We study the Serre-Green-Naghdi system under a non-hydrostatic formulation, modelling incompressible free surface flows in shallow water regimes. This system, unlike well-known (nonlinear) Saint-Venant equations, takes into account effects of pressure term as well dispersive phenomena. Two numerical schemes are designed, based on finite volume - difference type splitting scheme and iterative co...

A wide variety of hydraulic and coastal flows can be modeled using shallow water theories, where the so-called Serre-Green-Naghdi (SGN) equations constitute a fully nonlinear weakly dispersive wave theory that has been successfully applied in fluvial maritime contexts. In present contribution, we show SGN models with wave-breaking parameterizations reproduce challenging processes surf swash zon...

Abstract In this paper, we derive new shallow asymptotic models for the free boundary plasma-vacuum problem governed by magnetohydrodynamic equations which are vital when describing large-scale processes in flows of astrophysical plasma. More precisely, present magnetic analogue 2D Green–Naghdi water waves under a weak pressure assumption presence weakly sheared vorticity and currents. Our meth...