Dispersive shallow water wave modelling. Part II: Numerical simulation on a globally flat space

Gayaz Khakimzyanov; Denys Dutykh; Oleg Gusev; Nina Yu Shokina

doi:10.4208/CICP.OA-2016-0179B

Dispersive shallow water wave modelling. Part II: Numerical simulation on a globally flat space

Gayaz Khakimzyanov, Denys Dutykh, Oleg Gusev, Nina Yu Shokina

Mathematics

Academy of Sciences

Research output: Contribution to journal › Article › peer-review

18 Scopus citations

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 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 linear elliptic equation. Moreover, this form of governing equations allows to determine the natural form of boundary conditions to obtain a well-posed (numerical) problem.

Original language	British English
Pages (from-to)	30-92
Number of pages	63
Journal	Communications in Computational Physics
Volume	23
Issue number	1
DOIs	https://doi.org/10.4208/CICP.OA-2016-0179B
State	Published - 2018

Keywords

Conservative finite differences
Finite volumes
Moving adaptive grids
Non-hydrostatic pressure
Nonlinear dispersive waves

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10.4208/CICP.OA-2016-0179B

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title = "Dispersive shallow water wave modelling. Part II: Numerical simulation on a globally flat space",

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 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 linear elliptic equation. Moreover, this form of governing equations allows to determine the natural form of boundary conditions to obtain a well-posed (numerical) problem.",

keywords = "Conservative finite differences, Finite volumes, Moving adaptive grids, Non-hydrostatic pressure, Nonlinear dispersive waves",

author = "Gayaz Khakimzyanov and Denys Dutykh and Oleg Gusev and Shokina, {Nina Yu}",

note = "Funding Information: This research was supported by RSCF project No 14–17–00219. The authors would like to thank Prof. Emmanuel AUDUSSE (Universit{\'e} Paris 13, France) who brought our attention to the problem of boundary conditions for the SGN equations. Publisher Copyright: {\textcopyright} 2018 Global-Science Press",

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doi = "10.4208/CICP.OA-2016-0179B",

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T1 - Dispersive shallow water wave modelling. Part II

T2 - Numerical simulation on a globally flat space

AU - Khakimzyanov, Gayaz

AU - Dutykh, Denys

AU - Gusev, Oleg

AU - Shokina, Nina Yu

N1 - Funding Information: This research was supported by RSCF project No 14–17–00219. The authors would like to thank Prof. Emmanuel AUDUSSE (Université Paris 13, France) who brought our attention to the problem of boundary conditions for the SGN equations. Publisher Copyright: © 2018 Global-Science Press

PY - 2018

Y1 - 2018

N2 - 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 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 linear elliptic equation. Moreover, this form of governing equations allows to determine the natural form of boundary conditions to obtain a well-posed (numerical) problem.

AB - 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 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 linear elliptic equation. Moreover, this form of governing equations allows to determine the natural form of boundary conditions to obtain a well-posed (numerical) problem.

KW - Conservative finite differences

KW - Finite volumes

KW - Moving adaptive grids

KW - Non-hydrostatic pressure

KW - Nonlinear dispersive waves

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EP - 92

JO - Communications in Computational Physics

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IS - 1

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Dispersive shallow water wave modelling. Part II: Numerical simulation on a globally flat space

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Keywords

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