  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.
