Keywords: wind modelling, mass consistent models, finite element method, tetrahedral meshes, parameter estimation.

Mass consistent models have been widely used in three-dimensional wind modelling by the 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, points often exist 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 two-dimensional mesh corresponding to the terrain surface, following the technique proposed in [1,2,3]. In this two-dimensional mesh we include a local refinement around several points which are previously defined by the user. We further 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 a greater density of nodes near the terrain. The regions where a greater density of points is needed to obtain 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.

1

Montenegro R, Montero G, Escobar JM, Rodríguez E, González- Yuste JM. Tetrahedral Mesh Generation for Environmental Problems over Complex Terrain. Lect Notes Comp Sci 2002;2329:335-44.

2

Montenegro R, Montero G, Escobar JM, Rodríguez E. Efficient Strategies for Adaptive 3-D Mesh Generation over Complex Orography. Neural, Par Sci Comput 2002;10:57-76.

3

Montero G, Montenegro R, Escobar JM, Rodríguez. Generación automática de mallas de tetraedros adaptadas a orografías irregulares. Rev Int Mét Num Cálc Dis Ing 2003;19(2):127-144.

4

Escobar JM, Rodríguez E, Montenegro R, Montero G, González-Yuste JM. Simultaneous untangling and smoothing of tetrahedral meshes. Comput Methods Appl Mech Engrg 2003;192:277-587 doi:10.1016/S0045-7825(03)00299-8

5

Escobar JM, Montero G, Montenegro R, Rodríguez E. An Algebraic Method for Smoothing Surface Triangulations on a Local Parametric Space. Int. J. Numer. Meth. Engng. In press. doi:10.1002/nme.1584

6

González-Yuste JM, Montenegro R, Escobar JM, Montero G, Rodríguez E. Local Refinement of 3-D Triangulations Using Object-Oriented Methods. Adv Engrg Soft 2004;35:693-702. doi:10.1016/j.advengsoft.2003.07.003

7

Montero G, Montenegro R, Escobar JM. A 3-D Diagnostic Model for Wind Field Adjustment. J Wind Engrg Ind Aer 1998;74-76:249-261. doi:10.1016/S0167-6105(98)00022-1

8

Montero G, Rodríguez E., Montenegro R, Escobar JM, González- Yuste JM. Genetic Algorithms for an Improved Parameter Estimation with Local Refinenent of Tetrahedral Meshes in a Wind Model. Adv Engrg Soft 2005;36:3-10. doi:10.1016/j.advengsoft.2004.03.011

9

Michalewicz Z, Genetic Algorithms + Data Structures = Evolution Problems. Springer Verlag, Berlin-Heidelberg-New York, 1994.

10

Rodríguez E, Montero G, Montenegro R, Escobar JM, González- Yuste JM, Parameter Estimation in a Three-dimensional Wind Field Model Using Genetic Algorithms. Lect Notes in Comp Sci 2002;2329:950-959. doi:10.1007/3-540-46043-8_96

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