Shallow Water Equations

Introduction

The most favoured approximate model equations for studying nearshore hydrodynamics are both the classic nonlinear Shallow Water Equations (SWE) and the many available Boussinesq-type equations which all stem from the work of Peregrine. Although in recent years most of the research and literature was focussed on the latters SWE posses some distinctive advantages which make them very suitable for modelling flows occurring in shallow depths.

For this reason in collaboration with Prof. Maurizio Brocchini of the DIAM at the Univerity of Genoa and Istituto di Idraulica of the University of Ancona a computer code has been developed fro the numerical solution of SWE.

The Software

The software, called "nlswe2D", uses the WAF method in its core solver. SOme of its main characteristics are:

• a dedicated module for the bottom generation considering submerged breakwater and other type of structures
• run-up description with analysis of dry-wet areas
• solution in the time domain with intra-waves resolution
• input signal as time series with inclined waves front
• perfect absorbing-generating boundary condition

The software is freely available under the GPL licence. To request the source send an e-mail to the following contact.
A complete description of the core numerical methods used can be found in

• "An efficient solver for nearshore flows based on the WAF method", COASTAL ENGINEERING, 43(2), 2001, pp. 105 - 129

Dependancies

The software is written in FORTRAN77 using for compilation:

• GNU/Make
• g77

The following libraries have to be linked

• BLAS (present in any GNU/Linux distribution)
• dislin free of charge for non commercial use

Examples

At this stage the software has no GUI so it is possible to input the bottom characteristics inputting the sections of the bottom and the the software build the necessary mesh

A river topography can be modelled as well as in this case.

The numericla solution outputs the velocity field and the total depth allowing for the calculation of the flow characteristics like vorticity evolution

To Do

The main task at the moment is to shift from the dislin graphic library to some other graphic library released under some free software license.

The following is a not exhaustive list of useful things to add (not in order of importance)

• adding a GUI
• species concentration evolution
• cyclic boundary conditions
• etc...

Aknowlegments

Special thanks to Ing. Patrizia Scalas and Phd Alessandra Piattella for supply some of the figures

-- RobertoBernetti - 07 Jun 2005