If supervisor has no expertise in your research work, is it possible to do a PhD under that supervisor? In my PhD, I am assigned mathematical modeling topics and my supervisor's work is related to mathematical biology. But I don't want to work in mathematical biology. Because actually there is not so much real application of that and I don't like biology. Instead, I want to work in fluid dynamics. But my supervisor's research area is totally different. Is it possible  to do independent research work without supervision of supervisor?
In summary: is it possible? Yes. Should one do it? No.

You need an advisor to tell you which problem is important to solve, which direction may not be feasible to investigate, which conference to submit your work etc etc. If you have to do all these alone, you may waste years going nowhere.

That being said, I happen to know a couple of people who successfully did their PhD without working with their advisors. All are very talented, and extremely confident with their research. One of them is a very young PhD student in my former school, who has published 3 solo papers (and co-authored some others), and invented a new sub-field of cryptography.