@inbook{2e485c5605ef458d95e333aa30b31d00,

title = "Numerical Simulation on a Globally Flat Space",

abstract = "In this chapter we describe a numerical method to solve numerically the weakly dispersive fully nonlinear Serre–Green–Naghdi (SGN) celebrated model. Namely, our scheme is based on reliable finite volume methods, proven to be very efficient for the hyperbolic part of equations. The particularity of our study is that we develop an adaptive numerical model using moving grids. Moreover, we use a special form of the SGN equations where non-hydrostatic part of pressure is found by solving a nonlinear elliptic equation. Moreover, this form of governing equations allows to determine the natural form of boundary conditions to obtain a well-posed (numerical) problem.",

author = "Gayaz Khakimzyanov and Denys Dutykh and Zinaida Fedotova and Oleg Gusev",

note = "Publisher Copyright: {\textcopyright} 2020, Springer Nature Switzerland AG.",

year = "2020",

doi = "10.1007/978-3-030-46267-3_2",

language = "British English",

series = "Lecture Notes in Geosystems Mathematics and Computing",

publisher = "Springer Nature",

pages = "45--134",

booktitle = "Lecture Notes in Geosystems Mathematics and Computing",

address = "United Kingdom",

}