1. Algorithms.
The numerical algorithm research involves developing high-order compact schemes (such as discontinuous spectral Galerkin/collocation methods for Euler and Navier-Stokes equations and variants thereof) and efficient techniques for stochastic partial differential equations. It includes level procedures for front tracking such as shock waves. The work in high-performance computing involves the implementation of these algorithms on parallel platforms such as SP4 and NCSA Xeon Linux Cluster.

2. Computational fluid dynamics.
The program in computational fluid dynamics includes direct numerical simulation and large-eddy simulation of transition and turbulence, high-speed combustion (scramjet flow-field and detonation), aeroacoustics (of jets and wing-tip vortices), electromagnetics (based on time-domain approach to Maxwell equations), environmental engineering (optimal placement of wind turbines and street canyon flow-fields), forest fires, and multiphase flows. It also includes fluid dynamics control, which is concerned with the application of control theory to laminar flow control and aeroacoustics control.

3. Control and optimization.
Control and optimization research comprises laminar flow control, active control of unstable boundary-layer flow, airfoil shape optimization (to reduce drag), and optimization of inlet-liner impedance factor (to reduce radiated engine noise). It also includes optimal control, stochastic parameter estimation, and uncertain data assimilation.

4. Cryogenics.
This research pertains to atomic propellant feed systems (which will propel the far future generation of spacecrafts) that require the production, storage, and transport of solid hydrogen particles in cryogenic fluids. The basic research deals with the generation of hydrogen droplets of optimal size and shape, and the physics of their solidification in cryogenic helium. It also involves studying the two-phase flow of liquid helium containing solid hydrogen particles.

5. Nano fluids and materials.
Nano fluid and materials research focuses on developing theory and computation to complement experiments in the area of laser-assisted steam cleaning of, for example, semiconductor devices; it further includes simulation of carbon nanotube reinforced polymers with a view to unravel the basic mechanisms underlying reorientation of carbon nanotubes and reorganization of polymer chains under high intensity magnetic field.

6. Networks.
Networks research relates to quantifying survivability/reliability inherent in a given network topology, developing new topologies of enhanced survivability to multiple faults, and creating structural analysis tools for detecting and isolating faults. Current applications focus on the integrated power system in an all-electric ship and communication systems.

7. Uncertainty and sensitivity analyses.
Quantification and propagation of parametric uncertainty in simulations is based on probability tools such as Monte Carlo techniques and polynomial chaos. Sensitivity analysis involves computing Sobol indices. This research includes improving the efficiency of these techniques for practical applications. Model form (epistemic) uncertainty analysis employs evidence theory tools to study uncertainty associated with auxiliary models such as turbulence models in aerodynamic simulations.

8. Visualization, sensing and imaging.
A scientific visualization effort cuts across all these program areas, the common theme being interactive, real-time visualization. Current research in this area is confined to vector-field visualization in fluid flows. It includes visualization of qualitative features of stochastic simulations.