Mechanical Engineering

My research involves theoretical analysis and numerically intensive computations of fluid flow and heat transfer. This includes application of singular perturbation techniques such as the method of matched asymptotic expansions to external natural-convection and mixed-convection boundary layer flows over wavy surfaces using non-orthogonal boundary-fitted coordinates, ‘interactive’ boundary-layer analysis of the ‘triple-deck’ structure of high Reynolds number flows over small protrusions on plates, analysis of the ‘double-deck’ structure of natural-convection boundary-layer flows near small protrusions on vertical plates, weakly nonlinear analysis of instability using the method of multiple scales, application of the rapid distortion theory of turbulence, numerical solution of the Navier-Stokes system for incompressible flows using finite difference, finite volume and spectral methods, numerical solution of the non-similar boundary-layer equations using adaptive marching techniques, and computation of two-fluid incompressible flows using interface capturing methods such as the level-set method. I am interested in solving challenging problems of fundamental nature.
My doctoral research involved the development of a vectorized computer program for solving the three-dimensional time-dependent Navier-Stokes equations using a Fourier-Chebyshev spectral method. The computer code was used to perform direct numerical simulations of instability and transition in mixed convection flows and rotating Taylor-Couette flows, using the CRAY XMP supercomputer at Arizona State University and the CRAY C90 supercomputer at the Pittsburg Supercomputing Center; the results demonstrated the existence of multiple equilibrium states, dependent on initial conditions, and the importance of non-linear interactions in determining the equilibrium state of the flow. My students have been involved in developing accurate numerical methods for simulating two-fluid incompressible flows using level-set methods and solving problems of hydrodynamic stability using Chebyshev collocation methods employing primitive variables on non-staggered grids. The level set method has been used to simulate liquid sloshing. The Chebyshev collocation method has been used to study the stability of buoyancy-driven flows.