A reduced basis for a local high definition wind model

Abstract

In this paper we present an application of the reduced basis method to a local high definition adjusted wind model. The model provides a precise description of the wind in 3D and takes into account topography and thermal gradients on the surface by solving only 2D linear equations; the buoyancy forces, slope effects, and mass conservation are also considered. The wind field is adjusted to the point measurements through an optimal control problem in which the wind flux acts as a control on the boundary. In order to use a reduced basis method, we consider an affine decomposition in terms of the parameter related to the friction coefficient and the wind measures at some given observation points. We also design an a posteriori error estimator that is needed to conduct our reduced basis process. Finally, two numerical examples are presented: a test problem and a real-data scenario, we corroborate the correct behavior of the method in both cases.