107 citations · 3.2k across the 144 of their papers we have counts for
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Dispersive shallow water wave modelling. Part III: Model derivation on a globally spherical geometry
Gayaz Khakimzyanov, Denys Dutykh, Zinaida Fedotova
The present article is the third part of a series of papers devoted to the shallow water wave modelling. In this part, we investigate the derivation of some long wave models on a d…
Dispersive shallow water wave modelling. Part II: Numerical simulation on a globally flat space
Gayaz Khakimzyanov, Denys Dutykh, Oleg Gusev +1
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 r…
Dispersive shallow water wave modelling. Part I: Model derivation on a globally flat space
Gayaz Khakimzyanov, Denys Dutykh, Zinaida Fedotova +1
In this paper, we review the history and current state-of-the-art in the modelling of long nonlinear dispersive waves. For the sake of conciseness of this review, we omit the unidi…
Numerical modelling of surface water wave interaction with a moving wall
Gayaz Khakimzyanov, Denys Dutykh
In the present manuscript, we consider the practical problem of wave interaction with a vertical wall. However, the novelty here consists in the fact that the wall can move horizon…
On the modelling of shallow turbidity flows
Valery Liapidevskii, Denys Dutykh, Marguerite Gisclon
In this study we investigate shallow turbidity density currents and underflows from mechanical point of view. We propose a simple hyperbolic model for such flows. On one hand, our…
Non-dispersive conservative regularisation of nonlinear shallow water (and isothermal Euler) equations
Didier Clamond, Denys Dutykh
A new regularisation of the shallow water (and isentropic Euler) equations is proposed. The regularised equations are non-dissipative, non-dispersive and possess a variational stru…