Hyperbolic relaxation technique for solving the dispersive Serre Equations with topography

03/01/2021

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by   Jean-Luc Guermond, et al.

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The objective of this note is to propose a relaxation technique that accounts for the topography effects in the dispersive Serre equations (also known as Serre–Green–Naghdi or fully non-linear Boussinesq equations, etc.) introduced in [https://doi.org/10.1017/S0022112087000594]. This is done by revisiting the relaxation technique introduced in [https://doi.org/10.1016/j.jcp.2019.108917]. We also derive a family of analytical solutions for the one-dimensional dispersive Serre equations that are used to validate the proposed relaxed model. The method is then numerically illustrated by comparison with experimental results.