The present work is focused on the numerical approximation of the shallow water equations. When studying this problem, one faces at least two important issues, namely the ability of the scheme to preserve the positiveness ...

Water waves generated by a solid mass is a complex phenomenon discussed in this paper by numerical and experimental approaches. A model based on shallow water equations with shocks (Saint Venant) has developed. It can ...

Water waves generated by a solid mass is a complex phenomenon discussed in this paper by numerical and experimental approaches. A model based on shallow water equations with shocks (Saint Venant) has developed. It can ...

The Serre equations are a pair of strongly nonlinear, weakly dispersive, Boussinesq-type partial differential equations. They model the evolution of the surface elevation and the depth-averaged horizontal velocity of an ...

We discuss the use of time adaptivity applied to the one dimensional diffusive wave approximation to the shallow water equations. A simple and computationally economical error estimator is discussed which enables time-step ...

In this paper, we describe the diffusive shallow water equation (DSW) and discuss a numerical strategy to solve it using the generalized-alpha method as a method for temporal discretization. This method provides a good ...

We present the projective Riccati equations method to obtainexact solutions for the generalized shallow water wave equation (GSWW). We show the behavior of solutions with a graph.

In this paper, we consider the propagation of water waves in a long-wave asymptotic regime, when the bottom topography is periodic on a short length scale. We perform a multiscale asymptotic analysis of the full potential ...