106 citations · 730 across the 45 of their papers we have counts for
11 papers · 1 filter
On weakly singular and fully nonlinear travelling shallow capillary-gravity waves in the critical regime
Dimitrios Mitsotakis, Denys Dutykh, Aydar Assylbekuly +1
In this Letter we consider long capillary-gravity waves described by a fully nonlinear weakly dispersive model. First, using the phase space analysis methods we describe all possib…
Conservative modified Serre-Green-Naghdi equations with improved dispersion characteristics
Didier Clamond, Denys Dutykh, Dimitrios Mitsotakis
For surface gravity waves propagating in shallow water, we propose a variant of the fully nonlinear Serre-Green-Naghdi equations involving a free parameter that can be chosen to im…
On the Galerkin / finite-element method for the Serre equations
Dimitrios Mitsotakis, Boaz Ilan, Denys Dutykh
A highly accurate numerical scheme is presented for the Serre system of partial differential equations, which models the propagation of dispersive shallow water waves in the fully-…
On the Galilean invariance of some dispersive wave equations
Angel Duran, Denys Dutykh, Dimitrios Mitsotakis
Surface water waves in ideal fluids have been typically modeled by asymptotic approximations of the full Euler equations. Some of these simplified models lose relevant properties o…
Long wave runup on random beaches
Denys Dutykh, Céline Labart, Dimitrios Mitsotakis
The estimation of the maximum wave sunup height is a problem of practical importance. Most of the analytical and numerical studies are limited to a constant slope plain shore and t…
Finite volume schemes for Boussinesq type equations
Denys Dutykh, Theodoros Katsaounis, Dimitrios Mitsotakis
Finite volume schemes are commonly used to construct approximate solutions to conservation laws. In this study we extend the framework of the finite volume methods to dispersive wa…