A numerical scheme for an improved Green–Naghdi model in the Camassa–Holm regime for the propagation of internal waves

A Generalised Serre-Green-Naghdi Equations for Variable Rectangular Open Channel Hydraulics and Its Finite Volume Approximation

“…As expected, the obtain numerical order is slow because of the numerical dissipation of the solitary wave (as already pointed out in several works, see for instance [3] for which we obtain almost the same order of convergence in the case of uniform section). Moreover, as expected, cross-sectional variations have no influence on the convergence rate.…”

“…This section is devoted to the numerical method to solve the reformulated dispersive model (26). It is rather natural to split the hyperbolic part to the dispersive one as done by several authors (see for instance [5,4,3]).…”

Simulation of complex free surface flows

“…By making use of Equation (1a), of the duality relation (7) and since X satisfies Equations (1e-1f), we obtain the expected result.…”

“…Due to the duality relation (7) and the boundary conditions (3)(4), the variational problem associated to (9) reads:…”

“…Figure 3 shows the dispersive effects generated by System (1) when using discontinuous initial data. Here, we chose more cells (8000) because it is claimed in [7,21] that dispersive effects are hard to capture. It is recommended that high-order numerical schemes be used but that is not the topic of this paper.…”