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The efficiency of a mass consistent model for wind field adjustment depends on several parameters that arise in various stages of the process. On one hand, those involved in the construction of the initial wind field using horizontal interpolation and vertical extrapolation of the wind measures registered at meteorological stations. On the other hand, the stability parameter which allows from a strictly horizontal wind adjustment to a pure vertical one. In general, the values of all of these parameters are based on empirical laws. The main goal of this work is the estimation of these parameters using genetic algorithms, such that some of the wind velocities observed at the measurement station are regenerated as accurately as possible by the model. In addition, we study the effect of the mesh refinement on the parameter estimation in several numerical experiments.

SUMMARYThis paper presents a new procedure to improve the quality of triangular meshes defined on surfaces. The improvement is obtained by an iterative process in which each node of the mesh is moved to a new position that minimizes a certain objective function. This objective function is derived from algebraic quality measures of the local mesh (the set of triangles connected to the adjustable or free node). If we allow the free node to move on the surface without imposing any restriction, only guided by the improvement of the quality, the optimization procedure can construct a high-quality local mesh, but with this node in an unacceptable position. To avoid this problem the optimization is done in the parametric mesh, where the presence of barriers in the objective function maintains the free node inside the feasible region. In this way, the original problem on the surface is transformed into a two-dimensional one on the parametric space. In our case, the parametric space is a plane, chosen in terms of the local mesh, in such a way that this mesh can be optimally projected performing a valid mesh, that is, without inverted elements. Several examples and applications presented in this work show how this technique is capable of improving the quality of triangular surface meshes.

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In previous works, many authors have widely used mass consistent models for wind field simulation by the finite element method. On one hand, we have developed a 3-D mass consistent model by using tetrahedral meshes which are simultaneously adapted to complex orography and to terrain roughness length. In addition, we have included a local refinement strategy around several measurement or control points, significant contours, as for example shorelines, or numerical solution singularities. On the other hand, we have developed a 2.5-D model for simulating the wind velocity in a 3-D domain in terms of the terrain elevation, the surface temperature and the meteorological wind, which is consider as an averaged wind on vertical boundaries. Using the meteorological wind as datum, the 2.5-D model provides a 3-D local wind modified by topography and thermal gradients on the surface by solving only a 2-D optimal control problem where the boundary condition is the control. In this case, the finite element discretization consists on a triangular mesh adapted to the terrain topography and roughness length. In both models, the wind field adjusts to several wind speed measurements at several points in the 3-D domain and eventually to an average wind flux on the boundary.In this paper we introduce several advances in the 2.5-D and 3-D wind models and we compare their results on a region located in the Province of Lugo (Spain) with realistic data that have been provided by the company Desarrollos Eólicos S.A. (DESA). In order to obtain the best adjustment of models results to the measurements, the main parameters governing the models are estimated by using genetic algorithms with a parallel implementation.

This paper introduces a new automatic strategy for adaptive tetrahedral mesh generation. A local refinement/derefinement algorithm for nested triangulations and a simultaneous untangling and smoothing procedure are the main involved techniques. The mesh generator is applied to 3-D complex domains whose boundaries are projectable on external faces of a meccano approximation composed of cuboids. The domain surfaces must be given by a mapping between meccano surfaces and object boundary. This mapping can be defined by analytical or discrete functions. At present, we have fixed mappings with orthogonal, cylindrical and radial projections, but any other one-to-one projection may be considered. The mesh generator starts from a coarse and valid hexahedral mesh that is obtained by an admissible subdivision of the meccano cuboids. The automatic subdivision of each hexahedron into six tetrahedra produces an initial tetrahedral mesh of the meccano approximation. The main idea is to construct a sequence of nested meshes by refining only those tetrahedra with a face on the meccano boundary. The virtual projection of meccano external faces defines a valid triangulation on the domain boundary. Then a 3-D local refinement/derefinement is carried out so that the approximation of domain surfaces verifies a given precision. Once this objective is reached, those nodes placed on the meccano boundary are really projected on their corresponding true boundary, and inner nodes are relocated using a suitable mapping. As the mesh topology is kept during node movement, poor quality or even inverted elements could appear in the resulting mesh; therefore, we finally apply a mesh optimization procedure. The efficiency of the proposed technique is shown with several applications to complex objects.