@Article{CiCP-17-3,
author = {},
title = {Discontinuous-Galerkin Discretization of a New Class of Green-Naghdi Equations},
journal = {Communications in Computational Physics},
year = {2015},
volume = {17},
number = {3},
pages = {721--760},
abstract = {<p style="text-align: justify;">We describe in this work a discontinuous-Galerkin Finite-Element method
to approximate the solutions of a new family of 1d Green-Naghdi models. These new
models are shown to be more computationally efficient, while being asymptotically
equivalent to the initial formulation with regard to the shallowness parameter. Using
the free surface instead of the water height as a conservative variable, the models are
recasted under a pre-balanced formulation and discretized using a nodal expansion basis.
Independently from the polynomial degree in the approximation space, the preservation
of the motionless steady-states is automatically ensured, and the water height
positivity is enforced. A simple numerical procedure devoted to stabilizing the computations
in the vicinity of broken waves is also described. The validity of the resulting
model is assessed through extensive numerical validations.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.150414.101014a},
url = {https://global-sci.com/article/80396/discontinuous-galerkin-discretization-of-a-new-class-of-green-naghdi-equations}
}