A Finite Volume Model For The Resolution Of
The Shallow Water Equations With Moving
Boundary Conditions
Author(s)
J. Fe, F. Navarrina & J. Puertas
Abstract
A numerical model for the two dimensional ShallowWater Equations is described
and tested. The Finite Volume Method is applied, upwinding the flux and geometric
source terms, but not the friction term. The performance of the model in
different situations is shown, including the advance of a shock over an horizontal
dry bed and the simulation of an hydraulic jump. The results confirm the good
behaviour of the model.
Keywords: shallow water equations, free surface flows, dry bed.
1 Introduction
The Navier–Stokes Equations (NSE) are a non linear hyperbolic system of conservation
laws, that controls the behaviour of viscous fluids in three dimensions.
In many flows, such as estuaries or wide channels, the horizontal dimensions are
predominant. If the vertical variation of the horizontal components of the velocity
is small and the vertical acceleration is negligible, then the flow can be properly
described by the two-dimensional Shallow Water Equations. SWE can be
solved through first-order schemes, easy to implement, and it is rather common
the upwinding of the flux term of the equations to stabilize the model and give
more importance to the side from which the information comes.
The work is distributed as follows: in section 2 the obtaining of the SWE is
summarized and the hypothesis used in it are enumerate. In section 3 the applying
of the Finite Volume Method (FVM) to the equations is described and, in section 4,
some examples of validation–involving different boundary conditions– are shown.
Keywords
shallow water equations, free surface flows, dry bed.
Related Book
Other papers in this volume
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