SUMMARYThe 2-D simpliÿed wildland ÿre model presented here is based on conservation laws and takes into account radiation as the dominant thermal transfer mechanism, as well as convection, which represents the e ect of the wind and the slope. The non-dimensional equations are obtained using the FrankKamenestkii change of variables. The existence of weak solutions of the non-linear reaction di usion problem obtained is established as a particular case of more general existence results using a compactness method. The uniqueness of the weak solution is shown for a given initial data and ÿxed parameters of the equations. The approximate solution is obtained using a mixed ÿnite element method. This preserves the continuity of the ux through the inter-element boundaries and allows to represent high gradients in the solution. Semi-discrete error estimation is presented. The convective term is solved by a splitting technique using Godunov's method. The numerical examples show the e ciency of the algorithm in capturing the ÿre front, even for critical values of the parameters.
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.
SUMMARYWe present a set of equations modelling wind velocity in a 3D domain in terms of the ground height function, the ground temperature and the wind on the boundary. The wind field is adjusted to several punctual wind velocity measurements at different points in the 3D domain by an optimal control problem in which the (unknown) wind on the boundary is the control. Using the meteorological wind punctual measures as datum, the model provides locally a detailed 3D wind that takes into account topography and thermal gradients on the surface by solving only 2D linear equations. We consider briefly the numerical approximation and two examples, including one with real data to control the accuracy of the model.
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