The dynamics of the atmosphere and oceans pose a severe challenge to the numerical modeler, due in large part to the broad range of scales of length and time that are encompassed. Modern numerical methods based on nonoscillatory finite volume (NFV) approximations provide a simple and effective means for mitigating this challenge by reproducing the large scale behavior of turbulent flows with no need for explicit subgrid-scale models. In this paper, we describe the remarkable properties of a particular NFV model, multidimensional positive definite advection transport algorithm, and highlight its application to a variety of meteorological and turbulent flows.
1.
Implicit Large Eddy Simulation: Computing Turbulent Fluid Dynamics
, F. F.
Grinstein
, L. G.
Margolin
, and W.
Rider
, eds., (2007), pp. 552
.2.
Smagorinsky
, J.
, 1993, “Some Historical Remarks on the Use of Nonlinear Viscosities
,” in Large Eddy Simulation of Complex Engineering and Geophysical Flows
, B.
Galperin
and S. A.
Orszag
, eds., Cambridge University Press
, New York
, pp. 3
–36
.3.
Smolarkiewicz
, P. K.
, and Prusa
, J. M.
, 2002, “Forward-In-Time Differencing for Fluids: Simulation of Geophysical Turbulence
,” in Turbulent Flow Computation
, D.
Drikakis
and B. J.
Guertz
, eds., Kluwer Academic
, Boston
, Chap. 8, pp. 279
–312
.4.
Margolin
, L. G.
, Rider
, W. J.
, and Grinstein
, F. F.
, 2006, “Modeling Turbulent Flow With Implicit LES
,” J. Turbul.
1468-5248, 7
(15
), pp. 1
–27
.5.
Margolin
, L. G.
, Smolarkiewicz
, P. K.
, and Sorbjan
, Z.
, 1999, “Large-Eddy Simulations of Convective Boundary Layers Using Nonoscillatory Differencing
,” Physica D
0167-2789, 133
, pp. 390
–397
.6.
Smolarkiewicz
, P. K.
, and Margolin
, L. G.
, 1998, “MPDATA: A Finite-Difference Solver for Geophysical Flows
,” J. Comput. Phys.
0021-9991, 140
, pp. 459
–480
.7.
Smolarkiewicz
, P. K.
, 2006, “Multidimensional Positive Definite Advection Transport Algorithm: An Overview
,” Int. J. Numer. Methods Fluids
0271-2091, 50
, pp. 1123
–1144
.8.
Smolarkiewicz
, P. K.
, and Prusa
, J. M.
, 2002, “VLES Modeling of Geophysical Fluids With Nonoscillatory Forward-in-Time Schemes
,” Int. J. Numer. Methods Fluids
0271-2091, 39
, pp. 799
–819
.9.
Margolin
, L. G.
, Smolarkiewicz
, P. K.
, and Wyszogrodzki
, A. A.
, 2002, “Implicit Turbulence Modeling for High Reynolds Number Flows
,” ASME Trans. J. Fluids Eng.
0098-2202, 124
, pp. 862
–867
.10.
Domaradzki
, J. A.
, Xiao
, Z.
, and Smolarkiewicz
, P. K.
, 2003, “Effective Eddy Viscosities in Implicit Large Eddy Simulations of Turbulent Flows
,” Phys. Fluids
1070-6631, 15
, pp. 3890
–3893
.11.
Margolin
, L. G.
, Smolarkiewicz
, P. K.
, and Wyszogrodzki
, A. A.
, 2006, “Dissipation in Implicit Turbulence Models: A Computational Study
,” Trans. ASME, J. Appl. Mech.
0021-8936, 73
, pp. 469
–4737
.12.
Margolin
, L. G.
, and Rider
, W. J.
, 2002, “A Rationale for Implicit Turbulence Modeling
,” Int. J. Numer. Methods Fluids
0271-2091, 39
, pp. 799
–819
.13.
Szmelter
, J.
, 2006, “MPDATA Methods
,” Int. J. Numer. Methods Fluids
0271-2091, 50
, pp. 1121
–1293
.14.
Domaradzki
, J. A.
, and Adams
, N. A.
, 2002, “Direct Modelling of Subgrid Scales of Turbulence in Large Eddy Simulation
,” J. Turbul.
1468-5248, 3
, pp. 1
–19
.15.
Smolarkiewicz
, P. K.
, and Szmelter
, J.
, 2005, “MPDATA: An Edge-Based Unstructured-Grid Formulation
,” J. Comput. Phys.
0021-9991, 206
, pp. 624
–649
.16.
Smolarkiewicz
, P. K.
, and Margolin
, L. G.
, 1993, “On Forward-in-Time Differencing for Fluids: Extension to a Curvilinear Framework
,” Mon. Weather Rev.
0027-0644, 121
, pp. 1847
–1859
.17.
Prusa
, J. M.
, and Smolarkiewicz
, P. K.
, 2003, “An All-Scale Anelastic Model for Geophysical Flows: Dynamic Grid Deformations
,” J. Comput. Phys.
0021-9991, 190
, pp. 601
–622
.18.
Wedi
, N. P.
, and Smolarkiewicz
, P. K.
, 2004, “Extending Gal-Chen and Somerville Terrain-Following Coordinate Transformation on Time Dependent Curvilinear Boundaries
,” J. Comput. Phys.
0021-9991, 193
, pp. 1
–20
.19.
Smolarkiewicz
, P. K.
, and Prusa
, J. M.
, 2005, “Towards Mesh Adaptivity for Geophysical Turbulence
,” Int. J. Numer. Methods Fluids
0271-2091, 47
, pp. 1369
–1374
.20.
Smolarkiewicz
, P. K.
, Margolin
, L. G.
, and Wyszogrodzki
, A. A.
, 2001, “A Class of Nonhydrostatic Global Models
,” J. Atmos. Sci.
0022-4928, 58
, pp. 349
–364
.21.
Davis
, T.
, Staniforth
, A.
, Wood
, N.
, and Thuburn
, J.
, 2003, “Validity of Anelastic and Other Equation Sets as Inferred from Normal-Mode Analysis
,” Q. J. R. Meteorol. Soc.
0035-9009, 129
, pp. 2761
–2775
.22.
Durran
, D. R.
, 1999, Numerical Methods for Wave Equations in Geophysical Fluid Dynamics
, Springer-Verlag
, New York
.23.
Smolarkiewicz
, P. K.
, and Margolin
, L. G.
, 2007, “Studies in Geophysics
,” in Implicit Large Eddy Simulation: Computing Turbulent Fluid Dynamics
, F. F.
Grinstein
, L.
Margolin
, and W.
Rider
, eds., pp. 413
–438
.24.
Warn-Varnas
, A.
, Hawkins
, J.
, Smolarkiewicz
, P. K.
, Chin-Bing
, S. A.
, King
, D.
, and Hallock
, Z.
, 2007, “Solitary Wave Effects North of Strait of Messina
,” Ocean Model.
, 18
, pp. 97
–121
.25.
Cotter
, C. S.
, Smolarkiewicz
, P. K.
, and Szczyrba
, I. N.
, 2002, “A Viscoelastic Model for Brain Injuries
,” Int. J. Numer. Methods Fluids
0271-2091, 40
, pp. 303
–311
.26.
Elliott
, J. R.
, and Smolarkiewicz
, P. K.
, 2002, “Eddy Resolving Simulations of Turbulent Solar Convection
,” Int. J. Numer. Methods Fluids
0271-2091, 39
, pp. 855
–864
.27.
Wedi
, N. P.
, and Smolarkiewicz
, P. K.
, 2006, “Direct Numerical Simulation of the Plumb-Mcewan Laboratory Analogue of the QBO
,” J. Atmos. Sci.
0022-4928, 63
, pp. 3226
–3252
.28.
Ortiz
, P.
, and Smolarkiewicz
, P. K.
, 2006, “Numerical Simulation of Sand Dune Evolution in Severe Winds
,” Int. J. Numer. Methods Fluids
0271-2091, 50
, pp. 1229
–1246
.29.
Andrejczuk
, A.
, Grabowski
, W. W.
, Malinowski
, S. P.
, and Smolarkiewicz
, P. K.
, 2006, “Numerical Simulation of Cloud-Clear Air Interfacial Mixing: Effects on Cloud Microphysics
,” J. Atmos. Sci.
0022-4928, 63
, pp. 3204
–3225
.30.
Schmidt
, H.
, and Schumann
, U.
, 1989, “Coherent Structure of the Convective Boundary Layer Derived from Large-Eddy Simulation
,” J. Fluid Mech.
0022-1120, 200
, pp. 511
–562
.31.
Smolarkiewicz
, P. K.
, and Sharman
, R.
, 2004, “Pentagon Shield: Experiments With a Nonoscillatory Forward-In-Time CFD Code (EULAG) to Simulate Flow Around the Pentagon
,” 18th Annual George Mason University Conference on Atmospheric Transport and Dispersion Modeling
, George Mason University Fairfax
, VA, Jul. 13–15 (http://www.rap.ucar.edu/projects/shield/references/gmu04/EuLag_gmu.pdfhttp://www.rap.ucar.edu/projects/shield/references/gmu04/EuLag_gmu.pdf).32.
Wyszogrodzki
, A. A.
, Vendenberghe
, F.
, and Warner
, T.
, 2006: “The Use of Coupled Mesoscale and LES Models for Calculating Urban Climatologies of Street Level and Boundary Layer Winds With Risk Assessment Implications
,” Tenth Annual George Mason University Conference on Atmospheric Transport and Dispersion Modeling
, George Mason University Fairfax, VA, Aug. 1–3.33.
Held
, I. M.
, and Suarez
, M. J.
, 1994, “A Proposal for Intercomparison of the Dynamical Cores of Atmospheric General Circulation Models
,” Bull. Am. Meteorol. Soc.
0003-0007, 75
, pp. 1825
–1830
.34.
Roache
, P. J.
, 1972, Computational Fluid Dynamics.
, Hermosa
, Albuquerque
.35.
Arakawa
, A.
, 1996, “Computational Design for Long-Term Numerical Integration of the Equations of Fluid Motions: Two-Dimensional Incompressible Flow
,” J. Comput. Phys.
0021-9991, 1
, pp. 119
–143
.Copyright © 2007
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