Mass consistent models for wind distribution in complex terrain — Fast algorithms for three dimensional problems

Abstract

Mass consistent models for wind distribution in complex terrain are extremely useful and readily applied to many practical situations, such as the siting of wind turbines, or as input in the estimation of diffusion and transport of pollutants in complex terrain. These models are based on the numerical solution of the steady state three dimensional continuity equation for the mean wind components. The momentum and energy equations are not solved explicitly, but considered indirectly using parametric relations and wind data. In practical applications the equations must be solved numerous times (e.g. for each time interval). Standard techniques for numerical solution of three dimensional problems are frequently very expensive and thus not suitable for practical needs. In the present work, great emphasis is given to the development of fast algorithms, and techniques based on the multigrid approach are shown. Two mass consistent programs are described, the first based on the parametric representation of one of the wind components, and the second based on a few wind measurements and a variational principle. To verify the reliability of the variational approach, a measurement program related to a project of wind energy, is being performed at Har-Ahim, a site located in the Galilee.