Toward a multiscale approach for computational atmospheric modeling

Monthly Weather Review

Volumn 139, Issue 12, 2011, Pages 3906-3922

  Alam, Jahrul M ^a  

^a MEMORIAL UNIVERSITY OF NEWFOUNDLAND   (Canada)

Author keywords

Multigrid models; Wavelets

Indexed keywords

ADAPTIVE MODELS; ADAPTIVE WAVELETS; ASYMPTOTICALLY OPTIMAL; ATMOSPHERIC FLOWS; ATMOSPHERIC MODEL; ATMOSPHERIC MODELING; ATMOSPHERIC MOTIONS; CONVERGENCE AND STABILITY; CPU TIME; DEFORMATIONAL FLOW; DRY ATMOSPHERES; EXPLICIT TIME INTEGRATION SCHEME; FINE GRIDS; GRID POINTS; HIGH RESOLUTION; METEOROLOGICAL SIMULATIONS; MULTI-GRID MODEL; MULTI-SCALE APPROACHES; MULTI-SCALE FEATURES; MULTI-SCALE MODELING; MULTISCALES; PROGNOSTIC VARIABLES; REFERENCE MODELS; STABLE STRATIFICATION; THERMAL SIMULATIONS; TIME STEP; TIME-SCALES; VORTEX PAIR; WAVELETS;

MODELS; NUMERICAL METHODS; VORTEX FLOW;

COMPUTER SIMULATION;

ATMOSPHERIC MODELING; BENCHMARKING; CONVERGENCE; NUMERICAL MODEL; STABILITY ANALYSIS; TIMESCALE; WAVELET;

EID: 84855766228     PISSN: 00270644     EISSN: None     Source Type: Journal    
DOI: 10.1175/2011MWR3533.1     Document Type: Article

References (67)

1. Alam, J. M., 2006: A space-time adaptive wavelet method for turbulence. Ph.D. thesis, McMaster University, 152 pp.
2. Alam, J. M., 2010: A multiscale method for simulating geophysical flows. ExtendedAbstracts, 31stAnnualMeeting of the Canadian Applied and Industrial Mathematics Society, Newfoundland, Canada, Canadian Applied and Industrial Mathematics Society, 33.
3. Alam, J. M., and J. C. Lin, 2008: Toward a fully Lagrangian atmospheric modelling system. Mon. Wea. Rev., 136, 4653-4667.
4. Alam, J. M., N. K.-R. Kevlahan, and O. Vasilyev, 2006: Simultaneous space-time adaptive solution of nonlinear parabolic differential equations. J. Comput. Phys., 214, 829-857.
5. Bacon, D. P., Coauthors, 2000: A dynamically adapting weather and dispersion model: The Operational Multiscale Environment Model with Grid Adaptivity (OMEGA). Mon. Wea. Rev., 128, 2044-2076.
6. Bacon, D. P., Coauthors, 2003: Dynamically adapting unstructured triangular grids: Anew paradigmfor geophysical fluid dynamics modeling. Proc. Indian Natl. Sci. Acad., 69A (5), 457-470.
7. Bacon, D. P., N. N. Ahmad, T. J. Dunn, S. G. Gopalakrishnan, M. S. Hall, and A. Sarma, 2007:Hurricane track forecastingwithOMEGA. Nat. Hazards, 41 (3), 457-470.
8. Behrens, J., 1996: An adaptive semi-Lagrangian advection scheme and its parallelization. Mon. Wea. Rev., 124, 2386-2395.
9. Behrens, J., 1998: Atmospheric and ocean modelling with an adaptive finite element solver for the shallow-water equations. Appl. Numer. Math., 26 (1-2), 217-226.
10. Behrens, J., 2006: Adaptive Atmospheric Modelling: Key Techniques in Grid Generation, Data Structures, and Numerical Operations with Applications (Lecture Notes in Computational Science and Engineering). Springer-Verlag, 233 pp.
11. Berger, M. J., and P. Colella, 1989: Local adaptive mesh refinement for shock hydrodynamics. J. Comput. Phys., 82 (1), 64-84.
12. Bernsen, E., H. A. Dijkstra, J. Thies, and F. W. Wubs, 2010: The application of Jacobian-free Newton-Krylov methods to reduce the spin-up time of ocean general circulation models. J. Comput. Phys., 229 (21), 8167-8179.
13. Blayo, E., and L. Debreu, 1999: Adaptive mesh refinement for finite-difference ocean models: First experiments. J. Phys. Oceanogr., 29, 1239-1250.
14. Boybeyi, Z., N. N. Ahmad, D. P. Bacon, T. J. Dunn, M. S. Hall, P. C. S. Lee, R. A. Sarma, and T. R. Wait, 2001: Evaluation of the operational multiscale environment model with grid adaptivity against the European tracer experiment. J. Appl. Meteor., 40, 1541-1558.
15. Brandt, L. K., and K. K. Nomura, 2007: The physics of vortex merger and the effects of ambient stable stratification. J. Fluid Mech., 592, 413-446.
16. Bryan, G. H., and J. M. Fritsch, 2002: A benchmark simulation for moist nonhydrostatic numerical models. Mon. Wea. Rev., 130, 2917-2928.
17. Carpenter, R. L. J., K. K. Droegemeier, P. R. Woodward, and C. E. Hane, 1990: Application of the piecewise parabolic method (PPM) to meteorological modeling. Mon. Wea. Rev., 118, 586-612.
18. Cohen, A., 2003: Numerical Analysis of Wavelet Method. Elsevier, 336 pp.
19. Cohen, A., W. Dahmen, and R. DeVore, 2001: Adaptive wavelet methods for elliptic operator equations: Convergence rates. Math. Comput., 70 (233), 27-75.
20. Defant, F., 1951: Local winds. Compendium of Meteorology, T. F. Maloney, Ed., Amer. Meteor. Soc., 655-672.
21. De Stefano, G., and O. V. Vasilyev, 2010: Stochastic coherent adaptive large eddy simulation of forced isotropic turbulence. J. Fluid Mech., 646, 453-470.
22. DeVore, R.A., 1998: Nonlinear approximation. ActaNumer., 7, 51-150.
23. Donoho, D. L., 1992: Interpolating wavelet transforms. Tech. Rep. 408, Dept. of Statistics, Stanford University, 54 pp.
24. Durran, D. R., and A. Arakawa, 2007: Generalizing the Boussinesq approximation to stratified compressible flow. C. R. Mécanique, 335 (9-10), 655-664, doi:10.1016/j.crme.2007.08.010.
25. Grossmann, A., and J. Morlet, 1984: Decomposition of hardy functions into square integrable wavelets of constant shape. SIAM J. Math. Anal., 15 (4), 723-736, doi:10.1137/0515056.
26. Hamilton, K., and W. Ohfuchi, Eds., 2007: High Resolution Numerical Modelling of the Atmosphere and Ocean. Springer, 310 pp.
27. Hardenberg, J., A. McWilliams, J. C. Provenzale, A. Shchepetkin, and J. Weiss, 2000: Vortex merging in quasi-geostrophic flows. J. Fluid Mech., 412, 331-353.
28. Hooke, W. H., and R. M. Jones, 1986: Dissipative waves excited by gravity wave encounters with the stably stratified planetary boundary layer. J. Atmos. Sci., 43, 2048-2060.
29. Iida, O., N. Kasagi, and Y. Nagano, 2002: Direct numerical simulation of turbulent channel flow under stable density stratification. Int. J. Heat Mass Transfer, 45 (8), 1693-1703.
30. Jablonowski, C., 2004: Adaptive grids in weather and climate modeling. Ph.D. thesis, University of Michigan, 292 pp.
31. Jablonowski, C., M. Herzog, J. E. Penner, R. C. Oehmke, Q. F. Stout, B. van Leer, and K. G. Powell, 2006: Block-structured adaptive grids on the sphere: Advection experiments. Mon. Wea. Rev., 134, 3691-3713.
32. Jameson, L., and T. Miyama, 2000: Wavelet analysis and ocean modeling:Adynamically adaptive numerical method WOFDAHO. Mon. Wea. Rev., 128, 1536-1549.
33. Kevlahan, N.-R., and O. Vasilyev, 2005: An adaptive wavelet collocation method for fluid-structure interaction. SIAM J. Sci. Comput., 26 (6), 1894-1915.
34. Kevlahan, N.-R., J. Alam, and O. Vasilyev, 2007: Scaling of space-time modes with the Reynolds number in two-dimensional turbulence. J. Fluid Mech., 570, 217-226.
35. Knoll, D. A., and D. E. Keyes, 2004: Jacobian-free Newton-Krylov methods:Asurvey of approaches and applications. J. Comput. Phys., 193 (2), 357-397.
36. Lane, T. P., 2008: The vortical response to penetrative convection and the associated gravity-wave generation. Atmos. Sci. Lett., 9, 103-110.
37. Lauter, M., D. Handorf, N. Rakowsky, J. Behrens, S. Frickenhaus, M. Best, K. Dethloff, and W. Hiller, 2007: A parallel adaptive barotropic model of the atmosphere. J. Comput. Phys., 223 (2), 609-628.
38. Lundquist, K. A., F. K. Chow, and J. K. Lundquist, 2010: An immersed boundary method for the weather research and forecasting model. Mon. Wea. Rev., 138, 796-817.
39. Mallat, S., 1999: A Wavelet Tour of Signal Processing. Academic Press, 805 pp.
40. Manton, M. J., 1978: On dry penetrative convection. Bound.-Layer Meteor., 14 (3), 301-322.
41. Martin, C. L., and R. A. Pielke, 1983: The adequacy of the hydorostatic assumption in sea breeze modeling over flat terrain. J. Atmos. Sci., 40, 1472-1481.
42. Mehra, M., and N. K.-R. Kevlahan, 2008: An adaptive wavelet collocation method for the solution of partial differential equations on the sphere. J. Comput. Phys., 227 (11), 5610-5632.
43. Moeng, C.-H., 1984: A large-eddy-simulation model for the study of planetary boundary-layer turbulence. J. Atmos. Sci., 41, 2052-2062.
44. Nikiforakis, N., 2005: AMR for global atmospheric modelling. Adaptive Mesh Refinement-Theory and Applications (Lecture Notes in Computational Science and Engineering), T. Plewa, T. Linde, and V. G. Weirs, Eds., Vol. 41, Springer, 505-526.
45. Ogura, Y., and N. A. Phillips, 1962: Scale analysis of deep and shallow convection in the atmosphere. J. Atmos. Sci., 19, 173-179.
46. Pielke, R. A., 2002: Mesoscale Meterological Modelling. Academic Press, 676 pp.
47. Reisner, J., V. Mousseau, and D. Knoll, 2001: Application of the Newton-Krylov method to geophysical flows. Mon. Wea. Rev., 129, 2404-2415.
48. Rosenberg, D., A. Fournier, P. Fischer, and A. Pouquet, 2006: Geophysical-Astrophysical Spectral-Element Adaptive Refinement (GASPAR): Object-oriented h-adaptive fluid dynamics simulation. J. Comput. Phys., 215, 59-80, doi:10.1016/j.jcp.2005.10.031.
49. Saad, Y., and M. H. Schultz, 1986: GMRES:Ageneralized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput., 7 (3), 856-869.
50. Saffman, P.G., 1992: VortexDynamics. CambridgeUniversity Press, 311 pp.
51. Schär, C., D. Leuenberger, O. Fuhrer, D. Lthi, and C. Girard, 2002: A new terrain-following vertical coordinate formulation for atmospheric prediction models. Mon. Wea. Rev., 130, 2459-2480.
52. Schneider, K., and O. V. Vasilyev, 2010: Wavelet methods in computational fluid dynamics. Annu. Rev. Fluid Mech., 42, 473-503.
53. Skamarock, W., J. Oliger, and R. L. Street, 1989: Adaptive grid refinement for numerical weather prediction. J. Comput. Phys., 80, 27-60.
54. Smolarkiewicz, P. K., 1982: The multi-dimensional Crowley advection scheme. Mon. Wea. Rev., 110, 1968-1983.
55. Staniforth, A., J. Coté, and J. Pudykjewicz, 1987: Comments on "Swolarkiewicz's deformational flow." Mon. Wea. Rev., 115, 894-900.
56. Sweldens, W., 1995: The construction and application of wavelets in numerical analysis. Ph.D. thesis, University of Belgium, 267 pp.
57. Sykes, R. I., and D. S. Henn, 1995: Representation of velocity gradient effects in a Gaussian puff model. J. Appl. Meteor., 34, 2715-2723.
58. Tannehill, J. C., D. A. Anderson, and R. H. Pletcher, 1997: Computational Fluid Mechanics Heat Transfer. Taylor and Francis, 792 pp.
59. Tomlin, A., M. Berzins, J. Ware, J. Smith, and M. J. Pilling, 1997: On the use of adaptive gridding methods for modelling chemical transport from multi-scale sources. Atmos. Environ., 31 (18), 2945-2959.
60. Urban, K., 2002: Wavelets in Numerical Simulation: Problem Adapted Construction and Application. Springer, 212 pp.
61. Vasilyev, O. V., and C. Bowman, 2000: Second-generation wavelet collocation method for the solution of partial differential equations. J. Comput. Phys., 165, 660-693.
62. Vasilyev, O. V., and N.-R. Kevlahan, 2005: An adaptive multilevel wavelet collocation method for elliptic problems. J. Comput. Phys., 206, 412-431.
63. Wehner, M., L. Oliker, and J. Shalf, 2008: Towards ultra-high resolution models of climate and weather. Int. J. High Perform. Comput. Appl., 22 (2), 149-165, doi:10.1177/1094342007085023.
64. Wesseling, P., 2004: An Introduction to Multigrid Methods. R.T. Edwards, Inc., 284 pp.
65. Whitaker, S., 1996: The Forchheimer equation: A theoretical development. Transp. Porous Media, 25, 27-61.
66. Wicker, L. J., and W. C. Skamarock, 1998: A time-splitting scheme for the elastic equations incorporating second-order Runge- Kutta time differencing. Mon. Wea. Rev., 126, 1992-1999.
67. Wilson, J. D., and B. L. Sawford, 1995: Review of Lagrangian stochastic models for trajectories in the turbulent atmosphere. Bound.-Layer Meteor., 78, 191-210.