How much math for fluid dynamics?

[member 428835]

hey all

im taking a graduate level fluid mechanics course. we are using a good amount of vector calculus (expected) and also tensor algebra, leading into the kronecker delta and Levi-Civita symbol (shockingly never saw these before, though implicitly used them). it seems linear algebra is being introduced.

for those of you who have studied far in the field, how much math is required for masters and phd level courses? i only ask because my undergrad is math, where i covered linear algebra, pde's, and vector calculus; am i missing anything or do i have the basic "tool kit" that advanced coursework in fluids requires?

thanks!

 

[SteamKing]

If you get really hard-core, there will be solving PDEs out your ying-yang eventually. In the graduate courses, don't be surprised if you have to know something about solving integral equations (differential equations' lesser known, more evil cousin). Linear algebra is the least of your worries.

In solving actual fluid mechanics problems, you'll probably also get some exposure to the finite element method and the boundary element method. Both methods rely on using assumed solutions to the fluid mechanics equations and then optimizing them to account for the actual geometry of the flow. Green's functions will probably also make an appearance at some point.

 

[boneh3ad]

It is one of the more math-heavy branches of engineering, that's for sure. Also depending on what branch of fluid mechanics you study, you may end up needing a fair amount of statistics, perturbation methods, Fourier and Laplace analysis and more. If you really start delving deeper into some topics, I've started running across topics that start scratching the surface of things like real and functional analysis, abstract algebra and topology, though these so far seem to be pretty niche applications.