Hyperbolic relaxation technique for solving the dispersive Serre-Green-Naghdi equations with topography

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 [14] and [24]. This is done by revisiting a similar relaxation technique introduced in [17] 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 of the proposed relaxed model. The method is then numerically illustrated and validated by comparison with experimental results. (C) 2021 Elsevier Inc. All rights reserved.

Automated summary

The objective of this paper is to propose a hyperbolic relaxation technique for the dispersive Serre-Green-Naghdi equations with full topography effects, and it is validated by comparison with experimental results.