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
.
You do not currently have access to this content.