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 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) Seabra-Santos el al Mec.h, 176, 117-134, 1997). This done by revisiting similar Guermond Comput. Phys., 399, 108917, 2019) partial effects. We also derive family analytical solutions one-dimensional that are used verify correctness proposed relaxed model. method then numerically illustrated validated comparison experimental results.