Mathematics for CFD
 

As an mechanical undergrad student wishing to further my career in the field of CFD, I am in a constant dilemma over not knowing where to draw the line while studying math.

I feel its the work of the mathematicians to bring in the "new methods" which are turned into solving codes by "computer science engineers". But then, am I not just pressing buttons if I don't know the math behind it? If I do chose to study the numerical techniques of solving the system of linear equations for quenching my thirst of knowledge, which would take not just a few weeks but a considerable amount of time, what would i gain from it If there can always be a computer science engineer who can write more optimized and efficient solvers than me?

If you consider CFD only in terms of using a CFD software the learning of math is limited to few topics. But if you consider extending CFD background you need math and numerical analysis, physics, fluid dynamics and also some programming skill. And this is a long way ...