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.

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This paper describes the development of a two-dimensional water quality model that solves hydrodynamic equations tied to transport equations with reactions mechanisms inherent in the processes. This enables us to perform an accurate assessment of the pollution in a coastal ecosystem. The model was developed with data drawn from the ecosystem found in Mexico’s southeast state of Tabasco. The coastal ecosystem consists of the interaction of El Yucateco lagoon with Chicozapote and Tonalá rivers that connect the lagoon with the Gulf of Mexico. The results of pollutants transport simulation in the coastal ecosystem are presented, focusing on toxic parameters for two hydrodynamic scenarios: wet and dry seasons. As it is of interest in the zone, the transport of four metals is studied: Cadmium, Chromium, Nickel, and Lead. In order to address these objectives, a self-posed mathematical problem is solved numerically, which is based on the measured data. The performed simulations show how to characterise metals transport with an acceptable accuracy, agreeing well with measured data in total concentrations in four control points along the water body. Although for the accurate implementation of the hydrodynamic-based water quality model herein presented boundary (geometry, tides, wind, etc.) and initial (concentrations measurements) conditions are required, it poses an excellent option when the distribution of solutes with high accuracy is required, easing environmental, economic, and social management of coastal ecosystems. It ought to be remarked that this constitutes a robust differential equation-based water quality model for the transport of heavy metals. Models with these characteristics are not common to be found elsewhere.