Abstract
This study presents a three dimensional model for the transport of conservative contaminants, which can be used for bodies of water which are affected by winds and/or tides. The model solves the equation of mass transport, based on results obtained using a hydrodynamic model for shallow waters that works in a finite volume scheme and a type of hierarchical grid, called multiquadtree, which is adaptable to the bathymetry. To solve the vertical coordinates, the coordinate z is transformed into a sigma (s) coordinate, thus allowing the same number of layers in the vertical, regardless of depth. This hydrodynamic model is validated using two cases: a long wave propagated in a channel of variable width and bottom and wind action in a rectangular basin. Finally, the results obtained are presented for a hypothetical single port outfall in the bay of Campeche, Mexico. The model developed here is both quick and easy to use and is efficient when compared with models presented by other authors since it uses adaptable grids which allow detailed solutions to be obtained for areas of interest such as coastlines and the area around an outfall.
Highlights
The run-time and solution accuracy of a computational fluid mechanics model depends, essentially, on both the numerical scheme used and the quality of the mesh over which the governing equations and boundary conditions are discretized.In this article a multi-quadtree, finite volume approach for modelling coastal hydrodynamics and water quality is presented
This study presents a three dimensional model for the transport of conservative contaminants, which can be used for bodies of water which are affected by winds and/or tides
The model solves the equation of mass transport, based on results obtained using a hydrodynamic model for shallow waters that works in a finite volume scheme and a type of hierarchical grid, called multiquadtree, which is adaptable to the bathymetry
Summary
The run-time and solution accuracy of a computational fluid mechanics model depends, essentially, on both the numerical scheme used and the quality of the mesh over which the governing equations and boundary conditions are discretized. The multi-quadtree has been developed from the quadtree approach This uses an adaptive mesh generation based upon iterative subdivision of a square domain to produce a hierarchical solution grid for the model. The generation of a hierarchical multi-quadtree mesh begins with the division of the entire region of study, such as a river or a coastal lagoon, into a number of adjoining square sub-regions. For each of these subregions a quadtree mesh is generated. By way of an example, the multi-quadtree mesh generation is applied to the Bay of Acapulco, México, (Fig. 3) For this illustration the study region is first divided into 2 2 square sub-regions. In the second sub-model the results of the 2D model are considered as the initial data and from these the velocities for each cell in the x, y and z directions, referred to as u, v and w, are obtained
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