Numerical study of the Serre-Green-Naghdi equations and a fully dispersive counterpart
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866916381157490688 |
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| author | Duchêne, Vincent Klein, Christian |
| author_facet | Duchêne, Vincent Klein, Christian |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2005_13234 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Numerical study of the Serre-Green-Naghdi equations and a fully dispersive counterpart Duchêne, Vincent Klein, Christian Analysis of PDEs 65M70, 35Q35, 76B15, 35B35 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. |
| title | Numerical study of the Serre-Green-Naghdi equations and a fully dispersive counterpart |
| topic | Analysis of PDEs 65M70, 35Q35, 76B15, 35B35 |
| url | https://arxiv.org/abs/2005.13234 |