What type of computing / problem solving do super computers do?

it could also be used in predicting the up and downs in the economy of a country, problem related to DNA decoding,decryption of confidential files by military ,simulation of nuclear reactor,wind tunnel analysis

1. Solving Superconductor problems. #-Link-Snipped-#
2. Virus structure and visualization: <a href="https://www.ncsa.illinois.edu/" target="_blank" rel="nofollow noopener noreferrer">Home - NCSA</a>
3. In defence of use of supercomps by defence: #-Link-Snipped-#
4. Space exploration: #-Link-Snipped-#
5. Like TATA claims,'they also predict weather!': #-Link-Snipped-#

#-Link-Snipped-# : I'm more interested in knowing why do the problems mentioned above require so much of computing power?

Mainly because of the huge number of data points to be processed. The calculations may be quite elementary but their numbers are huge. It takes enormous time to shift through a lot of data. Quite often much has to be dropped after processing because of detected irrelevance.
Image processing of course needs enormous computational capacity. Fluid flow, aerodynamics and space simulations as well as some of the astronomical calculations need astronomical processing capacity as well.I am also told that a considerable amount of processing is for house keeping. That is to cross verify what is being done by the computer.
Medical imaging like the 4d ultrasound needs a lot of computing power. I have myself seen in US a 4d real time image of my grand daughter yawning incongruously inside the womb of my daughter in the US, rather like this one:
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That is quite interesting. 😀

Hmm.. One application I can think of, for which any amount of astronomical computing power is welcome, is Cryptanalysis. There are many branches in cryptanalysis and I'm sure each will have it's own behemoth computing requirements. One area which I'm interested in is prime numbers. The largest known prime number currently is "<a href="https://primes.utm.edu/largest.html" target="_blank" rel="nofollow noopener noreferrer">The Largest Known Primes (database sumary)</a>". What is the next prime number? Nobody knows, as of now. There are <a href="https://www.eff.org/awards/coop" target="_blank" rel="nofollow noopener noreferrer">EFF Cooperative Computing Awards | Electronic Frontier Foundation</a> being offered for anyone who could find the next big prime number with a particular number of digits.

Now, why are prime numbers so important? They play a crucial role in encryption, and by extension, prime numbers are very essential for internet security as a whole. Generally, in computing, multiplication is a lot easier than factorization. If you are given 2 numbers, you can multiply them very fast, no matter how big the numbers are. There are techniques like Fast Fourier Transform to do just that. But the reverse is not so easy. ie., given a large number, it's a very huge task to factorize them into prime factors. Again, this is important because, in encryption techniques, we use two large prime numbers and multiply them. Use them as keys. To break the encryption, we need to know wat exactly were the prime numbers that were used originally.

We can't just try to factorize them by brute force. Most encryption algos rely on the assumption that factoring large numbers is computationally unfeasible. But as computing power increases more and more, there are more chances of such factorization attempts succeeding. We would therefore need to use larger and larger primes in out encryptions, as general computing power increases.