Editorial Type:
Article
Article Type:
Research Article

An h-Adaptive Finite-Element Technique for Constructing 3D Wind Fields

Darrell W. Pepper Nevada Center for Advanced Computational Methods, University of Nevada, Las Vegas, Las Vegas, Nevada

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Xiuling Wang Purdue University Calumet, Calumet, Indiana

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Print Publication:
01 Mar 2009
DOI:
https://doi.org/10.1175/2008JAMC1680.1
Page(s):
580–599
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Abstract

An h-adaptive, mass-consistent finite-element model (FEM) has been developed for constructing 3D wind fields over irregular terrain utilizing sparse meteorological tower data. The element size in the computational domain is dynamically controlled by an a posteriori error estimator based on the L2 norm. In the h-adaptive FEM algorithm, large element sizes are typically associated with smooth flow regions and small errors; small element sizes are attributed to fast-changing flow regions and large errors. The adaptive procedure employed in this model uses mesh refinement–unrefinement to satisfy error criteria. Results are presented for wind fields using sparse data obtained from two regions within Nevada: 1) the Nevada Test Site, located approximately 65 mi (1 mi ≈ 1.6 km) northwest of Las Vegas, and 2) the central region of Nevada, about 100 mi southeast of Reno.

Corresponding author address: Darrell W. Pepper, Department of Mechanical Engineering, University of Nevada, Las Vegas, 4505 Maryland Parkway, Las Vegas, NV 89154-4027. Email: dwpepper@nscee.edu

Abstract

An h-adaptive, mass-consistent finite-element model (FEM) has been developed for constructing 3D wind fields over irregular terrain utilizing sparse meteorological tower data. The element size in the computational domain is dynamically controlled by an a posteriori error estimator based on the L2 norm. In the h-adaptive FEM algorithm, large element sizes are typically associated with smooth flow regions and small errors; small element sizes are attributed to fast-changing flow regions and large errors. The adaptive procedure employed in this model uses mesh refinement–unrefinement to satisfy error criteria. Results are presented for wind fields using sparse data obtained from two regions within Nevada: 1) the Nevada Test Site, located approximately 65 mi (1 mi ≈ 1.6 km) northwest of Las Vegas, and 2) the central region of Nevada, about 100 mi southeast of Reno.

Corresponding author address: Darrell W. Pepper, Department of Mechanical Engineering, University of Nevada, Las Vegas, 4505 Maryland Parkway, Las Vegas, NV 89154-4027. Email: dwpepper@nscee.edu

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Journal of Applied Meteorology and Climatology

  • Ainsworth, M., and J. T. Oden, 2000: A Posteriori Error Estimation in Finite Element Analysis. Pure and Applied Mathematics, Series of Texts, Monographs and Tracts, Wiley-Interscience, 264 pp.

    • Search Google Scholar
    • Export Citation

  • Biswas, R., and R. C. Strawn, 1998: Tetrahedral and hexahedral mesh adaptation for CFD problems. Appl. Numer. Math, 26 , 135–151.

  • Demkowicz, L., 2006: Computing with hp-Adaptive Finite Elements. Vols. 1 and 2, Dimensional Elliptic and Maxwell Problems, CRC Press, 398 pp.

    • Search Google Scholar
    • Export Citation

  • Demkowicz, L., J. T. Oden, W. Rachowicz, and O. Hardy, 1989: Toward a universal h-p adaptive finite element strategy, Part 1. Constrained approximation and data structures. Comput. Methods Appl. Mech. Eng., 77 , 79–112.

    • Search Google Scholar
    • Export Citation

  • Dickerson, M. H., 1978: MASCON-A mass consistent atmospheric flux model for regions with complex terrain. J. Appl. Meteor., 17 , 241–253.

    • Search Google Scholar
    • Export Citation

  • Finardi, S., G. Tinarelli, P. Faggian, and G. Brusasca, 1998: Evaluation of different wind field modeling techniques for wind energy applications over complex topography. J. Wind Eng. Ind. Aerodyn., 74–76 , 283–294.

    • Search Google Scholar
    • Export Citation

  • Goodin, W. R., G. J. Mcrae, and J. H. Seinfeld, 1979: A comparison of interpolation methods for sparse data: Application to wind and concentration fields. J. Appl. Meteor., 18 , 761–771.

    • Search Google Scholar
    • Export Citation

  • Goodin, W. R., G. J. Mcrae, and J. H. Seinfeld, 1980: An objective analysis technique for constructing three-dimensional urban-scale wind fields. J. Appl. Meteor., 19 , 98–108.

    • Search Google Scholar
    • Export Citation

  • Guo, B., and I. Babuska, 1986a: The h-p version of the finite element method—Part 1: The basic approximation results. Comput. Mech., 1 , 21–41.

    • Search Google Scholar
    • Export Citation

  • Guo, B., and I. Babuska, 1986b: The h-p version of the finite element method—Part 2: General results and applications. Comput. Mech., 1 , 203–220.

    • Search Google Scholar
    • Export Citation

  • Heinrich, J. C., and D. W. Pepper, 1999: Intermediate Finite Element Method: Fluid Flow and Heat Transfer Applications. Taylor and Francis, 600 pp.

    • Search Google Scholar
    • Export Citation

  • Kitada, T., A. Kaki, H. Ueda, and L. K. Peters, 1983: Estimation of vertical air motion from limited horizontal wind data-A numerical experiment. Atmos. Environ., 17 , 2181–2192.

    • Search Google Scholar
    • Export Citation

  • Lange, R., 1978: A three-dimensional transport-diffusion model for the dispersal of atmospheric pollutants and its validation against regional tracer studies. J. Appl. Meteor., 17 , 241–256.

    • Search Google Scholar
    • Export Citation

  • Mathur, R., and L. K. Peters, 1990: Adjustment of wind fields for application in air pollution modeling. Atmos. Environ., 24 , 1095–1106.

    • Search Google Scholar
    • Export Citation

  • Montero, G., and N. Sanin, 2001: 3-D modeling of wind field adjustment using finite differences in a terrain conformal coordinate system. J. Wind Eng. Ind. Aerodyn., 89 , 471–488.

    • Search Google Scholar
    • Export Citation

  • Montero, G., E. Rodríguez, R. Montenegro, J. M. Escobar, and J. M. González-Yuste, 2005: Genetic algorithms for an improved parameter estimation with local refinement of tetrahedral meshes in a wind model. Adv. Eng. Software, 36 , 3–10.

    • Search Google Scholar
    • Export Citation

  • Nithiarasu, P., and O. C. Zienkiewicz, 2000: Adaptive mesh generation for fluid mechanics problems. Int. J. Numer. Methods Eng., 47 , 629–662.

    • Search Google Scholar
    • Export Citation

  • Oñate, E., and G. Bugeda, 1994: Mesh optimality criteria for adaptive finite element computations. The Mathematics of Finite Elements and Applications: Highlights 1993, J. R. Whiteman, Ed., John Wiley and Sons, 121–135.

    • Search Google Scholar
    • Export Citation

  • Pepper, D. W., 1991: A finite element model for calculating 3-d wind fields over Vandenberg Air Force Base. 29th AIAA Aerospace Sciences Meeting, AIAA Paper 91-0451, Reno, NV, American Institute of Aeronautics and Astronautics, 1–8.

    • Search Google Scholar
    • Export Citation

  • Pepper, D. W., and D. E. Stephenson, 1995: An adaptive finite element model for calculating subsurface transport of contaminant. Ground Water, 33 , 486–496.

    • Search Google Scholar
    • Export Citation

  • Pepper, D. W., and D. B. Carrington, 1999: Application of h-adaptation for environmental fluid flow and species transport. Int. J. Numer. Methods Fluids, 31 , 275–283.

    • Search Google Scholar
    • Export Citation

  • Pepper, D. W., and J. C. Heinrich, 2006: The Finite Element Method: Basic Concepts and Applications. 2nd ed. Taylor and Francis, 312 pp.

    • Search Google Scholar
    • Export Citation

  • Pepper, D. W., and X. Wang, 2007: Application of an h-adaptive FEM for wind energy assessment in Nevada. Renewable Energy, 32 , 1705–1722.

    • Search Google Scholar
    • Export Citation

  • Pielke, R., 1984: Mesoscale Meteorological Modeling. Academic Press, 612 pp.

  • Ratto, C. F., R. Festa, C. Romeo, O. A. Frumento, and M. Galluzzi, 1994: Mass-consistent models for wind fields over complex terrain: The state of the art. Environ. Software, 9 , 247–268.

    • Search Google Scholar
    • Export Citation

  • Sasaki, Y., 1958: An objective analysis based on the variational method. J. Meteor. Soc. Japan, 36 , 77–88.

  • Schaefer, J. T., and C. A. Doswell III, 1979: On the interpolation of a vector field. Mon. Wea. Rev., 107 , 458–476.

  • Sherman, C. A., 1978: A mass-consistent model for wind field over complex terrain. J. Appl. Meteor., 17 , 312–319.

  • Wang, X., and D. W. Pepper, 2007a: Application of an hp-adaptive FEM for solving thermal flow problems. AIAA J. Thermophys. Heat Transfer, 21 , 190–198.

    • Search Google Scholar
    • Export Citation

  • Wang, X., and D. W. Pepper, 2007b: Application of h-, p- and hp-adaptation for convection heat transfer problems. 45th AIAA Aerospace Sciences Meeting, Reno, NV, American Institute of Aeronautics and Astronautics, 9792–9800.

    • Search Google Scholar
    • Export Citation

  • Warner, T. T., R. R. Fizz, and N. L. Seaman, 1983: A comparison of two types of atmospheric transport models—Use of observed winds versus dynamically predicted winds. J. Climate Appl. Meteor., 22 , 394–406.

    • Search Google Scholar
    • Export Citation

  • Winter, G., G. Montero, L. Ferragut, and R. Montenegro, 1995: Adaptive strategies using standard and mixed finite elements for wind field adjustment. Sol. Energy, 54 , 49–56.

    • Search Google Scholar
    • Export Citation

  • Zienkiewicz, O. C., and R. J. Z. Zhu, 1987: A simple error estimator and adaptive procedure for practical engineering analysis. Int. J. Numer. Methods Eng., 24 , 337–357.

    • Search Google Scholar
    • Export Citation
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