@article{nadiga08,
title = {Orientation of eddy fluxes in geostrophic
turbulence},
author = { B.T. Nadiga},
journal = {Philosophical Transactions of the Royal Society A:
Mathematical, Physical and Engineering Sciences},
volume = 366,
number = 1875,
pages = {2491-2510},
year = 2008,
abstract = { Given its importance in parametrizing eddies, we
consider the orientation of eddy flux of potential
vorticity (PV) in geostrophic turbulence. We take
two different points of view, a classical ensemble-
or time-average point of view and a second scale
decomposition point of view. A net alignment of the
eddy flux of PV with the appropriate mean gradient
or the large-scale gradient of PV is
required. However, we find this alignment to be very
weak. A key finding of our study is that in the
scale decomposition approach, there is a strong
correlation between the eddy flux and a nonlinear
combination of resolved gradients. This strong
correlation is absent in the classical
decomposition. This finding points to a new model to
parametrize the effects of eddies in global ocean
circulation. CPY 2008 The Royal Society.},
keywords = {Fluxes ; Alignment ; Atmospheric turbulence ;
Correlation methods ; Flow of fluids ; Gradient
methods ; Oceanography ; Turbulence ; Eddy fluxes ;
(1 1 1) orientation ; Strong correlations ;
Geostrophic turbulence ; new model ; Nonlinear
combination ; decomposition approach ; Global ocean
circulation ; Potential vorticity (PV)},
issn = {1364-503X},
language = {English},
url = {http://public.lanl.gov/balu/nadiga-08.pdf},
copyright = { Copyright Elsevier}
}
@article{nadiga07,
title = {Instability of the perfect subgrid model in
implicit-filtering large eddy simulation of
geostrophic turbulence},
author = { B.T. Nadiga and D. Livescu},
journal = {Physical Review E (Statistical, Nonlinear, and Soft
Matter Physics) },
volume = 75,
number = 4,
pages = {46303-1-6},
address = {USA},
publisher = {APS through AIP},
year = 2007,
abstract = { We demonstrate, in the context of
implicit-filtering large eddy simulations (LESs) of
geostrophic turbulence, that while the attractor of
a well-resolved statistically stationary turbulent
flow can be reached in a coarsely resolved LES that
is forced by the subgrid scale (SGS) terms diagnosed
from the well-resolved computation, the attractor is
generically unstable: the coarsely resolved LES
system forced by the diagnosed SGS eddy terms has
multiple attractors. This points to the importance
of interpreting the diagnosed SGS forcing terms in a
well-resolved computation or experiment from a
combined physical-numerical point of view rather
than from a purely physical point of view},
keywords = {flow instability ; flow simulation ; geophysical
fluid dynamics ; turbulence ; instability ; subgrid
model ; implicit-filtering large eddy simulation ;
geostrophic turbulence ; attractor ; stationary
turbulent flow ; coarsely resolved system ;
diagnosed SGS eddy terms ; A4720 ; Hydrodynamic
stability and instability ; A4725 ; Turbulent flows,
convection, and heat transfer ; A4710 ; General
fluid dynamics theory, simulation and other
computational methods},
issn = {1539-3755},
doi = {10.1103/PhysRevE.75.046303},
language = {English},
url = {http://public.lanl.gov/balu/nadiga-07.pdf},
copyright = { Copyright The Institution of Engineering and
Technology}
}
@article{nadiga07duan,
title = {Stochastic parameterization for large eddy
simulation of geophysical flows},
author = {Jinqiao Duan and Balasubramanya T. Nadiga},
journal = {Proceedings of the American Mathematical Society},
volume = 135,
number = 4,
pages = {1187-1196},
address = {201 CHARLES ST, PROVIDENCE, RI 02940-2213 USA},
publisher = {AMER MATHEMATICAL SOC},
year = 2007,
abstract = { Recently, stochastic, as opposed to deterministic,
parameterizations are being investigated to model
the effects of unresolved subgrid scales ( SGS) in
large eddy simulations ( LES) of geophysical
flows. We analyse such a stochastic approach in the
barotropic vorticity equation to show that ( i) if
the stochastic parameterization approximates the
actual SGS stresses, then the solution of the
stochastic LES approximates the "true"
solution at appropriate scale sizes; and that ( ii)
when the filter scale size approaches zero, the
solution of the stochastic LES approaches the true
solution.},
keywords = {D PN MATHEMATICS, APPLIED ; D PQ MATHEMATICS ;
ISOTROPIC TURBULENCE ; MODEL ; CIRCULATION ; WIND ;
EDDIES ; OCEAN},
issn = {0002-9939},
language = {EN English},
url = {http://public.lanl.gov/balu/nadiga07duan.pdf},
copyright = { Copyright Thomson Corporation}
}
@article{nadiga06jet,
title = {On zonal jets in oceans},
author = { B.T. Nadiga},
journal = {Geophysical Research Letters},
volume = 33,
number = 10,
pages = {4 pp.},
address = {USA},
publisher = {American Geophys. Union},
year = 2006,
abstract = { We find that in parameter regimes relevant to the
recently observed alternating zonal jets in oceans,
the formation of these jets can be explained as due
to an arrest of the turbulent inverse-cascade of
energy by free Rossby waves (as opposed to
Rossby basin modes) and a subsequent
redirection of that energy into zonal modes. This
mechanism, originally studied in the context of
alternating jets in Jovian atmospheres and two
dimensional turbulence in zonally-periodic
configurations survives in spite of the presence of
the meridional boundaries in the oceanic context},
keywords = {jets ; oceanography ; turbulence ; zonal jets ;
oceans ; jets formation ; turbulent inverse-cascade
; Rossby waves ; Jovian atmospheres ; 2D turbulence
; zonally-periodic configurations ; meridional
boundaries ; oceanic context ; A9210F ; Dynamics of
the upper ocean ; A9210L ; Turbulence, diffusion,
mixing, and convection in the oceans ; A4755C ; Jets
in fluid dynamics},
issn = {0094-8276},
doi = {10.1029/2006GL025865},
language = {English},
url = {http://public.lanl.gov/balu/nadiga-06.pdf},
copyright = { Copyright The Institution of Engineering and
Technology}
}
@article{nadiga06ipop,
title = {Ocean modelling for climate studies: Eliminating
short time scales in long-term, high-resolution
studies of ocean circulation},
author = {B.T. Nadiga and M. Taylor and J. Lorenz},
journal = {Mathematical and Computer Modelling},
volume = 44,
number = {9-10},
pages = {870-86},
address = {UK},
publisher = {Elsevier},
year = 2006,
abstract = { On the decadal to centennial time scale, changes in
climate are controlled strongly by changes in ocean
circulation. However, because of limitations
inherent to the time integration schemes used in
present-day ocean models,state-of-the-art climate
change simulations resolve the oceans only very
coarsely. With an aim to enable long-term
simulations of ocean circulation at the high
resolutions required for a better representation of
global ocean dynamics, we have implemented
fully-implicit time integration schemes in a version
of the popular ocean general circulation model POP
(Parallel Ocean Program), employing Jacobian-free
Newton-Krylov techniques. Here, we describe the
numerical principles underlying iPOP in some detail
and present a few computational results. While there
are many advantages to this approach, including a
consistent and uniform treatment of the terms in the
governing equations, the primary advantage lies in
the ability to take time steps that are of relevance
to the physical phenomenon that is being
studied. The time step is not limited (for stability
reasons) by the fastest modes of the system. [All
rights reserved Elsevier]},
keywords = {climatology ; geophysics computing ; integration ;
Newton method ; oceanographic techniques ; parallel
programming ; ocean modelling ; climate change
simulation ; decadal time scale ; centennial time
scale ; time integration scheme ; global ocean
dynamics ; ocean general circulation model ;
parallel ocean program ; Jacobian-free Newton-Krylov
iteration ; C7340 ; Geophysics computing ; C4130 ;
Interpolation and function approximation (numerical
analysis) ; C4160 ; Numerical integration and
differentiation ; C6150N ; Distributed systems
software},
issn = {0895-7177},
doi = {10.1016/j.mcm.2006.02.021},
language = {English},
url = {http://public.lanl.gov/balu/nadiga-06b.pdf},
copyright = { Copyright The Institution of Engineering and
Technology}
}
@article{nadiga03,
title = {Modeling mesoscale turbulence in the barotropic
double-gyre circulation},
author = { DD Holm and BT Nadiga},
journal = {Journal of Physical Oceanography},
volume = 33,
number = 11,
pages = {2355-2365},
address = {45 BEACON ST, BOSTON, MA 02108-3693 USA},
publisher = {AMER METEOROLOGICAL SOC},
year = 2003,
abstract = { This paper presents analytical and numerical
results for a class of turbulence closure models
called "alpha models,'' in which
Lagrangian averaging and turbulence closure
assumptions modify the Eulerian nonlinearity. The
alpha models are investigated in the setting of the
barotropic, double-gyre circulation in an ocean
basin. Two variants of the alpha models for the
barotropic vorticity (BV) equation are found to
produce the correct four-gyre configuration for the
mean barotropic circulation in numerical simulations
performed at a resolution 4 times as coarse as that
required in a resolved BV model. These are the
BV-alpha model and the BV-Leray-alpha
model. However, at a resolution 8 times as coarse,
only the BV-alpha model produces the proper
four-gyre configuration. Thus, the combination of
modified nonlinearity and viscous dissipation (the
viscosity is the same in all of the runs) in the
BV-alpha model is found to provide a promising
approach to modeling the mean effects of unresolved
mesoscale (subgrid scale) activity in this problem.},
keywords = {D SI OCEANOGRAPHY ; STOKES-ALPHA MODEL ; EQUATIONS ;
EDDIES ; PARAMETERIZATION ; MOTION ; FLOW},
issn = {0022-3670},
language = {EN English},
url = {http://public.lanl.gov/balu/nadiga-03.pdf},
copyright = { Copyright Thomson Corporation}
}
@article{nadiga01shkoller,
title = {Enhancement of the inverse-cascade of energy in the
two-dimensional Lagrangian-averaged Navier-Stokes
equations},
author = { B.T. Nadiga and S. Shkoller},
journal = {Physics of Fluids},
volume = 13,
number = 5,
pages = {1528-31},
address = {USA},
publisher = {AIP},
year = 2001,
abstract = { The recently derived Lagrangian-averaged
Navier-Stokes equations model the large-scale flow
of the Navier-Stokes fluid at spatial scales larger
than some a priori fixed α>0,
while coarse-graining the behavior of the small
scales. In this communication, we numerically study
the behavior of the two-dimensional (2D) isotropic
version of this model, also known as the α
model. The inviscid dynamics of this model exactly
coincide with the vortex blob algorithm for a
certain choice of smoothing kernel, as well as the
equations of an inviscid second-grade non-Newtonian
fluid. While previous studies of this system in 3D
have noted the suppression of nonlinear interaction
between modes smaller than α, we show that the
modification of the nonlinear advection term also
acts to enhance the inverse-cascade of energy in 2D
turbulence and thereby affects scales of motion
larger than α as well. This, we note, (a) may
preclude a straightforward use of the model
as a subgrid model in coarsely resolved 2D
computations, (b) is reminiscent of the
drag-reduction that occurs in a turbulent flow when
a dilute polymer is added, and (c) can be
qualitatively understood in terms of known
dimensional arguments},
keywords = {Navier-Stokes equations ; non-Newtonian flow ;
polymer solutions ; turbulence ; vortices ;
two-dimensional Lagrangian-averaged Navier-Stokes
equations ; energy inverse-cascade ; Lagrangian
averaging procedure ; volume-preserving
diffeomorphisms ; 2D isotropic version ; vortex blob
algorithm ; smoothing kernel ; inviscid second-grade
nonNewtonian fluid ; nonlinear interaction ; 2D
turbulence ; dilute polymer ; drag-reduction ; A4710
; General fluid dynamics theory, simulation and
other computational methods ; A4725 ; Turbulent
flows, convection, and heat transfer ; A4750 ;
Non-Newtonian dynamics ; A4730 ; Rotational flow,
vortices, buoyancy and other flows involving body
forces},
issn = {1070-6631},
doi = {10.1063/1.1359764},
language = {English},
url = {http://public.lanl.gov/balu/nadiga-shkoller.pdf},
copyright = { Copyright The Institution of Engineering and
Technology}
}
@article{nadiga01luce,
title = {Global bifurcation of Shilnikov type in a
double-gyre ocean model },
author = { B.T. Nadiga and B.P. Luce},
journal = {Journal of Physical Oceanography},
volume = 31,
number = 9,
pages = {2669-90},
address = {USA},
publisher = {American Meteorol. Soc},
year = 2001,
abstract = { The dynamics of an idealized wind-driven
double-gyre circulation in an ocean basin are
studied from a dynamical systems point of view in an
effort to better understand its variability. While
previous analyses of this circulation have mostly
dealt with local bifurcations of steady states and
limit cycles, this study demonstrates the importance
of considering global bifurcations as well. In one
case, a coherent picture of the global dynamics
spanning a range of parameters from where there are
only stable steady-state solutions to where there is
chaotic eddy shedding is presented. A simple but
novel use of power spectra along with dynamical
projections of the dynamics suggests that just
beyond the regime in which there are only stable
steady states, the system exhibits a complicated
global bifurcation known as the “Shilnikov
phenomenon”},
keywords = {chaos ; oceanography ; ocean ; current ; dynamics ;
circulation ; global bifurcation ; Shilnikov type ;
double gyre ocean model ; wind-driven double-gyre ;
ocean basin ; variability ; global dynamics ;
chaotic eddy shedding ; Shilnikov phenomenon ; chaos
; A9210F ; Dynamics of the upper ocean },
issn = {0022-3670},
language = {English},
url = {http://public.lanl.gov/balu/nadiga-01.pdf},
copyright = { Copyright The Institution of Engineering and
Technology}
}
@article{nadiga01len,
title = {Dispersive-dissipative eddy parameterization in a
barotropic model },
author = { B.T. Nadiga and L.G. Margolin},
journal = {Journal of Physical Oceanography},
volume = 31,
number = 8,
pages = {2525-31},
address = {USA},
publisher = {American Meteorol. Soc},
year = 2001,
abstract = { Recently a new class of coarse-grained equations,
known as α models, have been proposed for the
mean motion of an ideal incompressible fluid. The
use of one such model to represent the time-mean
component of a turbulent β-plane circulation
characterized by potential vorticity mixing is
considered. In particular, the focus is on the
wind-driven circulation in a shallow ocean basin, a
problem well studied as a prototype of more
realistic ocean dynamics. The authors demonstrate
the ability of an α model to reproduce
qualitatively the structure of a four-gyre
circulation that forms (in the time mean) when the
barotropic vorticity equation is driven by a
symmetric, double-gyre wind forcing, and when the
dissipation is weak. This is offered as a first step
in assessing the utility of the α-model
approach to simulating more complex geophysical
flows},
keywords = {geophysical fluid dynamics ; oceanography ; vortices
; ocean ; turbulence ; dynamics ;
dispersive-dissipative eddy parameterization ; eddy
; barotropic model ; dispersion ; dissipation ;
coarse grained equations ; α model ; ideal
incompressible fluid ; time mean component ;
turbulent β-plane circulation ; potential
vorticity mixing ; wind driven circulation ; shallow
ocean basin ; four gyre circulation ; barotropic
vorticity equation ; double gyre wind forcing ;
A9210F ; Dynamics of the upper ocean ; A9210D ;
Dynamics of the deep ocean ; A4730 ; Rotational
flow, vortices, buoyancy and other flows involving
body forces ; A9210L ; Turbulence, diffusion,
mixing, and convection in the oceans},
issn = {0022-3670},
language = {English},
url = {http://public.lanl.gov/balu/nadiga01len.pdf},
copyright = { Copyright The Institution of Engineering and
Technology}
}
@article{nadiga00jsp,
title = {Scaling properties of an inviscid mean-motion fluid
model},
author = { B.T. Nadiga},
journal = {Journal of Statistical Physics},
volume = 98,
number = {3-4},
pages = {935-48},
address = {USA},
publisher = {Kluwer Academic/Plenum Publishers},
year = 2000,
abstract = { An inviscid two-dimensional fluid model with
nonlinear dispersion that arises simultaneously in
coarse-grained descriptions of the dynamics of the
Euler equation and in the description of
non-Newtonian fluids of second grade is
considered. The scaling of the equilibrium states of
this model for conserved energy and enstrophy
retains the corresponding scaling for the Euler
equations on the large scales and at the same time
greatly deemphasizes the importance of small
scales. This is the first clear demonstration of the
beneficial effect of nonlinear dispersion in the
model, and should highlight its utility as a subgrid
model in more realistic situations},
keywords = {non-Newtonian flow ; vortices ; scaling properties ;
inviscid mean-motion fluid model ; inviscid
two-dimensional fluid model ; nonlinear dispersion ;
coarse-grained descriptions ; Euler equation ;
nonNewtonian fluids ; equilibrium states ; conserved
energy ; enstrophy ; subgrid model ; A4750 ;
Non-Newtonian dynamics ; A4730 ; Rotational flow,
vortices, buoyancy and other flows involving body
forces},
issn = {0022-4715},
language = {English},
url = {http://public.lanl.gov/balu/nadiga-00.pdf},
copyright = { Copyright The Institution of Engineering and
Technology}
}
@article{nadiga00four,
title = {Four-gyre circulation in a barotropic model with
double-gyre wind forcing},
author = { RJ Greatbatch and BT Nadiga},
journal = {Journal of Physical Oceanography},
volume = 30,
number = 6,
pages = {1461-1471},
address = {45 BEACON ST, BOSTON, MA 02108-3693 USA},
publisher = {AMER METEOROLOGICAL SOC},
year = 2000,
abstract = { Results from a barotropic vorticity equation model
driven by symmetric, double-gyre wind forcing are
described. The authors work in a regime in which the
model reaches a state of turbulent equilibrium. The
time-average of the statistically steady state
exhibits a four-gyre structure, in contrast to the
usual two gyres associated with symmetric
double-gyre wind forcing. The four-gyre structure is
found in model runs using either free-slip or
superslip boundary conditions, and with either
Laplacian or biharmonic mixing for the
dissipation. It is shown that the vorticity budget
of both the inner and outer gyres is dominated by a
balance between the wind stress curl and the
divergence of the eddy potential vorticity flux,
with the explicit dissipation playing a much smaller
role. The two inner gyres circulate in the same
sense as the wind stress curl and are equilibriated,
for the most part, by the eddy flux of potential
vorticity. The outer gyres, on the other hand,
circulate in the opposite sense to the wind stress
curl and are driven by the eddy flux of potential
vorticity. It is shown that the gross features of
the time-averaged state can be reproduced by a
parameterized model in which the divergent part of
the potential vorticity flux is represented as a
downgradient transfer, and a boundary condition of
no normal flux of potential vorticity is applied
along the model boundaries. In contrast to the eddy
resolving model, the four-gyre structure in the
parameterized model depends strongly on the choice
of side boundary condition.},
keywords = {D SI OCEANOGRAPHY ; QUASI-GEOSTROPHIC OCEAN ;
MULTIPLE EQUILIBRIA ; POTENTIAL VORTICITY ;
REDUCED-GRAVITY ; INERTIAL GYRES ; DRIVEN ;
TURBULENCE ; RECIRCULATION ; EMERGENCE ; FLOWS},
issn = {0022-3670},
language = {EN English},
url = {http://public.lanl.gov/balu/nadiga00four.pdf},
copyright = { Copyright Thomson Corporation}
}
@article{nadiga97moa,
title = {On simulating flows with multiple time scales using
a method of averages},
author = { B.T. Nadiga and M.W. Hecht and L.G. Margolin and
P.K. Smolarkiewicz},
journal = {Theoretical and Computational Fluid Dynamics},
volume = 9,
number = {3-4},
pages = {281-92},
address = {Germany},
publisher = {Springer-Verlag},
year = 1997,
abstract = { We present a new method, based on averaging, to
simulate certain systems with multiple time scales
efficiently and demonstrate its utility in the
context of the shallow-water equations. We first
develop the method in a simple linear setting and
analytically prove its stability. This is followed
by an extension to the full equations and a
presentation of a computational model for it. In
this preliminary study, we find that the new method
produces results that are very close to a fully
explicit (spatially and temporally) second-order
accurate scheme and much better than a fully
explicit (spatially and temporally) first-order
accurate scheme, while costing less than the
first-order accurate scheme},
keywords = {error analysis ; flow simulation ; geophysical fluid
dynamics ; numerical stability ; ocean waves ; flow
simulation ; multiple time scales ; averages method
; shallow-water equations ; numerical stability ;
first-order accurate scheme ; A9210H ; Surface
waves, tides, and sea level ; A0620D ; Measurement
and error theory ; A0260 ; Numerical approximation
and analysis ; A4710 ; General fluid dynamics
theory, simulation and other computational methods},
issn = {0935-4964},
language = {English},
url = {http://public.lanl.gov/balu/nadiga-hecht-97.pdf},
copyright = { Copyright The Institution of Engineering and
Technology}
}
@article{nadiga96zaleski,
title = {Investigations of a two-phase fluid model},
author = { B.T. Nadiga and S. Zaleski},
journal = {European Journal of Mechanics, B/Fluids},
volume = 15,
number = 6,
pages = {885-96},
address = {France},
publisher = {Gauthier-Villars},
year = 1996,
abstract = { We study an interface-capturing two-phase fluid
model in which the interfacial tension is modelled
as a volumetric stress. Since these stresses are
obtainable from a van der Waals-Cahn-Hilliard free
energy, the model is, to a certain degree,
thermodynamically realistic. Thermal fluctuations
are not considered presently for reasons of
simplicity. The utility of the model lies in its
momentum-conservative representation of surface
tension and the simplicity of its numerical
implementation resulting from the volumetric
modelling of the interfacial dynamics. After
validation of the model in two spatial dimensions,
two prototypical applications-capillary instability
of an initially high-Reynolds-number liquid jet in
the gaseous phase and spinodal decomposition in a
liquid-gas system-are presented},
keywords = {flow instability ; free energy ; jets ; spinodal
decomposition ; surface tension ; two-phase flow ;
two-phase fluid model ; interface-capturing
two-phase fluid ; interfacial tension ; volumetric
stress ; van der Waals-Cahn-Hilliard free energy ;
thermodynamically realistic model ; thermal
fluctuations ; momentum-conservative representation
; numerical implementation ; volumetric modelling ;
interfacial dynamics ; prototypical applications ;
capillary instability ; high-Reynolds-number liquid
jet ; gaseous phase ; spinodal decomposition ;
liquid-gas system ; A4755K ; Multiphase flows ;
A4755C ; Jets in fluid dynamics ; A6810C ; Fluid
surface energy (surface tension, interface tension,
angle of contact, etc.) ; A6550 ; Thermodynamic
properties and entropy ; A6475 ; Solubility,
segregation, and mixing ; A4720 ; Hydrodynamic
stability and instability},
issn = {0997-7546},
language = {English},
url = {http://xxx.lanl.gov/abs/comp-gas/9511003},
copyright = { Copyright The Institution of Engineering and
Technology}
}
@article{nadiga96obstacle,
title = {Different approximations of shallow fluid flow over
an obstacle},
author = { B.T. Nadiga and L.G. Margolin and
P.K. Smolarkiewicz},
journal = {Physics of Fluids},
volume = 8,
number = 8,
pages = {2066-77},
address = {USA},
publisher = {AIP},
year = 1996,
abstract = { Three different sets of shallow water equations,
representing different levels of approximation are
considered. The numerical solutions of these
different equations for flow past bottom topography
in several different flow regimes are compared. For
several cases the full Euler solutions are computed
as a reference, allowing the assessment of the
relative accuracies of the different
approximations. Further, the differences between the
dispersive shallow water (DSW) solutions and those
of the highly simplified, hyperbolic shallow water
(SW) equations is studied as a guide to determining
what level of approximation is required for a
particular flow. First, the Green-Naghdi (GN)
equations are derived as a vertically-integrated
rational approximation of the Euler equations, and
then the generalized Boussinesq (gB) equations are
obtained under the further assumption of weak
nonlinearity. A series of calculations, each
assuming different values of a set of
parameters-undisturbed upstream Froude number, and
the height and width of the obstacle, are then
presented and discussed. In almost all regions of
the parameter space, the SW and DSW theories yield
different results; it is only when the flows are
entirely subcritical or entirely supercritical and
when the obstacles are very wide compared to the
depth of the fluid that the SW and DSW theories are
in qualitative and quantitative agreement. It is
also found that while the gB solutions are accurate
only for small bottom topographies (less than 20% of
the undisturbed fluid depth), the GN solutions are
accurate for much larger topographies (up to 65% of
the undisturbed fluid depth). The limitation of the
gB approximation to small topographies is primarily
due to the generation of large amplitude upstream
propagating solitary waves at transcritical Froude
numbers, and is consistent with previous
analysis. The GN approximation, which makes no
assumptions about the size of the nonlinearity, is
thus verified to be a better system to use in cases
where the bottom topographies are large or when the
bottom topographies are moderate but the flow
transcritical},
keywords = {external flows ; water waves ; shallow fluid flow ;
obstacle ; shallow water equations ; numerical
solutions ; flow past bottom topography ; Euler
solutions ; dispersive shallow water solutions ;
highly simplified hyperbolic shallow water equations
; Green-Naghdi equations ; vertically-integrated
rational approximation ; Euler equations ;
generalized Boussinesq equations ; undisturbed
upstream Froude number ; transcritical flow ; large
amplitude upstream propagating solitary waves ;
transcritical Froude numbers ; A4735 ; Waves in
fluid dynamics},
issn = {1070-6631},
language = {English},
url = {http://public.lanl.gov/balu/nadiga-96.pdf},
copyright = { Copyright The Institution of Engineering and
Technology}
}
@article{nadiga96cm5,
title = {Semi-Lagrangian shallow water modeling on the CM-5},
author = { B.T. Nadiga and L.G. Margolin and
P.K. Smolarkiewicz},
journal = {Proceedings of the Parallel Computational Fluid
Dynamics , 26-29 June 1995 , Pasedena, CA, USA ;
1996 ; 529-36},
booktitle = {Parallel Computational Fluid
Dynamics. Implementations and Results Using Parallel
Computers. Proceedings of the Parallel CFD'95
Conference},
editor = { A. Ecer and J. Periaux and N. Satofuka and
S. Taylor},
address = {Amsterdam, Netherlands},
publisher = {Elsevier},
year = 1996,
abstract = { We discuss the parallel implementation of a semi
Lagrangian shallow water model on the massively
parallel Connection Machine CM-5. The four important
issues we address are: (i) two alternative
formulations of the elliptic problem and their
relative efficiencies; (ii) the performance of two
successive orders of a generalized conjugate
residual elliptic solver; (iii) the time spent in
unstructured communication-an unavoidable feature of
semi lagrangian schemes; and (iv) the scalability of
the algorithm},
keywords = {fluid dynamics ; geophysics computing ; mechanical
engineering computing ; oceanography ; parallel
machines ; parallel programming ; water ; semi
Lagrangian shallow water model ; massively parallel
Connection Machine CM-5 ; elliptic problem ;
successive orders ; generalized conjugate residual
elliptic solver ; unstructured communication ; semi
lagrangian schemes ; algorithm scalability ; C7440 ;
Civil and mechanical engineering computing ; C6110P
; Parallel programming ; C5440 ; Multiprocessing
systems ; C7340 ; Geophysics computing},
isbn = {0 444 82322 0},
language = {English},
url = {},
copyright = { Copyright The Institution of Engineering and
Technology}
}
@article{nadiga95sw,
title = {An adaptive discrete-velocity model for the shallow
water equations},
author = { B.T. Nadiga},
journal = {Journal of Computational Physics },
volume = 121,
number = 2,
pages = {271-280},
year = 1995,
abstract = { A new approach to solving the shallow water
equations is presented. This involves using discrete
velocities of an adaptive nature in a finite volume
context. The origin of the discrete-velocity space
and the magnitudes of the discrete-velocities are
both spatially and temporally variable. The
near-equilibrium flow method of Nadiga and Pullin is
used to arrive at a robust second-order (in both
space and time) scheme - the adaptive discrete
velocity (ADV) scheme - which captures hydraulic
jumps with no oscillations. The flow over a
two-dimensional ridge, over a wide range of
undisturbed upstream Frounde numbers prove the
robustness and accuracy of the scheme. A comparison
of the interaction of two circular vortex patches in
the presence of bottom topography as obtained by the
ADV scheme and a semi-Lagrangian scheme more than
validates the new scheme in two dimensions. 19
refs., 12 figs., 1 tab.},
keywords = {42 ENGINEERING NOT INCLUDED IN OTHER CATEGORIES ; 99
MATHEMATICS, COMPUTERS, INFORMATION SCIENCE,
MANAGEMENT, LAW, MISCELLANEOUS ; WAVE EQUATIONS ;
CALCULATION METHODS ; WATER WAVES ; DIFFERENTIAL
EQUATIONS ; WAVE FORCES},
issn = {0021-9991},
language = {English},
url = {http://public.lanl.gov/balu/nadiga95sw.pdf},
copyright = { }
}
@article{nadiga95adv,
title = {An Euler solver based on locally adaptive discrete
velocities},
author = { B.T. Nadiga},
journal = {Journal of Statistical Physics },
volume = 81,
number = {1-2},
pages = {129-146},
address = {United States},
year = 1995,
abstract = { A new discrete-velocity model is presented to solve
the three-dimensional Euler equations. The
velocities in the model are of an adaptive
nature-both the origin of the discrete-velocity
space and the magnitudes of the discrete velocities
are dependent on the local flow-and are used in a
finite-volume context. The numerical implementation
of the model follows the near-equilibrium flow
method of Nadiga and Pullin and results in a scheme
which is second order in space (in the smooth
regions and between first and second order at
discontinuities) and second order in time. (The
three-dimensional code is included.) For one choice
of the scaling between the magnitude of the discrete
velocities and the local internal energy of the
flow, the method reduces to a flux-splitting scheme
based on characteristics. As a preliminary exercise,
the result of the Sod shock-tube simulation is
compared to the exact solution.},
keywords = {66 PHYSICS ; 42 ENGINEERING NOT INCLUDED IN OTHER
CATEGORIES ; GAS FLOW ; FLOW MODELS ; SHOCK WAVES ;
COMPUTERIZED SIMULATION ; NUMERICAL SOLUTION ; SHOCK
TUBES ; C CODES ; BOLTZMANN STATISTICS},
issn = {0022-4715},
language = {English},
url = {http://public.lanl.gov/balu/nadiga95euler.pdf},
copyright = { }
}
@article{nadiga94pullin,
title = {A method for near-equilibrium discrete-velocity gas
flows},
author = { B.T. Nadiga and D.I. Pullin},
howpublished = {Journal of Computational Physics ; Vol/Issue: 112:1},
journal = {Journal of Computational Physics },
volume = { 112},
number = 1,
pages = {162-172},
address = {United States},
year = 1994,
abstract = { We present a simulation scheme for
discrete-velocity gases based on local thermodynamic
equilibrium.^Exploting the kinetic nature of
discrete-velocity gases, in that context, results in
a natural splitting of fluxes, and the resultant
scheme strongly resembles the original process.^The
kinetic nature of the scheme and the modeling of the
infinite collision rate limit, result in a small
value of the coefficient of (numerical)-viscosity,
the behavior of which is remarkably physical.^A
first-order method and two second-order methods
using the total variation diminishing principle are
developed and an example application is
presented.^Given the same computer resources, it is
expected that with this approach, a much higher
Reynold`s number will be achievable than presently
possible with either lattice gas automata or lattice
Boltzmann approaches.^The ideas being general, the
scheme is applicable to any discrete-velocity model
and to lattice gases as well.^17 refs., 4 figs.},
keywords = {420400 -- Engineering-- Heat Transfer & Fluid Flow ;
990200 -- Mathematics & Computers ; BOLTZMANN
EQUATION-- NUMERICAL SOLUTION ; COUETTE FLOW--
COMPUTERIZED SIMULATION ; DIFFERENTIAL EQUATIONS ;
EQUATIONS ; FLUID FLOW ; PARTIAL DIFFERENTIAL
EQUATIONS ; SIMULATION ; VISCOUS FLOW},
issn = {0021-9991},
language = {English},
url = {.please-contact},
copyright = { }
}
@article{nadiga94levermore,
title = {Moment realizability and the validity of the
Navier{endash}Stokes equations for rarefied gas
dynamics},
author = { C.D. Levermore and W.J. Morokoff and B.T. Nadiga},
journal = {Physics of Fluids},
year = 1994,
volume = 10,
number = 12,
pages = {3214-3226},
abstract = { We present criteria for monitoring the validity of
the Navier{endash}Stokes approximation during the
simulation of a rarefied gas. Our approach is based
on an underlying kinetic formulation through which
one can construct nondimensional non-negative
definite matrices from moments of the molecular
distribution. We then identify one such 3{times}3
matrix that can be evaluated intrinsically in the
Navier{endash}Stokes approximation. Our criteria are
based on deviations of the eigenvalues of this
matrix from their equilibrium value of unity. Not
being tied to a particular benchmark problem, the
resulting criteria are portable and may be applied
to any Navier{endash}Stokes simulation. We study its
utility here by comparing stationary planar shock
profiles computed using the Navier{endash}Stokes
equations with those computed using Monte Carlo
simulations.{copyright}{ital 1998 American Institute
of Physics.}},
keywords = {66 PHYSICS ; NAVIER-STOKES EQUATIONS ; GAS-FLOW
PROCESSES ; RAREFIED GASES ; SHOCK WAVES ; MATRICES
; MONTE CARLO METHOD ; COMPUTERIZED SIMULATION},
issn = {1070-6631},
language = {English},
url = {Metadata Permalink:
http://permalink.lanl.gov/adore-permalink/object?rft_id=info:lanl-repo/ecd/300076},
copyright = { }
}
@article{nadiga94,
title = {Shock structure in a nine-velocity gas},
author = { B.T. Nadiga and B. Sturtevant},
journal = {Physica D},
volume = 73,
number = 3,
pages = {205-16},
address = {Netherlands},
year = 1994,
abstract = { The exact structure of a shock is computed in a
multiple-speed discrete-velocity gas, the
nine-velocity gas, wherein the multiplicity of
speeds ensures non-trivial thermodynamics. Obtained
as a solution of the model Boltzmann equations, the
procedure consists of tracking the shock as a
trajectory of a three-dimensional dynamical system
connecting an equilibrium upstream state to an
equilibrium downstream state. The two equilibria
satisfy the jump conditions obtained from the model
Euler equations. Comparison of the shock structure
to that in a monatomic perfect gas, as given by the
Navier-Stokes equation, shows excellent
agreement. The shock in the nine-velocity gas has an
overshoot in entropy alone, like in a monatomic
gas. The near-equilibrium flow technique for
discrete-velocity gases [B.T. Nadiga and
D.I. Pullin, J. Comp. Phys., submitted], a kinetic
flux-splitting method based on the local
thermodynamic equilibrium, is also seen to capture
the shock structure remarkably well},
keywords = {Boltzmann equation ; entropy ; fluid dynamics ;
Navier-Stokes equations ; thermodynamics ;
nine-velocity gas ; shock structure ; multiple-speed
discrete-velocity gas ; speed multiplicity ;
nontrivial thermodynamics ; 3D dynamical system ;
equilibrium upstream state ; equilibrium downstream
state ; model Euler equations ; monatomic perfect
gas ; Navier-Stokes equation ; near-equilibrium flow
; kinetic flux-splitting method ; A4710 ; General
fluid dynamics theory, simulation and other
computational methods ; A0560 ; Transport processes:
theory ; A0570C ; Thermodynamic functions and
equations of state},
issn = {0167-2789},
language = {English},
url = {Metadata Permalink:
http://permalink.lanl.gov/adore-permalink/object?rft_id=info:lanl-repo/inspec/4710039},
copyright = { Copyright The Institution of Engineering and
Technology}
}
@article{nadiga94aiaa,
title = {PLANE-WAVES IN A MULTISPEED DISCRETE VELOCITY GAS},
author = { BT Nadiga},
journal = {Progress in Astronautics and Aeronautics},
volume = {159},
pages = {313-327},
publisher = {AMER INST AERONAUTICS & ASTRONAUTICS},
year = {1994},
issn = {0079-6050},
isbn = {1-56347-080-2},
url = {Metadata Permalink: http://permalink.lanl.gov/adore-permalink/object?rft_id=info:lanl-repo/pro/A1994BB63Q00028},
copyright = { Copyright Thomson Corporation}
}
@article{nadiga94goldstein,
title = {COMPRESSIBLE CHANNEL FLOW USING 2 DISCRETE VELOCITY GAS MODELS},
author = { D Goldstein and BT Nadiga},
journal = {Progress in Astronautics and Aeronautics},
volume = {159},
pages = {3-14},
publisher = {AMER INST AERONAUTICS & ASTRONAUTICS},
year = {1994},
issn = {0079-6050},
isbn = {1-56347-080-2},
url = {Metadata Permalink: http://permalink.lanl.gov/adore-permalink/object?rft_id=info:lanl-repo/pro/A1994BB63Q00001},
copyright = { Copyright Thomson Corporation}
}
@article{nadiga89,
title = {Study of a Multispeed Cellular Automaton},
author = {B.T Nadiga and J.E. Broadwell and B. Sturtevant},
journal = {Progress in Astronautics and Aeronautics},
volume = {118},
pages = {155--170},
publisher = {AMER INST AERONAUTICS & ASTRONAUTICS},
year = {1989},
url = {Metadata Permalink: http://permalink.lanl.gov/adore-permalink/object?rft_id=info:lanl-repo/pro/A1994BB63Q00001}
}
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