  A dispersive wave hydro-morphodynamic model coupling the Green-Naghdi
equations (the hydrodynamic part) with the sediment continuity Exner equation
(the morphodynamic part) is presented. Numerical solution algorithms based on
discontinuous Galerkin finite element discretizations of the model are
proposed. The algorithms include both coupled and decoupled approaches for
solving the hydrodynamic and morphodynamic parts simultaneously and separately
from each other, respectively. The Strang operator splitting technique is
employed to treat the dispersive terms separately, and it provides the ability
to ignore the dispersive terms in specified regions, such as surf zones.
Algorithms that can handle wetting-drying and detect wave breaking are
presented. The numerical solution algorithms are validated with numerical
experiments to demonstrate the ability of the algorithms to accurately resolve
hydrodynamics of solitary and regular waves, and morphodynamic changes induced
by such waves. The results indicate that the model has the potential to be used
in studies of coastal morphodynamics driven by dispersive water waves, given
that the hydrodynamic part resolves the water motion and dispersive wave
effects with sufficient accuracy up to swash zones, and the morphodynamic model
can capture the major features of bed erosion and deposition.
