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Depth‐integrated, non‐hydrostatic model for wave breaking and run‐up
Author(s) -
Yamazaki Yoshiki,
Kowalik Zygmunt,
Cheung Kwok Fai
Publication year - 2008
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1952
Subject(s) - momentum (technical analysis) , breaking wave , hydrostatic equilibrium , nonlinear system , dissipation , shallow water equations , computation , mechanics , flow (mathematics) , advection , finite difference , transformation (genetics) , mathematics , classical mechanics , mathematical analysis , wave propagation , physics , algorithm , biochemistry , chemistry , finance , quantum mechanics , gene , economics , thermodynamics
This paper describes the formulation, verification, and validation of a depth‐integrated, non‐hydrostatic model with a semi‐implicit, finite difference scheme. The formulation builds on the nonlinear shallow‐water equations and utilizes a non‐hydrostatic pressure term to describe weakly dispersive waves. A momentum‐conserved advection scheme enables modeling of breaking waves without the aid of analytical solutions for bore approximation or empirical equations for energy dissipation. An upwind scheme extrapolates the free‐surface elevation instead of the flow depth to provide the flux in the momentum and continuity equations. This greatly improves the model stability, which is essential for computation of energetic breaking waves and run‐up. The computed results show very good agreement with laboratory data for wave propagation, transformation, breaking, and run‐up. Since the numerical scheme to the momentum and continuity equations remains explicit, the implicit non‐hydrostatic solution is directly applicable to existing nonlinear shallow‐water models. Copyright © 2008 John Wiley & Sons, Ltd.