NUMERICAL ENTROPY PRODUCTION OF THE ONE-AND-A-HALF-DIMENSIONAL SHALLOW WATER EQUATIONS WITH TOPOGRAPHY

Shallow water equations with a complete Coriolis force and topography

This paper derives a set of two dimensional equations describing a thin inviscid fluid layer flowing over topography in a frame rotating about an arbitrary axis. These equations retain various terms involving the locally horizontal components of the angular velocity vector that are discarded in the usual shallow water equations. The obliquely rotating shallow water equations are derived both by...

On the Numerical Solution of the One-dimensional Shallow Water Equations in Constant-depth Environment

This paper presents a parametric finite-difference scheme concerning the numerical solution of theone-dimensional Boussinesq-type set of equations, as they were introduced byPeregrine, in the case of wavesrelatively long with small amplitudes in water of constant depth. The method which is used can be considered asa generalization of the Crank-Nickolson method and it has been ap...

Numerical solution of the two-layer shallow water equations with bottom topography

We present a simple, robust numerical method for solving the two-layer shallow water equations with arbitrarybottom topography.Using the techniqueof operator splitting,we write the equationsas a pair of hyperbolic systems with readily computed characteristics, and apply third-order-upwind differences to the resulting wave equations. To prevent the thickness of either layer from vanishing, we mo...

Numerical Techniques for the Shallow Water Equations

In this report we will discuss some numerical techniques for approximating the Shallow Water equations. In particular we will discuss finite difference schemes, adaptations of Roe’s approximate Riemann solver and the Q-Schemes of Bermudez & Vazquez with the objective of accurately approximating the solution of the Shallow Water equations. We consider four different test problems for the Shallow...

Numerical Approximation of the Nonlinear Shallow Water Equations with Topography and Dry Beds: A Godunov-Type Scheme