  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.
