Fast Wave Averaging for the Equatorial Shallow Water Equations

On asymptotically equivalent shallow water wave equations

The integrable 3rd-order Korteweg-de Vries (KdV) equation emerges uniquely at linear order in the asymptotic expansion for unidirectional shallow water waves. However, at quadratic order, this asymptotic expansion produces an entire family of shallow water wave equations that are asymptotically equivalent to each other, under a group of nonlinear, nonlocal, normal-form transformations introduce...

The EHTA for Two Shallow Water Wave Equations

A Fast and Compact Solver for the Shallow Water Equations

This paper presents a fast and simple method for solving the shallow water equations. The water velocity and height variables are collocated on a uniform grid and a novel, unified scheme is used to advect all quantities together. Furthermore, we treat the fluid as weakly compressible to avoid solving a pressure Poisson equation. We sacrifice accuracy and unconditional stability for speed, but w...

A Numerical Method for Extended Boussinesq Shallow-Water Wave Equations

The accurate numerical simulation of wave disturbance within harbours requires consideration of both nonlinear and dispersive wave processes in order to capture such physical effects as wave refraction and diffraction, and nonlinear wave interactions such as the generation of harmonic waves. The Boussinesq equations are the simplest class of mathematical model that contain all these effects in ...

On the diffusive wave approximation of the shallow water equations

In this paper, we study basic properties of the diffusive wave approximation of the shallow water equations (DSW). This equation is a doubly non-linear diffusion equation arising in shallow water flow models. It has been used as a model to simulate water flow driven mainly by gravitational forces and dominated by shear stress, that is, under uniform and fully developed turbulent flow conditions...