Numerical Simulations of a Dispersive Model Approximating Free-Surface Euler Equations

Abstract In some configurations, dispersion effects must be taken into account to improve the simulation of complex fluid flows. A family free-surface dispersive models has been derived in Fernández-Nieto et al. (Commun Math Sci 16(05):1169–1202, 2018). The hierarchy is based on a Galerkin approach and parameterised by number discrete layers along vertical axis. this paper we propose numerical schemes designed for these 1D open channel. cornerstone Serre – Green-Naghdi model which extensively studied literature from both theoretical points view. More precisely, goal method $$LDNH_2$$ L D N H 2 that projection extended one-layer case any layers. To do so, addressed means projection-correction applied non-standard differential operator. special attention paid boundary conditions. This several thanks an original relabelling unknowns. tests show convergence its accuracy compared $$LDNH_0$$ 0 model.