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 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.
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Soumis le : jeudi 29 juin 2017 - 20:56:22
Dernière modification le : samedi 8 juillet 2017 - 01:04:43

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  • HAL Id : hal-01551075, version 1
  • ARXIV : 1707.01304

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Gayaz Khakimzyanov, Denys Dutykh, Oleg Gusev, Nina Shokina. Dispersive shallow water wave modelling. Part II: Numerical simulation on a globally flat space. 67 pages, 17 figures, 3 tables, 149 references. Accepted to Commun. Comput. Phys. Other author's .. 2017. 〈hal-01551075〉

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