full
search.png

Search

close.png

Cancel

arrow
Volume 23, Issue 1
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

Commun. Comput. Phys., 23 (2018), pp. 30-92.

Published online: 2018-01

Preview Full PDF 4356 37966

Cited by

google scholar semantic scholar
Export citation
  • 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

Nonlinear dispersive waves, non-hydrostatic pressure, moving adaptive grids, finite volumes, conservative finite differences.

  • AMS Subject Headings

76B15, 76M12, 65N08, 65N06

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{CiCP-23-30, author = {Gayaz Khakimzyanov, Denys Dutykh, Oleg Gusev and Nina Yu. Shokina}, title = {Dispersive Shallow Water Wave Modelling. Part II: Numerical Simulation on a Globally Flat Space}, journal = {Communications in Computational Physics}, year = {2018}, volume = {23}, number = {1}, pages = {30--92}, 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2016-0179b}, url = {http://global-sci.org/intro/article_detail/cicp/10520.html} }
TY - JOUR T1 - Dispersive Shallow Water Wave Modelling. Part II: Numerical Simulation on a Globally Flat Space AU - Gayaz Khakimzyanov, Denys Dutykh, Oleg Gusev & Nina Yu. Shokina JO - Communications in Computational Physics VL - 1 SP - 30 EP - 92 PY - 2018 DA - 2018/01 SN - 23 DO - http://doi.org/10.4208/cicp.OA-2016-0179b UR - https://global-sci.org/intro/article_detail/cicp/10520.html KW - Nonlinear dispersive waves, non-hydrostatic pressure, moving adaptive grids, finite volumes, conservative finite differences. 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.

Gayaz Khakimzyanov, Denys Dutykh, Oleg Gusev and Nina Yu. Shokina. (2018). Dispersive Shallow Water Wave Modelling. Part II: Numerical Simulation on a Globally Flat Space. Communications in Computational Physics. 23 (1). 30-92. doi:10.4208/cicp.OA-2016-0179b
Copy to clipboard
BibteX RIS TXT
The citation has been copied to your clipboard