Editorial Type:
Article
Article Type:
Research Article

Dynamic Grid Adaptation Using the MPDATA Scheme

John P. Iselin Department of Mechanical Engineering, Bucknell University, Lewisburg, Pennsylvania

Search for other papers by John P. Iselin in
Current site
Google Scholar
PubMed Close
,
Joseph M. Prusa Department of Mechanical Engineering, Iowa State University, Ames, Iowa

Search for other papers by Joseph M. Prusa in
Current site
Google Scholar
PubMed Close
, and
William J. Gutowski Department of Geological and Atmospheric Sciences and Department of Agronomy, Iowa State University, Ames, Iowa

Search for other papers by William J. Gutowski in
Current site
Google Scholar
PubMed Close
Print Publication:
01 Apr 2002
DOI:
https://doi.org/10.1175/1520-0493(2002)130<1026:DGAUTM>2.0.CO;2
Page(s):
1026–1039
Restricted access

Abstract

A dynamic grid adaptation (DGA) scheme is developed using various combinations of the multidimensional positive definite advection transport algorithm (MPDATA) to show the applicability of DGA with the MPDATA scheme to solve advection problems. A one-dimensional model is used to show the effects of varying the number of grid points and the parameters that control the grid redistribution scheme, to determine a stability criteria for the scheme and to investigate the effect of several MPDATA options. A two-dimensional model is used to show the applicability of the scheme in multiple dimensions and to illustrate the effects of DGA in combination with MPDATA options. Diffusion errors are reduced by more than 90% using DGA when compared to static, uniformly spaced grid computations. Phase errors are reduced using certain MPDATA options by more than 25%.

Corresponding author address: Dr. John P. Iselin, Dept. of Mechanical Engineering, Bucknell University, Lewisburg, PA 17837. Email: iselin@bucknell.edu

Abstract

A dynamic grid adaptation (DGA) scheme is developed using various combinations of the multidimensional positive definite advection transport algorithm (MPDATA) to show the applicability of DGA with the MPDATA scheme to solve advection problems. A one-dimensional model is used to show the effects of varying the number of grid points and the parameters that control the grid redistribution scheme, to determine a stability criteria for the scheme and to investigate the effect of several MPDATA options. A two-dimensional model is used to show the applicability of the scheme in multiple dimensions and to illustrate the effects of DGA in combination with MPDATA options. Diffusion errors are reduced by more than 90% using DGA when compared to static, uniformly spaced grid computations. Phase errors are reduced using certain MPDATA options by more than 25%.

Corresponding author address: Dr. John P. Iselin, Dept. of Mechanical Engineering, Bucknell University, Lewisburg, PA 17837. Email: iselin@bucknell.edu

Save
Cover Monthly Weather Review
Monthly Weather Review

  • Bacon, D. P., and Coauthors. 2000: A dynamically adapting weather and dispersion model: The Operational Multiscale Environmental Model with Grid Adaptivity (OMEGA). Mon. Wea. Rev., 128 , 2044–2076.

    • Search Google Scholar
    • Export Citation

  • Behrens, J., 1996: An adaptive semi-Lagrangian advection scheme and its parallelization. Mon. Wea. Rev., 124 , 2386–2395.

  • Berger, M., and J. Oliger, 1984: Adaptive mesh refinement for hyperbolic partial differential equations. J. Comput. Phys., 53 , 484–512.

    • Search Google Scholar
    • Export Citation

  • Boris, J. P., and D. L. Book, 1973: Flux-corrected transport, I. SHASTA, a fluid transort algorithm that works. J. Comput. Phys., 11 , 38–69.

    • Search Google Scholar
    • Export Citation

  • Brackbill, J. U., and J. S. Saltzman, 1982: Adaptive zoning and singular problems in two dimensions. J. Comput. Phys., 46 , 342–368.

    • Search Google Scholar
    • Export Citation

  • DeMaria, M., S. D. Aberson, and K. A. Ooyama, 1992: A nested spectral model for hurricane track forecasting. Mon. Wea. Rev., 120 , 1628–1643.

    • Search Google Scholar
    • Export Citation

  • Dietachmayer, G. S., and K. K. Droegemeier, 1992: Application of continuous dynamic grid adaptation techniques to meteorological modeling. Part I: Basic formulation and accuracy. Mon. Wea. Rev., 120 , 1675–1706.

    • Search Google Scholar
    • Export Citation

  • Fiedler, B. H., and R. J. Trapp, 1993: A fast dynamic grid adaptation scheme for meteorological flows. Mon. Wea. Rev., 121 , 2879–2888.

    • Search Google Scholar
    • Export Citation

  • Finley, C. A., W. R. Cotton, and R. A. Pielke, 1998a: Numerical simulation of two tornadoes produced by a high-precipitation supercell. Preprints, 19th Conf. on Severe Local Storms, Minneapolis, MN, Amer. Meteor. Soc., 206–209.

    • Search Google Scholar
    • Export Citation

  • Finley, C. A., W. R. Cotton, and R. A. Pielke, . 1998b: Secondary vortex development in a tornado vortex produced by a simulated supercell thunderstorm. Preprints, 19th Conf. on Severe Local Storms, Minneapolis, MN, Amer. Meteor. Soc., 359–362.

    • Search Google Scholar
    • Export Citation

  • Hawken, D., J. Gottlieb, and J. Hansen, 1991: Review of some adaptive node-movement techniques in finite-element and finite-difference solutions of partial differential equations. J. Comput. Phys., 95 , 254–302.

    • Search Google Scholar
    • Export Citation

  • Iselin, J. P., 1999: A dynamic adaptive grid MPDATA scheme: Application to the computational solution of atmospheric tracer transport problems. Ph.D. dissertation, Iowa State University, 174 pp.

    • Search Google Scholar
    • Export Citation

  • Kim, J. K., and J. R. Thompson, 1990: Three-dimensional adaptive grid generation on a composite-block grid. AIAA J., 38 , 470–477.

    • Search Google Scholar
    • Export Citation

  • Margolin, L. G., and P. K. Smolarkiewicz, 1989: Antidiffusive velocities for multipass donor cell advection. Tech. Rep. UCID-21866, Lawerence Livermore National Laboratory, Livermore, CA, 44 pp.

    • Search Google Scholar
    • Export Citation

  • Prusa, J. M., P. K. Smolarkiewicz, and R. R. Garcia, 1996: Propogation and breaking at high altitudes of gravity waves excited by tropospheric forcing. J. Atmos. Sci., 53 , 2186–2216.

    • Search Google Scholar
    • Export Citation

  • Prusa, J. M., P. K. Smolarkiewicz, and A. A. Wyszogrodzki, 2001: Simulations of gravity wave induced trubulence using 512 PE CRAY T3E. Int. J. Appl. Math. Comput. Sci., 11 , 101–115.

    • Search Google Scholar
    • Export Citation

  • Skamarock, W., and J. B. Klemp, 1993: Adaptive grid refinement for two-dimensional and three-dimensional nonhydrostatic atmospheric flow. Mon. Wea. Rev., 121 , 788–804.

    • Search Google Scholar
    • Export Citation

  • Skamarock, W., M. L. Weisman, and J. B. Klemp, 1994: Three-dimensional evolution of simulated long-lived squall lines. J. Atmos. Sci., 51 , 2563–2583.

    • Search Google Scholar
    • Export Citation

  • Smolarkiewicz, P. K., and L. G. Margolin, 1998: MPDATA: A finite-difference solver for geophysical flows. J. Comput. Phys., 140 , 459–480.

    • Search Google Scholar
    • Export Citation

  • Smolarkiewicz, P. K., and J. M. Prusa, 2002: VLES modeling of geophysical fluids with nonoscillatory forward-in-time schemes. Int. J. Numer. Methods Fluids, in press.

    • Search Google Scholar
    • Export Citation

  • Thompson, J. F., Z. U. A. Warsi, and C. W. Mastin, 1985: Numerical Grid Generation: Foundations and Applications. Elsevier Science.

  • Tomlin, A., M. Berzens, J. Ware, J. Smith, and M. Pilling, 1997: On the use of adaptive gridding methods for modelling chemical transport from multi-scale sources. Atmos. Environ., 31 , 2945–2959.

    • Search Google Scholar
    • Export Citation

  • Yanenko, N., V. D. Lisseikin, and V. M. Kovenia, 1979: The method of the solution of gaz dynamical problems in moving meshes. Lect. Notes Phys., 91 , 48–61.

    • Search Google Scholar
    • Export Citation

  • Zalesak, T. S., 1979: Fully mulidimensional flux-corrected transport algorithms for fluids. J. Comput. Phys., 31 , 335–362.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 613 483 16
PDF Downloads 130 50 3