2018
Dispersive shallow water wave modelling. Part II: Numerical simulation on a globally flat space
CCommun. Comput. Phys.
G. Khakimzyanov, D. Dutykh, O. Gusev and N. Shokina
Commun. Comput. Phys. 23(1): 30-92 (2018)
Open Access
Abstract
In this paper, 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 effective 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 determining the natural form of boundary conditions to obtain a well-posed (numerical) problem.
Keywords
moving adaptive gridsnonlinear dispersive wavesnumerical simulationnonlinear elliptic equationadaptive numerical modelSerre-Green-Naghdi modelmoving gridsfinite volumesfinite volume methoddispersive shallow water wavesconservative finite differencesboundary conditions
Bibliographic record
BibTeX Citation
@article{Khakimzyanov2018dispersiveshallow,
author = {Khakimzyanov, G. and Dutykh, D. and Gusev, O. and Shokina, N.},
title = {Dispersive shallow water wave modelling. Part II: Numerical simulation on a globally flat space},
journal = {Commun. Comput. Phys.},
year = {2018},
volume = {23},
number = {1},
pages = {30--92},
doi = {10.4208/cicp.OA-2016-0179b},
abstract = {In this paper, 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 effective 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 determining the natural form of boundary conditions to obtain a well-posed (numerical) problem.},
keywords = {moving adaptive grids, nonlinear dispersive waves, numerical simulation, nonlinear elliptic equation, adaptive numerical model, Serre-Green-Naghdi model, moving grids, finite volumes, finite volume method, dispersive shallow water waves, conservative finite differences, boundary conditions}
}