Rigorous justification of the Favrie–Gavrilyuk approximation to the Serre–Green–Naghdi model

DOI10.1088/1361-6544/ab22fbzbMath1421.35208arXiv1807.06908OpenAlexW2883017781MaRDI QIDQ5234005

Vincent Duchêne

Publication date: 9 September 2019

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1807.06908

zbMATH Keywords

singular limit problemshallow-water approximationrelaxation systemlow Mach number limitspropagation of surface gravity wavesquasilinear system of balance laws

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Singular perturbations in context of PDEs (35B25) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Asymptotic methods, singular perturbations applied to problems in fluid mechanics (76M45) First-order nonlinear hyperbolic equations (35L60)

Related Items

Hyperbolic approximation of the BBM equation ⋮ Perfectly matched layers methods for mixed hyperbolic-dispersive equations ⋮ Well-balanced second-order convex limiting technique for solving the Serre-Green-Naghdi equations ⋮ Extended Lagrangian approach for the numerical study of multidimensional dispersive waves: applications to the Serre-Green-Naghdi equations ⋮ Phase and amplitude characteristics of higher-accuracy nonlinear dispersive models ⋮ Modeling shallow water waves ⋮ On high order ADER discontinuous Galerkin schemes for first order hyperbolic reformulations of nonlinear dispersive systems ⋮ An extension of the Boussinesq-type models to weakly compressible flows ⋮ Pseudo-compressibility, Dispersive Model and Acoustic Waves in Shallow Water Flows

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