Research Projects
Most of my recent research has been centered around
Large Eddy Simulation (LES).
LES is one of the most successful techniques for the numerical simulation of
turbulent flows.
Introduced more than 30 years ago for geophysical applications, LES has been
developed mainly in the engineering community.
LES aims at approximating the large structures (eddies) in the turbulent flow.
The effect of the small structures on the large ones is modeled, usually by
using physical insight.
Due to its low computational cost, LES is a popular approach for numerical
simulations of complex turbulent flows.
In my Ph.D. thesis I started a focused effort on providing a sound mathematical
support for the derivation and discretization of LES models.
Here are links to some of my papers on
mathematical modeling and analysis,
numerical validation and testing,
numerical analysis, and
boundary conditions
for some new LES models.
For the last couple of years,
Bill Layton,
Luigi Berselli,
and I have been writing a on
Mathematical Analysis of Large Eddy Simulation.
The book is in its final editing stages, and we are under contract with
Springer Verlag to submit it by the end of the year.

Large Eddy Simulation for Turbulent Flows,
Ph.D. thesis,
PDF file,
University of Pittsburgh, 2000.

Approximating the Larger Eddies in Fluid Motion III:
the Boussinesq Model for Turbulent Fluctuations,
(with W. J. Layton),
An. St. Univ. "Al. I. Cuza, vol. 44, 1998, pp. 245261.

Mathematical Analysis for the Rational Large Eddy Simulation Model,
(with L. C. Berselli, G. P. Galdi, and W. J. Layton),
Math. Models Meth. Appl. Sc., vol. 12 (8), 2002, pp. 11311152.

A Higher Order SubfilterScale Model for Large Eddy Simulation,
(with L. C. Berselli),
J. Comp. Appl. Math., vol. 159, 2003, pp. 411430.

A numerical study of a class of LES models,
(with V. John, W. J. Layton, G. Matthies and L. Tobiska),
Int. J. Comput. Fluid Dyn., vol. 17 (1), 2003, pp. 7585.

A 3D Channel Flow Simulation at Re_{\tau}=180 Using a Rational LES Model,
(with P. Fischer), Proceedings of Third AFOSR International Conference
on DNS/LES,
eds. C. Liu, L. Sakell, and T. Beutner,
Greyden Press, 2001, pp. 283290.

Large Eddy Simulation of Turbulent Channel Flows by the Rational LES Model,
(with P. Fischer),
Physics of Fluids, vol. 15(10), 2003, pp. 30363047.

Backscatter in the Rational LES Model,
(with P. Fischer),
Computers and Fluids, vol. 33(56), 2004, pp. 783790.

Genuinely Nonlinear Models for ConvectionDominated Problems,
PDF file,
Comput. Math. Appl.

Convergence of Finite Element Approximations of Large Eddy Motion,
(with V. John and W. J. Layton),
Num. Meth. P.D.E.s, vol. 18(6), 2002, pp. 689710.

Approximate Deconvolution Boundary Conditions for
Large Eddy Simulation,
(with J. Borggaard),
compressed postscript file,
submitted for publication, August 2004.
Much of my current research is on gravity currents, cold masses
of water protruding into warm ones.
The mixing between the cold and warm water takes place through the
KelvinHelmholtz instability (see figure above).
Gravity currents are believed to have a significant role in general
ocean circulation models.
However, their numerical simulation is very challenging due to the
large (geophysical scale) parameters involved.
My main interest in the numerical investigation of gravity currents is
the ability of LES to perform at parameters prohibitive for a Direct
Numerical Simulation (DNS) approach.
Here are some of my papers on gravity currents.

Threedimensional turbulent bottom density currents from a highorder
nonhydrostatic spectral element model,
(with T. Ozgokmen, P. Fischer, and J. Duan),
J. Phys. Oceanogr., vol. 34(9), 2004, pp. 20062026.

Entrainment in bottom gravity currents over complex topography from
threedimensional nonydrostatic simulations,
(with T. Ozgokmen, P. Fischer, and J. Duan),
Geophys. Res. Letters vol. 31(13), L13212, 2004.

Enstrophy and ergodicity of gravity currents,
(with V.P. BongolanWalsh, J. Duan, H. Go, T. Ozgokmen, and P.F. Fischer),
IMA volume on SPDEs, in press, 2004.
Two years ago, my colleague Jeff Borggaard and I, together with a group of
enthusiastic graduate students at Virginia Tech, started building a
computational platform for LES.
The scientific and engineering applications targeted yielded a couple
of requirements for our code:
(1) geometric flexibility for being able to treat complex
computational domains, such as those encountered in realistic
geophysical and engineering applications;
(2) parallelism for being able to tackle realistic parameters
in our numerical simulations.
Thus, ViTLES is a parallel, finite element computational platform.
For more details, please visit our
working web page.
Some of my earlier research focused on mesh adaptation.
Specifically, I investigated the use of edge swapping in
improving the solution quality in convectiondominated problems.
Here are a couple of papers on this subject:

A FlowAligning Algorithm for ConvectionDominated Problems,
Int. J. Num. Meth. Eng., vol. 46, No. 7, 1999, pp. 9931000.

A 3D FlowAligning Algorithm for ConvectionDiffusion Problems,
Appl. Math. Letters, vol. 4, No. 12, 1999, pp. 6770.
One project I worked on was Aluminum Reduction.
This international collaboration with the University of Puerto La Cruz,
Venezuela, aimed at efficient numerical simulation of aluminum reduction.
The ultimate goal was to optimize the process through a careful parameter
choice.
Here are some papers on this subject:

Distribucion de Temperatura en las Esquinas de una Celda de Reduccion de
Aluminio Tipo HallHeroult,
(with E. Gutierrez, N. Troyani and W. J. Layton),
IV Congreso Iberoamericano de Ingenieria Mecanica, Santiago de Chile, Chile, 1999.

Corner Distribution of Voltage in HallHeroult Aluminum Reduction Cells,
(with E. Gutierrez, N. Troyani and W. J. Layton),
IV International Congress: Energy, Environment and Technological Innovation,
Rome, 1999, pp. 14451451.

The Center Section Temperature Distribution in HallHeroult Aluminum Reduction
Cells from a ThreeDimensional Finite Element Simulation,
(with E. Gutierrez, N. Troyani and W. J. Layton),
International Thermal Energy Congress, Cesme, Izmir, Turkey, July 2001.

Algoritmos Computacionales para Resolver el Problema Termoelectrico en
Tres Dimensiones en Celdas de Reduccion de Aluminio del Tipo HallHeroult,
(with E. Gutierrez, N. Troyani and W. J. Layton),
Universidad Ciencia y Tecnologia, Vol. 3, No.12, pp. 1724, 1999.

Formulacion Variacional del Problema Termoelectrico de una Celda de Reduccion
HallHeroult en Tres Dimensiones,
(with E. Gutierrez, N. Troyani and W. J. Layton),
Universidad Ciencia y Tecnologia, Vol. 3, No. 9, pp. 2529, 1999.