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Article Dans Une Revue Discrete and Continuous Dynamical Systems - Series B Année : 2022

Numerical study of the Serre-Green-Naghdi equations and a fully dispersive counterpart

Résumé

We perform numerical experiments on the Serre-Green-Naghdi (SGN) equations and a fully dispersive "Whitham-Green-Naghdi" (WGN) counterpart in dimension 1. In particular, solitary wave solutions of the WGN equations are constructed and their stability, along with the explicit ones of the SGN equations, is studied. Additionally, the emergence of modulated oscillations and the possibility of a blow-up of solutions in various situations is investigated. We argue that a simple numerical scheme based on a Fourier spectral method combined with the Krylov subspace iterative technique GMRES to address the elliptic problem and a fourth order explicit Runge-Kutta scheme in time allows to address efficiently even computationally challenging problems.
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Dates et versions

hal-02617465 , version 1 (26-05-2020)
hal-02617465 , version 2 (17-11-2021)

Identifiants

Citer

Vincent Duchêne, Christian Klein. Numerical study of the Serre-Green-Naghdi equations and a fully dispersive counterpart. Discrete and Continuous Dynamical Systems - Series B, 2022, 27 (10), pp.5905-5933. ⟨10.3934/dcdsb.2021300⟩. ⟨hal-02617465v2⟩
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