A Scale-Aware Anticipated Potential Vorticity Method: On Variable-Resolution Meshes

Qingshan Chen Los Alamos National Laboratory, Los Alamos, New Mexico

Search for other papers by Qingshan Chen in
Current site
Google Scholar
PubMed
Close
,
Max Gunzburger The Florida State University, Tallahassee, Florida

Search for other papers by Max Gunzburger in
Current site
Google Scholar
PubMed
Close
, and
Todd Ringler Los Alamos National Laboratory, Los Alamos, New Mexico

Search for other papers by Todd Ringler in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

A scale-aware formulation of the anticipated potential vorticity method (APVM), previously derived for quasi-uniform unstructured grids, is evaluated on multiresolution grids. Comparison is made to the original, nonscale-aware formulation of the APVM. Numerical experiments are performed using the shallow-water standard test case 5. The scale awareness of the new formulation is demonstrated by the following observations: (i) the range of optimal values for the single parameter of the new formulation is much less sensitive to grid resolution than that of the original formulation; (ii) within the optimal parameter range, the new formulation is able to maintain proper dissipation across scales and is thus able to produce better results in terms of errors in the potential enstrophy spectrum curves; and (iii) the new formulation is robust in that a single optimal parameter obtained for a specific grid can be safely used on other grids as well.

Corresponding author address: Qingshan Chen, Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545. E-mail: qchen@lanl.gov

Abstract

A scale-aware formulation of the anticipated potential vorticity method (APVM), previously derived for quasi-uniform unstructured grids, is evaluated on multiresolution grids. Comparison is made to the original, nonscale-aware formulation of the APVM. Numerical experiments are performed using the shallow-water standard test case 5. The scale awareness of the new formulation is demonstrated by the following observations: (i) the range of optimal values for the single parameter of the new formulation is much less sensitive to grid resolution than that of the original formulation; (ii) within the optimal parameter range, the new formulation is able to maintain proper dissipation across scales and is thus able to produce better results in terms of errors in the potential enstrophy spectrum curves; and (iii) the new formulation is robust in that a single optimal parameter obtained for a specific grid can be safely used on other grids as well.

Corresponding author address: Qingshan Chen, Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545. E-mail: qchen@lanl.gov
Save
  • Chen, Q., M. Gunzburger, and T. Ringler, 2011: A scale-invariant formulation of the anticipated potential vorticity method. Mon. Wea. Rev., 139, 26142629.

    • Search Google Scholar
    • Export Citation
  • Courant, R., K. Friedrichs, and H. Lewy, 1967: On the partial difference equations of mathematical physics. IBM J. Res. Develop., 11, 215234.

    • Search Google Scholar
    • Export Citation
  • Du, Q., V. Faber, and M. Gunzburger, 1999: Centroidal Voronoi tessellations: Applications and algorithms. SIAM Rev., 41 (4), 637676.

  • Du, Q., M. Gunzburger, and L. Ju, 2003: Constrained centroidal Voronoi tessellations for surfaces. SIAM J. Sci. Comput., 24 (5), 14881506.

    • Search Google Scholar
    • Export Citation
  • Fox-Kemper, B., and D. Menemenlis, 2008: Can large eddy simulation techniques improve mesoscale-rich ocean models? Ocean Modeling in an Eddying Regime, Geophys. Monogr., Vol. 177, Amer. Geophys. Union, 319–338.

  • Pedlosky, J., 1987: Geophysical Fluid Dynamics. 2nd ed. Springer, xiv+710 pp.

  • Rhines, P. B., 1975: Waves and turbulence on a beta-plane. J. Fluid Mech., 69 (3), 417443.

  • Ringler, T., D. Jacobsen, M. Gunzburger, L. Ju, M. Duda, and W. Skamarock, 2011: Exploring a multi-resolution modeling approach within the shallow-water equations. Mon. Wea. Rev., 139, 33483368.

    • Search Google Scholar
    • Export Citation
  • Sadourny, R., and C. Basdevant, 1985: Parameterization of subgrid-scale barotropic and baroclinic eddies in quasi-geostrophic models: Anticipated potential vorticity method. J. Atmos. Sci., 42, 13531363.

    • Search Google Scholar
    • Export Citation
  • 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, 211224.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 113 63 1
PDF Downloads 46 28 0