Research Projects

Large Eddy Simulation (LES)

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 BOOK 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.

Mathematical Modeling and Analysis for LES

Numerical Validation and Testing for LES

Numerical Analysis for LES

Boundary Conditions for LES

Gravity Currents

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 Kelvin-Helmholtz 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.

ViTLES - The Virginia Tech Large Eddy Simulator

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.

Mesh Adaptation

Some of my earlier research focused on mesh adaptation. Specifically, I investigated the use of edge swapping in improving the solution quality in convection-dominated problems. Here are a couple of papers on this subject:

Aluminum Reduction

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: