MS (M.tech.)/ PhD in Computational Fluid Dynamics in IIT Madras

This is written for anyone who wants to do a masters or a doctorate in Computational Fluid Dynamics [CFD ] at IIT Madras under my supervision. I am primarily in the business of algorithm development. All my students and I develop codes.

What does this mean to you?

Typically, the CFD that my students and I do requires that you have a decent background in fluid mechanics, mathematics, and programming. I am really not interested in taking students who want to just run canned packages. So what do I mean by a decent background?

1. Fluid mechanics:

Clearly your mechanics background has to be sound. You should be comfortable with ideas of equilibrium, free body diagrams, equations of motion. So, now you are in a position to make sure you are okay in hydrostatics, rotational and irrotational flows and the associated governing equations. Ask yourself these questions: Can you derive all the equations without referring to a book? No, the question is not whether you have memorized the derivations. Do you understand the concepts of conservation/balance of mass, momentum, and energy as applied to a fluid?

2. Mathematics, Programming:

I club these together. In your mind you are thinking of programming in terms of the languages that you know. If you look carefully at fluid mechanics, you will see that it is described in the language of mathematics.

You clearly have to be sound in calculus: integration, differentiation, product rule, chain rule, mean value theorem, implicit function theorem, and the associated numerical schemes. Since we solve partial differential equations, you have to have some familiarity with differential equation, at least the kind that show up in fluid flow.

The programming part can be addressed clearly – can you write programs with as much ease and comfort with which you write a letter your mother? If programming is chore and you do not look forward to doing it, the CFD that I do is not for you.

Finally, you may be interested in fluid mechanics alone and may wish to study some phenomenon either experimentally or computationally employing a canned package. It is a worthy pursuit. Unfortunately, it is not what my students and I do.

I have an important point to make here. Please do not write to me suggesting that you will learn to program after you get here. The whole point of this section: this is material you should have already learnt. In this context, I have put up a chapter from my book on computational fluid dynamics. The chapter is a quick introduction to tensor calculus and equations of fluid motion. The complete book is here. Right, you have made it this far and think that you may still be interested in the MS/PhD and ask:

What kind of problems can I work on?

Once we are past the initial constraints, my interests are quite broad. My PhD students have worked on algorithms and codes:

to perform time-accurate computations of two dimensional incompressible flows using vortex particles
to accelerate two dimensional solvers using time-marching schemes employing a new multi-grid scheme.
to develop high resolution codes that work without fine tuning for a large range of Mach numbers with applications to scramjet engines.

My MS students on the other hand have

Conducted experiments on a Ranque-Hilsch vortex tube
Studied issues related to the pitch-up problem of aircraft
Developing algorithms to extract master curves for preliminary design from a large volume of CFD data
Development of a two dimensional code to compute flow through cavity based supersonic mixers.
Simple vortex based engineering tools to evaluate rotor fuselage interaction in an idealised helicopter
Developing a three dimensional, multi-block parallel code to solve problems in supersonic mixing
Developing a two dimensional computational plasma code for use in analysis of plasma torchs
Development of a multi-physics two dimensional solver to solve the conjugate heat transfer problem.
Develop a three dimensional solver for the problem of a supersonic mixer.
Extend a new integral scheme to two dimensional Euler equations.
Integrating an existing full potential code to an existing boundary layer code with applications to helicopter rotor in hover and forward flight

What about my academic background and the problem that I choose?

I have had students who had MSc Mathematics, MSc Physics, Mechanical engineering, Aerospace Engineering background work with me.

Let me give you an example. Say a student wants to work in the area of computational plasma dynamics. (Please remember this is only an example.)

I would expect any one who wants to work on computational plasma dynamics to have over and above the normal CFD requirement to have a strong aptitude and preferably a background in physics.

We could go on. If you were interested in computing blood flow, I would expect that over and above the normal CFD requirements, you would have some background in hemodynamics, non-Newtonian fluids and so on.

So, how long is it going to take me?

This depends completely on YOUR answers to the earlier questions. A mathematics student may not have studied engineering mechanics or thermodynamics. It is going to take time building up a background. The deeper the hole in your background that you need to fill before starting on your thesis in earnest, the longer it takes. An aerospace / mechanical engineering student with a good background [ the mathematics, fluid mechanics and programming that I mentioned earlier] can work hard and finish an MS in two years. In fact they actually have. On the other hand, I have had students who could have finished early take a little more time to learn things along way.

What do I expect from the student?

Yes, I look for students who have the background. This in itself is not enough. It also important that the student have the urge to learn. The attitude and drive to act on that urge and the strength and energy to sustain him/her through to the end. An MS/PhD is not about a destination. It is the particular path that a scholar takes. A problem that you pick only provides the direction in which you proceed. The “process” is the MS/PhD.

What next?

If you have come this far and are still interested in pursuing an MS / PhD under my guidance send me mail at krishna ae iitm ac in. If you are not an Indian national you should check out the rules for an international student who wants to do an MS or a PhD.