Saint-Venant equations over movable beds

Pages: 917 - 934, Volume 15, Issue 4, June 2011      doi:10.3934/dcdsb.2011.15.917

       Abstract        References        Full Text (470.3K)       Related Articles

Emmanuel Audusse - LAGA, Université Paris 13, 99 Av J.B. Clement, 93430 Villetaneuse, France (email)
Fayssal Benkhaldoun - LAGA, Université Paris 13, 99 Av J.B. Clement, 93430 Villetaneuse, France (email)
Jacques Sainte-Marie - Laboratoire d’Hydraulique Saint-Venant, 6 Quai Watier, BP 49, 78401 Chatou, France (email)
Mohammed Seaid - School of Engineering and Computing Sciences, University of Durham, South Road, Durham DH1 3LE, United Kingdom (email)

Abstract: We introduce a multilayer model to solve three-dimensional sediment transport by wind-driven shallow water flows. The proposed multilayer model avoids the expensive Navier-Stokes equations and captures stratified horizontal flow velocities. Forcing terms are included in the system to model momentum exchanges between the considered layers. The topography frictions are included in the bottom layer and the wind shear stresses are acting on the top layer. To model the bedload transport we consider an Exner equation for morphological evolution accounting for the velocity field on the bottom layer. The coupled equations form a system of conservation laws with source terms. As a numerical solver, we apply a kinetic scheme using the finite volume discretization. Preliminary numerical results are presented to demonstrate the performance of the proposed multilayer model and to confirm its capability to provide efficient simulations for sediment transport by wind-driven shallow water flows. Comparison between results obtained using the multilayer model and those obtained using the single-layer model are also presented.

Keywords:  Multilayer model, Saint-Venant equations, Sediment transport, Kinetic schemes.
Mathematics Subject Classification:  Primary: 58F15, 58F17; Secondary: 53C35.

Received: April 2010;      Revised: September 2010;      Available Online: March 2011.