This paper deals with time-advancing schemes for shallow water equations. We review
some of the existing numerical approaches, propose new schemes and investigate their …

The classical dam break problem has become the de facto standard in validating the
Nonlinear Shallow Water Equations (NSWE) solvers. Moreover, the NSWE are widely used …

We construct and analyse explicit methods for solving initial value problems for systems of
differential equations with expensive right-hand side functions whose Jacobian has its stiff …

This work represents a first step towards the simulation of the motion of water in a complex
hydrodynamic configuration, such as a channel network or a river delta, by means of a …

We analyse three-dimensional models for computing transport of salinity, pollutants,
suspended material (such as sediment or mud), etc. The main purpose of this paper is to …

In this paper we describe a time‐splitting method for the three‐dimensional shallow water
equations. The stability of this method neither depends on the vertical diffusion term nor on …

Smoothing techniques are frequently applied in the numerical solution of (initial-) boundary-
value problems for partial differential equations. Usually, the smoothing procedure consists …

A nonlinear wave equation is developed, modeling the evolution in time of shallow water
waves over a variable topography. As the usual assumptions of a perfect fluid and an …

Throughout this monograph we consider a fluid which is incompressible and inviscid.
Further, the only external force acting on the fluid is gravity. Specifically, we consider the …

We employ the method of asymptotic coordinate expansions in time and space to determine
the detailed structure of the solution to the linearised dambreak problem at the initial stage …