Vortex motion in shallow water with varying bottom topography and zero Froude number

Investigating vortex dynamics in shallow water with topography

Stability of a Cartesian grid projection method for zero Froude number shallow water flows

In this paper a Godunov-type projection method for computing approximate solutions of the zero Froude number (incompressible) shallow water equations is presented. It is second-order accurate and locally conserves height (mass) and momentum. To enforce the underlying divergence constraint on the velocity field, the predicted numerical fluxes, computed with a standard second order method for hyp...

A New Two-dimensional Shallow Water Model including Pressure Effects and Slow Varying Bottom Topography

The motion of an incompressible fluid confined to a shallow basin with a slightly varying bottom topography is considered. Coriolis force, surface wind and pressure stresses, together with bottom and lateral friction stresses are taken into account. We introduce appropriate scalings into a three-dimensional anisotropic eddy viscosity model; after averaging on the vertical direction and consider...

Central-Upwind Scheme for Shallow Water Equations with Discontinuous Bottom Topography

Finite-volume central-upwind schemes for shallow water equations were proposed in [A. Kurganov and G. Petrova, Commun. Math. Sci., 5 (2007), 133–160]. These schemes are capable of maintaining “lake-at-rest” steady states and preserving the positivity of the computed water depth. The well-balanced and positivity preserving features of the central-upwind schemes are achieved, in particular, by us...

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...