“Enfoque ráster” del problema hidrodinámico del flujo en lámina libre en 2D

Abstract

Geographical information systems traditionally provide information using two formats–raster and vector. Each one of these formats is handled according to their independent algorithms. Consequently, any type of hydraulic study performed in a territory contains information that can be classified by these two formats. LiDAR is the most precise technology used to generate Digital Elevation Models (DEM) for large areas, with a spatial resolution of 1 to 2 m and a minimum precision in height. It gives the cartographic information its raster characteristic, with the cell as its basic unit of information. Consequently, this kind of information is very suitable to the generation of structured quadrilateral meshes to numerically model free surface flow in two dimensions. The main objective of this work was to present an adaptation of the classic explicit first order finite volumes scheme to a finite square volumes (FSV) mesh which, directly and without interpolations, makes each cell in the DEM (or raster) equal to the corresponding FSV. Consequently, the dimensions of the FSV are those of the base DEM cell. This is presented herein as a raster approach to the hydrodynamic problem of free surface flow in two dimensions. With the raster approach, the database for the mesh topology does not need to be consulted for each instant of time and, therefore, the efficiency of the numeric process is greatly improved. Consequently, larger-sized problems can be addressed. An additional objective was to compare both approaches by solving an illustrative example