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

Abstract : We perform numerical experiments on the Serre-Green-Nagdi (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 onset of dispersive shock waves and the possibility of a blow-up of the 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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https://hal.archives-ouvertes.fr/hal-02617465
Contributor : Vincent Duchene <>
Submitted on : Tuesday, May 26, 2020 - 1:59:51 PM
Last modification on : Monday, July 6, 2020 - 3:38:13 PM

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### Identifiers

• HAL Id : hal-02617465, version 1
• ARXIV : 2005.13234

### Citation

Vincent Duchêne, Christian Klein. Numerical study of the Serre-Green-Naghdi equations and a fully dispersive counterpart. 2020. ⟨hal-02617465⟩

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