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 [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.
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