A three-dimensional mass consistent wind model using terrain adapted tetrahedral meshes

Abstract

Mass consistent models have been widely use in three-dimensional wind modelling by finite element method. In general, these problems are defined over regions with complex terrain and variable roughness length, therefore a suitable discretization of the studied zone will be necessary. In addition, there often exist points where more accuracy is required. We have used a method for constructing tetrahedral meshes which are simultaneously adapted to the terrain orography and the roughness length by using a refinement/derefinement process in a 2-D mesh corresponding to the terrain surface, following the technique proposed in [1, 2, 3]. In this 2-D mesh we include a local refinement around several points which are previously defined by the user. Besides, we develop a technique for adapting the mesh to any contour that has an important role in the simulation, like shorelines or roughness length contours [4, 5]. The final tetrahedral mesh is also constructed with more density of nodes near the terrain. The regions where more density of points is needed for obtaining a more accurate solution, are locally refined with the procedure proposed in [6]. This wind model improves that proposed in [7, 8]. The characterization of the atmospheric stability is carried out by means of the experimental measures of the intensities of turbulence. On the other hand, since several measures are often available at a same vertical line, we have constructed a least square optimization of such measures for developing a vertical profile of wind velocities from an optimum friction velocity. The three main parameters governing the model are estimated using genetic algorithms with a parallel implementation [8, 9, 10]. For a given episode, we periodically update these parameters. In order to test the model, some numerical experiments are presented, comparing the results with realistic measures.