Hyperbolic relaxation technique for solving the dispersive Serre-Green-Naghdi Equations with topography
Abstract
The objective of this paper is to propose a hyperbolic relaxation technique for the dispersive Serre-Green-Naghdi equations (also known as the fully non-linear Boussinesq equations) with full topography effects introduced in Green, A.E. and Naghdi, P.M. (J. Fluid Mech., 78, 237-246, 1976) and Seabra-Santos el al (J. Fluid Mec.h, 176, 117-134, 1997). This is done by revisiting a similar relaxation technique introduced in Guermond el al (J. Comput. Phys., 399, 108917, 2019) with partial topography effects. We also derive a family of analytical solutions for the one-dimensional dispersive Serre-Green-Naghdi equations that are used to verify the correctness the proposed relaxed model. The method is then numerically illustrated and validated by comparison with experimental results.
Keywords
Cite
@article{arxiv.2103.01286,
title = {Hyperbolic relaxation technique for solving the dispersive Serre-Green-Naghdi Equations with topography},
author = {Jean-Luc Guermond and Chris Kees and Bojan Popov and Eric Tovar},
journal= {arXiv preprint arXiv:2103.01286},
year = {2022}
}
Comments
Accepted by Journal of Computational Physics - October 25, 2021