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A Finite Element Flow Model over the Alsace Plain

  • P. Racher
  • F. X. Le Dimet
  • J. F. Roussel
  • P. Rosset
  • P. Mery
Part of the NATO · Challenges of Modern Society book series (NATS, volume 3)

Abstract

In a previous paper (Racher et al.,1), we have applied to the mid-Rhine valley a mass-consistent wind field model based on a variational technique for solving the incompressible continuity equation originally developed by Sherman2. Taking advantage of this variational approach which directly inserts the collected experimental information into the integration procedure itself, we depart from reference 2 mainly on three points. First, we use a terrain-following vertical coordinate (σ-coordinate), thus avoiding the problems of intersecting the topography. Secondly, as will be seen in next paragraph, we have generalized the boundary conditions so as to include the effects of inflow and outflow across the boundaries. And thirdly, we have designed an initialization procedure (Roussel3, Mac Lain4) which aims at retaining most of the meteorological information collected on an irregularly-distributed network of stations. This is an important point which deserves further discussion, since the final relaxed solution is rather strongly dependent upon the initial first-guess wind field. Our initialization scheme avoids too much smoothing in the measured wind field through local expansion of the solution for each horizontal wind component in terms of a polynomial basis function within every triangle obtained by joining the stations. The values thus obtained are then redistributed over the grid points of a regular grid covering the domain under study. In doing so, we retain some of the fine-scale atmospheric structures reflected into the local wind measurements. These structures involve radiative and thermal as well as dynamic effects at many spatial and temporal scales: the adjustment implied through the continuity equation bears only upon the wind components, though accomodating in part the non-dynamic effects which contribute to them. One can assume that a larger number of constraint equations would lead to a reduction in the crucial role played by the initialization procedure.

Keywords

Wind Field Finite Element Formulation Polynomial Basis Function Conjugate Gradient Type Variational Wind Field 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    P. Racher, R. Rosset and Y.Y. Caneill, A mass-consistent wind field model over the mid-Rhine valley, Proc. 11th NATO/CCMS International Technocal Meeting on Air Pollution Modeling and its Application, Amsterdam, The Netherlands, 24–27 nov. 1980.Google Scholar
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    C.E. Sherman, A mass-consistent model for wind fields over complex terrain, Journal Appl. Met., 17: 312 (1978).ADSCrossRefGoogle Scholar
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    J.F. Roussel, Une méthode d’analyse objective des champs basée sur une interpolation locale par fonctions de base, Rapport Scientifique n° 31 du LAMP, Univ. de Clermont II, janvier 1981.Google Scholar
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    D.R. Tuerpe, P.M. Gresho and R.L. Sani, Variational wind field adjustement over complex terrain using finite element techniques, Proc. A.M.S. Conf. on Sierra Nevada Meteo., South Lake Tahoe, Ca., June 19–21 1978.Google Scholar

Copyright information

© Plenum Press, New York 1983

Authors and Affiliations

  • P. Racher
    • 1
  • F. X. Le Dimet
    • 1
  • J. F. Roussel
    • 1
  • P. Rosset
    • 1
  • P. Mery
    • 2
  1. 1.LAMPUniv. Clermont IIAubièreFrance
  2. 2.Division MAPAEDF, Etudes et RecherchesChatouFrance

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