Courses I usually teach

ME 520 : Fluid Mechanics

This course is primarily aimed at the first level post graduate students. It mainly deals with viscous incompressible flows with a reasonable introduction to the potential theory. The topics usually covered are


(a) Ideas of Continuum, momentum equation in Eulerian description

(b) Approximate solution of the Navier Stokes equation

(c) Boundary layer theory

(d) Potential flows

(e) Free shear flows (optional)

(f) Hydrodynamic stability

(g) Introduction to turbulent flows


ME 670: Advanced Computational Fluid Dynamics

The target audience of this course is the second level Post Graduate students including Ph.D scholars working in relevant areas. I try to give a flavor of the following


(a) Advanced time integration and spatial discretization schemes

(b) Sparse linear solvers, Preconditioning technique, Multi grid method

(c) Numerical grid generation technique

(d) Various NS solvers, such as MAC, SIMPLE families, fractional step methods etc. in the framework of both finite-difference and finite volume method.

(e) Introduction to turbulent flow computations

(f) Special topics, such as Adaptive methods, Cartesian grid computations, Parallelization etc.


ME 501: Advanced Engineering Mathematics

This course is roughly a review of topics required in different branches in Mechanical Engineering. It touches upon


(a) Linear algebra: vector space, matrices, system of linear equations, eigenvalue problem, linear transformation.

(b) Vector calculus: differential geometry, tensors, vector differential and integral calculus

(c) ODE: analytical methods, stability and phase plane, Sturm-Liouville theory, special functions

(d) Fourier analysis: Fourier series, integral and transform, Laplace transform

(e) PDEs: modeling, hyperbolic, elliptic and parabolic equation, analytical tools

(f) Numerical methods: introduction to numerical analysis


ME 695: Turbulent Flows

This course is an introduction to physical aspects of turbulent flows aimed at second level post-graduate and PhDs. It roughly covers

(a) Dynamical equations: Equation for mean, fluctuations, turbulent kitectic energy eq., vorticity dynamics.

(b) Spectral dynamics: Spectral description of the Navier-Stokes equation, scales, regimes, Kolmogorov hypotheses

(c) Statistical description: Probabilistic approach, PDF, correlations, Ergodicity.

(d) Free shear flows: This shear layer, jets, wakes, mixing layer, intermittency.

(e) Wall bounded flows: Multi-layer structure, universal law of wall, channel flow, boundary layer.

(f) Modelling: Level of approximation, cost, applicability, DNS, LES, turbulence modelling.