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Journal of Applied Mathematics
Volume 2014, Article ID 714031, 10 pages
http://dx.doi.org/10.1155/2014/714031
Research Article

Modelling Shallow Water Wakes Using a Hybrid Turbulence Model

1Faculty of Engineering, Autonomous University of San Luis Potosí, 78290 San Luis Potosí, SLP, Mexico
2College of Engineering and Architecture, ESIA Zacatenco, National Polytechnic Institute, Gustavo A. Madero, 07738 Mexico, DF, Mexico
3Department of Industrial Engineering, University of Guanajuato Celaya-Salvatierra, Mutualismo 303 Colonia Suiza, 38060 Celaya, GTO, Mexico

Received 29 July 2014; Accepted 23 October 2014; Published 17 November 2014

Academic Editor: Alvaro Valencia

Copyright © 2014 Clemente Rodriguez-Cuevas et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A numerical research with different turbulence models for shallow water equations was carried out. This was done in order to investigate which model has the ability to reproduce more accurately the wakes produced by the shock of the water hitting a submerged island inside a canal. The study of this phenomenon is important for the numerical methods application advancement in the simulation of free surface flows since these models involve a number of simplifications and assumptions that can have a significant impact on the numerical solutions quality and thus can not reproduce correctly the physical phenomenon. The numerical experiments were carried out on an experimental case under controlled conditions, consisting of a channel with a submerged conical island. The numerical scheme is based on the Eulerian-Lagrangian finite volume method with four turbulence models, three mixing lengths (ml), and one joining on the horizontal axis with a mixing-length model (ml) on the vertical axis. The experimental results show that a with ml turbulence model makes it possible to approach the experimental results in a more qualitative manner. We found that when using only a model in the vertical and horizontal direction, the numerical results overestimate the experimental data. Additionally the computing time is reduced by simplifying the turbulence model.