Editorial Type:
Article
Article Type:
Research Article

A Global Multimoment Constrained Finite-Volume Scheme for Advection Transport on the Hexagonal Geodesic Grid

Chungang Chen School of Human Settlement and Civil Engineering, Xi’an Jiaotong University, Xi’an, and LHD, Institute of Mechanics, Chinese Academy of Sciences, Beijing, China

Search for other papers by Chungang Chen in
Current site
Google Scholar
PubMed Close
,
Juzhong Bin LHD, Institute of Mechanics, Chinese Academy of Sciences, Beijing, China

Search for other papers by Juzhong Bin in
Current site
Google Scholar
PubMed Close
, and
Feng Xiao Department of Energy Sciences, Tokyo Institute of Technology, Yokohama, Japan

Search for other papers by Feng Xiao in
Current site
Google Scholar
PubMed Close
Print Publication:
01 Feb 2011
DOI:
https://doi.org/10.1175/MWR-D-11-00095.1
Page(s):
941–955
Restricted access

Abstract

A third-order numerical model is developed for global advection transport computation. The multimoment constrained finite-volume scheme has been implemented to the hexagonal geodesic grid for spherical geometry. Two kinds of moments (i.e., point value and volume-integrated average) are used as the constraint conditions to derive the time evolution equations to update the computational variables, which are the values defined at the specified points over each mesh element in the present model. The numerical model has rigorous numerical conservation and third-order accuracy. One of the major merits of the present method is that it does not explicitly involve numerical quadrature, which leads to great convenience in accurately computing curved geometry and source terms. The present paper provides an accurate and practical formulation for advection calculation in the hexagonal-type geodesic grid.

Corresponding author address: Chungang Chen, School of Human Settlement and Civil Engineering, Xi’an Jiaotong University, Xi’an, 710049, China. E-mail: cgchen@mail.xjtu.edu.cn

Abstract

A third-order numerical model is developed for global advection transport computation. The multimoment constrained finite-volume scheme has been implemented to the hexagonal geodesic grid for spherical geometry. Two kinds of moments (i.e., point value and volume-integrated average) are used as the constraint conditions to derive the time evolution equations to update the computational variables, which are the values defined at the specified points over each mesh element in the present model. The numerical model has rigorous numerical conservation and third-order accuracy. One of the major merits of the present method is that it does not explicitly involve numerical quadrature, which leads to great convenience in accurately computing curved geometry and source terms. The present paper provides an accurate and practical formulation for advection calculation in the hexagonal-type geodesic grid.

Corresponding author address: Chungang Chen, School of Human Settlement and Civil Engineering, Xi’an Jiaotong University, Xi’an, 710049, China. E-mail: cgchen@mail.xjtu.edu.cn
Save
Cover Monthly Weather Review
Monthly Weather Review

  • Akoh, R., S. Ii, and F. Xiao, 2010: A multi-moment finite volume formulation for shallow water equations on unstructured mesh. J. Comput. Phys., 229, 4567–4590.

    • Search Google Scholar
    • Export Citation

  • Bonaventura, L., and T. Ringler, 2005: Analysis of discrete shallow-water models on geodesic Delaunay grids with C-type staggering. Mon. Wea. Rev., 133, 2351–2373.

    • Search Google Scholar
    • Export Citation

  • Friedrich, O., 1998: Weighted essentially non-oscillatory schemes for the interpolation of mean values on unstructured grids. J. Comput. Phys., 144, 194–212.

    • Search Google Scholar
    • Export Citation

  • Giraldo, F., 2006: High-order triangle-based discontinuous Galerkin methods for hyperbolic equations on a rotating sphere. J. Comput. Phys., 214, 447–465.

    • Search Google Scholar
    • Export Citation

  • Ii, S., and F. Xiao, 2009: High order multi-moment constrained finite volume method. Part I: Basic formulation. J. Comput. Phys., 228, 3669–3707.

    • Search Google Scholar
    • Export Citation

  • Ii, S., and F. Xiao, 2010: A global shallow water model using high order multi-moment constrained finite volume method and icosahedral grid. J. Comput. Phys., 229, 1774–1796.

    • Search Google Scholar
    • Export Citation

  • Ii, S., M. Shimuta, and F. Xiao, 2005: A 4th-order and single-cell-based advection scheme on unstructured grids using multi-moments. Comput. Phys. Commun., 173, 17–33.

    • Search Google Scholar
    • Export Citation

  • Lipscomb, W., and T. Ringler, 2005: An incremental remapping transport scheme on a spherical geodesic grid. Mon. Wea. Rev., 133, 2235–2250.

    • Search Google Scholar
    • Export Citation

  • Majewski, D., D. Liermann, P. Prohl, B. Ritter, M. Buchhold, T. Hanisch, G. Paul, and W. Wergen, 2002: The operational global icosahedral-hexagonal grid-point model GME: Description and high-resolution tests. Mon. Wea. Rev., 130, 319–338.

    • Search Google Scholar
    • Export Citation

  • Miura, H., 2007: An upwind-biased conservative advection scheme for spherical hexagonal-pentagonal grids. Mon. Wea. Rev., 135, 4038–4044.

    • Search Google Scholar
    • Export Citation

  • Nair, R. D., and C. Jablonowski, 2008: Moving vortices on the sphere: A test case for horizontal advection problems. Mon. Wea. Rev., 136, 699–711.

    • Search Google Scholar
    • Export Citation

  • Nair, R. D., and P. H. Lauritzen, 2010: A class of deformational flow test cases for linear transport problems on the sphere. J. Comput. Phys., 229 (23), 8868–8887.

    • Search Google Scholar
    • Export Citation

  • Nair, R. D., S. J. Stephen, and R. D. Loft, 2005: A discontinuous Galerkin transport scheme on the cubed sphere. Mon. Wea. Rev., 133, 814–828.

    • Search Google Scholar
    • Export Citation

  • Ringler, T., J. Thuburn, J. Klemp, and W. Skamarock, 2010: A unified approach to energy conservation and potential vorticity dynamics on arbitrarily structured C-grids. J. Comput. Phys., 229, 3065–3090.

    • Search Google Scholar
    • Export Citation

  • Sadourny, R., A. Arakawa, and Y. Mintz, 1968: Integration of the nondivergent barotropic vorticity equation with an icosahedral-hexagonal grid for the sphere. Mon. Wea. Rev., 96, 351–356.

    • Search Google Scholar
    • Export Citation

  • Shu, C. W., 1988: Total variation diminishing time discretization. SIAM J. Sci. Stat. Comput., 9, 1073–1084.

  • Skamarock, W. C., and M. Menchaca, 2010: Conservative transport schemes for spherical geodesic grids: High-order reconstructions for forward-in-time schemes. Mon. Wea. Rev., 138, 4497–4508.

    • Search Google Scholar
    • Export Citation

  • Stuhne, G., and W. Peltier, 1999: New icosahedral grid-point discretizations of the shallow water equations on the sphere. J. Comput. Phys., 148, 23–58.

    • Search Google Scholar
    • Export Citation

  • Tomita, H., M. Tshugawa, M. Satoh, and K. Goto, 2001: Shallow water model on a modified icosahedral geodesic grid by using spring dynamics. J. Comput. Phys., 174, 579–613.

    • Search Google Scholar
    • Export Citation

  • Weller, H., H. G. Weller, and A. Fournier, 2009: Voronoi, Delaunay, and block-structured mesh refinement for solution of the shallow-water equations on the sphere. Mon. Wea. Rev., 137, 4208–4224.

    • Search Google Scholar
    • Export Citation

  • Williamson, D. L., 1968: Integration of the barotropic vorticity equation on a spherical geodesic grid. Tellus, 20, 642–653.

  • Williamson, D. L., J. B. Drake, J. J. Hack, R. Jakob, and P. N. Swarztrauber, 1992: A standard test set for numerical approximations to the shallow water equations in spherical geometry. J. Comput. Phys., 102, 211–224.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 224 105 3
PDF Downloads 111 27 0