> But the bulk of the gains in the real world come from applying numerical technique on them.
> Most of the people doing research use numerical methods (often from first principles, so almost no analytical approach applied). They basically "won". When you look at the useful results in the discipline in the last 10-15 years, the numerical ones outnumber the analytical ones easily by a factor of 10.
I think this is probably true now in most fields (including fluid dynamics) but it doesn't mean that analytical techniques aren't useful. All it means is that they aren't used. Most people don't even attempt analytical techniques these days.
I've found time and time again people use very complicated (and difficult) numerical approaches where an analytical approach would get the same information faster, and often more information. It might take more thinking, yes, and not be as "sexy", but ultimately analytical approaches have their place.
I gave an example from my PhD in this other comment about how I analytically solved a series of nonlinear ODEs (approximately) to get a lot of insight into a problem that apparently people doing decades of numerical calculations couldn't figure out: https://news.ycombinator.com/item?id=24683038
I'm planning to publish another paper on the subject that builds on this work, and one point I'm going to make in the paper is that I don't see how someone doing experiments or simulations could figure out the main result of that paper. It's not impossible, but would be far more difficult
> Most of the people doing research use numerical methods (often from first principles, so almost no analytical approach applied). They basically "won". When you look at the useful results in the discipline in the last 10-15 years, the numerical ones outnumber the analytical ones easily by a factor of 10.
I think this is probably true now in most fields (including fluid dynamics) but it doesn't mean that analytical techniques aren't useful. All it means is that they aren't used. Most people don't even attempt analytical techniques these days.
I've found time and time again people use very complicated (and difficult) numerical approaches where an analytical approach would get the same information faster, and often more information. It might take more thinking, yes, and not be as "sexy", but ultimately analytical approaches have their place.
I gave an example from my PhD in this other comment about how I analytically solved a series of nonlinear ODEs (approximately) to get a lot of insight into a problem that apparently people doing decades of numerical calculations couldn't figure out: https://news.ycombinator.com/item?id=24683038
I'm planning to publish another paper on the subject that builds on this work, and one point I'm going to make in the paper is that I don't see how someone doing experiments or simulations could figure out the main result of that paper. It's not impossible, but would be far more difficult