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Voronoi Tessellations and Their Application to Climate and Global Modeling

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Numerical Techniques for Global Atmospheric Models

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 80))

Abstract

We review the use of Voronoi tessellations for grid generation, especially on the whole sphere or in regions on the sphere. Voronoi tessellations and the corresponding Delaunay tessellations in regions and surfaces on Euclidean space are defined and properties they possess that make them well-suited for grid generation purposes are discussed, as are algorithms for their construction. This is followed by a more detailed look at one very special type of Voronoi tessellation, the centroidal Voronoi tessellation (CVT). After defining them, discussing some of their properties, and presenting algorithms for their construction, we illustrate the use of CVTs for producing both quasi-uniform and variable resolution meshes in the plane and on the sphere. Finally, we briefly discuss the computational solution of model equations based on CVTs on the sphere.

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Acknowledgements

This work was supported by the US Department of Energy Office of Science Climate Change Prediction Program through grant numbers DE-FG02-07ER64431 and DE-FG02-07ER64432, and the US National Science Foundation under grant numbers DMS-0609575 and DMS-0913491.

The authors thank the reviewers and editors for the many helpful comments that resulted in substantial improvements to this chapter.

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Authors and Affiliations

  1. Department of Mathematics, University of South Carolina, Columbia, SC, 29208, USA

    Lili Ju

  2. T-3 Fluid Dynamics Group, Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA

    Todd Ringler

  3. Department of Scientific Computing, Florida State University, Tallahassee, FL, 32306-4120, USA

    Max Gunzburger

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  1. Lili Ju
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  2. Todd Ringler
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  3. Max Gunzburger
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Correspondence to Lili Ju .

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Editors and Affiliations

  1. Atmospheric Research, Dept. Climate/Global Dyn., National Center for, Boulder, Colorado, USA

    Peter Lauritzen

  2. Dept. Atmospheric, Oceanic &, Space Sciences, University of Michigan, Hayward St. 2455, Ann Arbor, 48109, Michigan, USA

    Christiane Jablonowski

  3. Organization 1433, MS-0370, Sandia National Laboratories, Albuquerque, New Mexico, USA

    Mark Taylor

  4. (NCAR), Inst. for Mathematics Applied to, National Center for Atmospheric Research, Boulder, Colorado, USA

    Ramachandran Nair

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Ju, L., Ringler, T., Gunzburger, M. (2011). Voronoi Tessellations and Their Application to Climate and Global Modeling. In: Lauritzen, P., Jablonowski, C., Taylor, M., Nair, R. (eds) Numerical Techniques for Global Atmospheric Models. Lecture Notes in Computational Science and Engineering, vol 80. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11640-7_10

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