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A hybrid finite volume/finite element method for shallow water waves by static deformation on seabeds

Al-Ghosoun, A.; Osman, A.S.; Seaid, M.

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Authors



Abstract

Purpose The purpose of this study is twofold: first, to derive a consistent model free-surface runup flow problems over deformable beds. The authors couple the nonlinear one-dimensional shallow water equations, including friction terms for the water free-surface and the two-dimensional second-order solid elastostatic equations for the bed deformation. Second, to develop a robust hybrid finite element/finite volume method for solving free-surface runup flow problems over deformable beds. The authors combine the finite volume for free-surface flows and the finite element method for bed elasticity. Design/methodology/approach The authors propose a new model for wave runup by static deformation on seabeds. The model consists of the depth-averaged shallow water system for the water free-surface coupled to the second-order elastostatic formulation for the bed deformation. At the interface between the water flow and the seabed, transfer conditions are implemented. Here, hydrostatic pressure and friction forces are considered for the elastostatic equations, whereas bathymetric forces are accounted for in the shallow water equations. As numerical solvers, the authors propose a well-balanced finite volume method for the flow system and a stabilized finite element method for elastostatics. Findings The developed coupled depth-averaged shallow water system and second-order solid elastostatic system is well suited for modeling wave runup by deformation on seabeds. The derived coupling conditions at the interface between the water flow and the bed topography resolve well the condition transfer between the two systems. The proposed hybrid finite volume element method is accurate and efficient for this class of models. The novel technique used for wet/dry treatment accurately captures the moving fronts in the computational domain without generating nonphysical oscillations. The presented numerical results demonstrate the high performance of the proposed methods. Originality/value Enhancing modeling and computations for wave runup problems is at an early stage in the literature, and it is a new and exciting area of research. To the best of our knowledge, solving wave runup problems by static deformation on seabeds using a hybrid finite volume element method is presented for the first time. The results of this research study, and the research methodologies, will have an important influence on a range of other scientists carrying out research in related fields.

Citation

Al-Ghosoun, A., Osman, A., & Seaid, M. (2021). A hybrid finite volume/finite element method for shallow water waves by static deformation on seabeds. Engineering Computations, 38(5), 2434-2459. https://doi.org/10.1108/ec-05-2020-0275

Journal Article Type Article
Acceptance Date Oct 13, 2020
Online Publication Date Dec 14, 2020
Publication Date 2021
Deposit Date Nov 22, 2020
Publicly Available Date Mar 28, 2024
Journal Engineering Computations
Print ISSN 0264-4401
Electronic ISSN 1758-7077
Publisher Emerald
Peer Reviewed Peer Reviewed
Volume 38
Issue 5
Pages 2434-2459
DOI https://doi.org/10.1108/ec-05-2020-0275

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© 2020, Emerald Publishing Limited. This AAM is provided for your own personal use only. It may not be used for resale, reprinting, systematic distribution, emailing, or for any other commercial purpose without the permission of the publisher.





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