A Local Meshless Method for Approximating 3D Wind Fields

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

Search for other papers by Darrell W. Pepper in
Current site
Google Scholar
PubMed
Close
and
Jiajia Waters Nevada Center for Advanced Computational Methods, University of Nevada, Las Vegas, Nevada

Search for other papers by Jiajia Waters in
Current site
Google Scholar
PubMed
Close
Restricted access

We are aware of a technical issue preventing figures and tables from showing in some newly published articles in the full-text HTML view.
While we are resolving the problem, please use the online PDF version of these articles to view figures and tables.

Abstract

An efficient, mesh-free numerical method has been developed for creating 3D wind fields using data from meteorological towers. Node points are placed within a region of interest, generally based upon topological features. Since meshless methods do not require connective mesh generation, storage is greatly reduced, permitting implementation of the code using MATLAB on a personal computer. Utilizing locally collocated nodes and radial basis functions, a 3D wind can be quickly created that satisfies mass consistency. The meshless method yields close approximations to results obtained with mesh-dependent finite-difference, finite-volume, and finite-element techniques.

Corresponding author address: Darrell W. Pepper, Department of Mechanical Engineering, University of Nevada, Las Vegas, 4505 Maryland Parkway, Las Vegas, NV 89154-4027. E-mail: darrell.pepper@unlv.edu

Abstract

An efficient, mesh-free numerical method has been developed for creating 3D wind fields using data from meteorological towers. Node points are placed within a region of interest, generally based upon topological features. Since meshless methods do not require connective mesh generation, storage is greatly reduced, permitting implementation of the code using MATLAB on a personal computer. Utilizing locally collocated nodes and radial basis functions, a 3D wind can be quickly created that satisfies mass consistency. The meshless method yields close approximations to results obtained with mesh-dependent finite-difference, finite-volume, and finite-element techniques.

Corresponding author address: Darrell W. Pepper, Department of Mechanical Engineering, University of Nevada, Las Vegas, 4505 Maryland Parkway, Las Vegas, NV 89154-4027. E-mail: darrell.pepper@unlv.edu
Save
  • Atluri, S. N., and T. Zhu, 1998: A new meshless local Petrov–Galerkin (MLPG) approach in computational mechanics. Comput. Mech., 22, 117–127, doi:10.1007/s004660050346.

    • Search Google Scholar
    • Export Citation
  • Balachandran, G. R., A. Rajagopal, and S. M. Sivakumar, 2008: Mesh-free Galerkin method based on natural neighbors and conformal mapping. Comput. Mech., 42, 885–905, doi:10.1007/s00466-008-0292-0.

    • Search Google Scholar
    • Export Citation
  • Choi, Y., and S. J. Kim, 1999: Node generation scheme for the mesh-less method by Voronoi diagram and weighted bubble packing. Proc. Fifth U.S. National Congress on Computational Mechanics, Boulder, CO, USACM.

  • Dickerson, M. H., 1978: MASCON—A mass consistent atmospheric flux model for regions with complex terrain. J. Appl. Meteor., 17, 241–253, doi:10.1175/1520-0450(1978)017<0241:MMCAFM>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Fasshauer, G. E., 2002: Newton iteration with multiquadrics for the solution of nonlinear PDEs. Comput. Math. Appl., 43, 423–438, doi:10.1016/S0898-1221(01)00296-6.

    • Search Google Scholar
    • Export Citation
  • Fasshauer, G. E., 2007: Meshfree Approximation Methods with MATLAB. Interdisciplinary Mathematical Sciences Series, Vol. 6, World Scientific, 500 pp.

    • Search Google Scholar
    • Export Citation
  • Franke, R., 1982: Scattered data interpolation: Tests of some methods. Math. Comput., 38, 181–200, doi:10.1090/S0025-5718-1982-0637296-4.

    • Search Google Scholar
    • Export Citation
  • Gewali, L., and D. W. Pepper, 2010: Adaptive node placement for mesh-free methods. Proc. ICCES’10, Las Vegas, NV, International Conference on Computational & Experimental Engineering and Sciences.

  • Hardy, R. L., 1971: Multiquadric equations of topography and other irregular surfaces. J. Geophys. Res., 76, 1905–1915, doi:10.1029/JB076i008p01905.

    • Search Google Scholar
    • Export Citation
  • Hecht, F., 2012: New development in FreeFEM++. J. Numer. Math., 20, 251–265, doi:10.1515/jnum-2012-0013.

  • Kansa, E. J., 2005: Highly accurate methods for solving elliptic and parabolic partial differential equations. WIT Trans. Model. Simul., 39, 5–15.

    • Search Google Scholar
    • Export Citation
  • Li, H., and S. S. Mulay, 2013: Meshless Methods and Their Numerical Properties. CRC Press, 429 pp.

  • Liu, G. R., 2003: Meshfree Methods: Moving Beyond the Finite Element Method. CRC Press, 692 pp.

  • Pepper, D. W., and X. Wang, 2009: An h-adaptive finite-element technique for constructing 3D wind fields. J. Appl. Meteor. Climatol., 48, 580–599, doi:10.1175/2008JAMC1680.1.

    • Search Google Scholar
    • Export Citation
  • Pepper, D. W., A. Kassab, and E. Divo, 2014a: Introduction to Finite Element, Boundary Element, and Meshless Methods. ASME Press, 269 pp.

  • Pepper, D. W., C. Rasmussen, and D. Fyda, 2014b: A meshless method for creating 3-D wind fields using sparse meteorological data. Proc. ICIPE 2014, Krakow, Poland, World Academy of Science, Engineering and Technology, 121–122.

    • Search Google Scholar
    • Export Citation
  • Roque, C. M. C., and A. J. M. Ferreira, 2009: Numerical experiments on optimal shape parameters for radial basis functions. Numer. Meth. Part. Differential Eq., 26, 675–689, doi:10.1002/num.20453.

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

  • Sherman, C. A., 1978: A mass-consistent model for wind fields over complex terrain. J. Appl. Meteor., 17, 312–319, doi:10.1175/1520-0450(1978)017<0312:AMCMFW>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Waters, J., and D. W. Pepper, 2015: Global versus localized RBF meshless methods for solving incompressible fluid flow with heat transfer. Numer. Heat Transf., 68B, 185–203, doi:10.1080/10407790.2015.1021590.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 622 323 148
PDF Downloads 280 63 1