Award Abstract # 0723440
CMG: Adaptive Mesh Refinement for Vortices in Climate and Weather-Forecasting: Comparing and Blending Finite Volume Methods with Vortex/Radial Basis Function Algorithms

NSF Org: AGS
Division of Atmospheric and Geospace Sciences
Recipient: REGENTS OF THE UNIVERSITY OF MICHIGAN
Initial Amendment Date: September 13, 2007
Latest Amendment Date: September 13, 2007
Award Number: 0723440
Award Instrument: Standard Grant
Program Manager: Eric DeWeaver
edeweave@nsf.gov
 (703)292-8527
AGS
 Division of Atmospheric and Geospace Sciences
GEO
 Directorate for Geosciences
Start Date: October 1, 2007
End Date: September 30, 2010 (Estimated)
Total Intended Award Amount: $423,865.00
Total Awarded Amount to Date: $423,865.00
Funds Obligated to Date: FY 2007 = $423,865.00
History of Investigator:
  • John Boyd (Principal Investigator)
    jpboyd@umich.edu
  • Robert Krasny (Co-Principal Investigator)
  • Christiane Jablonowski (Co-Principal Investigator)
Recipient Sponsored Research Office: Regents of the University of Michigan - Ann Arbor
1109 GEDDES AVE STE 3300
ANN ARBOR
MI  US  48109-1015
(734)763-6438
Sponsor Congressional District: 06
Primary Place of Performance: Regents of the University of Michigan - Ann Arbor
1109 GEDDES AVE STE 3300
ANN ARBOR
MI  US  48109-1015
Primary Place of Performance
Congressional District:
06
Unique Entity Identifier (UEI): GNJ7BBP73WE9
Parent UEI:
NSF Program(s): OPPORTUNITIES FOR RESEARCH CMG,
MATHEMATICAL GEOSCIENCES
Primary Program Source: app-0107 
Program Reference Code(s): 0000, 4444, 7232, 7303, OTHR
Program Element Code(s): 721500, 723200
Award Agency Code: 4900
Fund Agency Code: 4900
Assistance Listing Number(s): 47.050

ABSTRACT

A collaborating team of mathematicians, computational algorithm experts and atmospheric dynamacists have prioritized a series of challenging and largely unresolved questions in the topic area of adaptive mesh refinement of vortex dominated flows encountered in numerical weather prediction and climate modeling. A common underlying theme being adopted seeks the improvement of adaptive, multi-scale methods to better resolve the finer features of intense vortices which dominate these kinds of geophysical flows. This semi-structured feature-based goal is different from simple nesting of higher resolution gridding of vortex cores. Suggested approaches which will be explored to answer these questions include comparing and blending well-established numerical algorithms, such as finite volume and vortex blob methods, along with radial basis function schemes, tree codes and less well explored hybridizations of these.
Resolving fine structure in the representation of vortices is needed to strengthen predictive skill and long-time behavior in fields such as climate modeling and weather forecasting. Development of adaptive, multi-scale-resolving numerical schemes to treat vortex dominated flows are also expected to have wider application to areas outside of geophysics.

PUBLICATIONS PRODUCED AS A RESULT OF THIS RESEARCH

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(Showing: 1 - 10 of 21)
John P. Boyd and Lei Wang "Truncated RBF Differences Are Always Inferior to Finite Differences of the Same" Communications in Computational Physics , v.5 , 2009 , p.42
Cheng Zhou and John P. Boyd "Nonlinear Shallow Water Tropical Instability Waves on the Equatorial Beta-plane:Genesis of Two Distinct Types of Waves Genesis of Two Distinct Types of Waves" Geophys. Res. Lett. , v.36 , 2009 , p.23
Hualong Feng and Leon Kaganovskiy and Robert Krasny "Azimuthal Instability of a Vortex Ring Computed by a Vortex Sheet Panel Method" Journal of Fluid Mechanics , v.41 , 2009 , p.0514
Joh "Asymptotic Coefficients for Gaussian Radial Basis Function Interpolants" Applied Mathematics and Computation , 2009
John Boyd and Lei Wang "Asymptotic Coefficients for Gaussian Radial Basis Function Interpolants" Applied Mathematics and Computation , v.216 , 2009 , p.23
John P. Boyd "Error Saturation in Gaussian Radial Basis Functions on a Finite Interval" J. Comput. Appl. Math. , v.234 , 2001 , p.1
John P. Boyd "Evaluating of Dawson's Integral by Solving Its Differential Equation Using" Applied Mathematics and Computation , v.204 , 2008
John P. Boyd "Evaluating of Dawson's Integral by Solving Its Differential Equation Using" Applied Mathematics and Computation , v.204 , 2008
John P. Boyd "Icosahedral Anaster" Nature , v.453 , 2008 , p.256
John P. Boyd "Sensitivity of RBF Interpolation on an Otherwise Uniform Grid with a Point Omitted or Slightly Shifted" Applied Numerical Mathematics , v.60 , 2010 , p.659
John P. Boyd "The Uselessness of the Fast Gauss Transform for Summing Gaussian Radial Basis" Journal of Computational Physics , v.229 , 2009 , p.13
(Showing: 1 - 10 of 21)

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