Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 32731
A Finite Element/Finite Volume Method for Dam-Break Flows over Deformable Beds

Authors: Alia Alghosoun, Ashraf Osman, Mohammed Seaid


A coupled two-layer finite volume/finite element method was proposed for solving dam-break flow problem over deformable beds. The governing equations consist of the well-balanced two-layer shallow water equations for the water flow and a linear elastic model for the bed deformations. Deformations in the topography can be caused by a brutal localized force or simply by a class of sliding displacements on the bathymetry. This deformation in the bed is a source of perturbations, on the water surface generating water waves which propagate with different amplitudes and frequencies. Coupling conditions at the interface are also investigated in the current study and two mesh procedure is proposed for the transfer of information through the interface. In the present work a new procedure is implemented at the soil-water interface using the finite element and two-layer finite volume meshes with a conservative distribution of the forces at their intersections. The finite element method employs quadratic elements in an unstructured triangular mesh and the finite volume method uses the Rusanove to reconstruct the numerical fluxes. The numerical coupled method is highly efficient, accurate, well balanced, and it can handle complex geometries as well as rapidly varying flows. Numerical results are presented for several test examples of dam-break flows over deformable beds. Mesh convergence study is performed for both methods, the overall model provides new insight into the problems at minimal computational cost.

Keywords: Dam-break flows, deformable beds, finite element method, finite volume method, linear elasticity, Shallow water equations.

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 826


[1] M. Banner and W.Peirson. Wave breaking onset and strength for two dimensional deep water wave groups. J. Fluid Mech, 585:93–115, 2007.
[2] A. Bermudez, J. Ferrin, L. Savedra, and M. Vazques-Cendon. A projection hybrid finite volume/element method for low-mach number flows. J. Comput. Phys, 271:360–378, 2014.
[3] H. Dark and L. Stewart. An analytical model for predicting underwater noise radiated from offshore pile driving. In Proceedings of the fifth Asia pacific congress on computational mechanics Conference, pages 2–20, December 2013.
[4] H. Dark and L. Stewart. An analytical model for wind-driven arctic summer sea ice drift. The cryosphere, 10:227–244, 2016.
[5] U. Drahne, N. Goseberg, S. Vatar, N. Beisiegal, and J. Behrens. An experimental and numerical study of long wave run-up on a plane beach. Journal of marine science and engineering, 4:1–23, 2016.
[6] M. Le Gal, D. Violeau, R. Ata, and X. Wang. Shallow water numerical models for the 1947 gisborne and 2011 tohoku-oki tsunami with kinematic seismic generation. Coastal Engineering, 139:1–15, 2018.
[7] J. Greenberg and A. Leroux. A well-balanced scheme for the numerical processing of source terms in hyperbolic equations. SIAM J.Numer.Anal, 33:1–16, 2006.
[8] R. Harcourt. A second moment model of langmuir turbulance. J. Phys. Oceanogr, 43:673–697, 2013.
[9] C. Liao, Z. Lin, Y. Guo, and D. Jeng. Coupling model for waves propagating over a porous seabed. Theoritical and applied mechanics letters, 5:85–88, 2015.
[10] C. Ng. Water waves over a muddy bed: a two-layer strokes boundary layer model. Coastal engineering, 40:221–242, 2000.
[11] H. Poulos and E. Davis. Elastic solutions for soil and rock mechanics. The University of Sydney, Australia, 1991.
[12] D. Tong, C. Liao, J. Chen, and Q. Zhang. Numerical simulations of a sandy seabed response to water surface waves propagating on current. Journal of marine science and engineering, 6:1–14, 2018.