Aerospace Engineering

• High order method development, including spectral volume, spectral difference and discontinuous Galerkin methods
• Computational hypersonic heating (Zoby's method, MEIT method, x-based method, fin heating)
• Moving body simulations, including using overset grid methods
• Adaptive Cartesian and prism grid generation
• Parallel adaptive mesh refinement
• Parallel programming for large systems
• HPC, optimization techniques for multicore and many core architectures. 
• Preconditioning techniques including implicit LU_SGS, multigrid methods etc
• Fluid-structure interaction
• Radiation modelling (mainly diffusion approximation)
• Korteweg-de Vries equation modelling
• Simplified explosion modelling (TNT, C4)

Computational Medicine and Biology

• Developed Q3D, a fast, robust formulation to model the transport in biological cylindrical networks like the human vascular system, lymphatic network, neurons with a network of dendrites, and axons, microfluidic channels in biochips, and the lung airways. 
• Optimized drug delivery using high fidelity  and Quasi-3D (Q3D) computational methods : for nasal and oral deliveries.
• Spatially accurate drug absorption using Q3D computational methods (faster than traditional CFD methods, by a factor of 20000) for oral-inhalation and oral based drug deliveries. 
• Pharmacokinetics
• "Organ on Chip" modelling
• Whole body anatomy modelling using compartmental modelling
• Euler Lagrangian particle transport on unstructured "dirty" concave meshes, in quasi-3D wire meshes
• Optimization techniques for physiology

Others/Interdisciplinary

• Modelling the effects of directed energy (Laser, RF waves)
• Elastohydrodynamics
• Modelling of semiconductor devices