Unhappy with my PHD CS research topic. What should I do? I've been working for about 2 1/4 years on a PhD CS research topic, which is to speed up a certain type of simulation using a certain general approach. This approach is pretty much the only research topic our research group has to offer. However, in my opinion, this approach is also fundamentally broken and beyond repair: It is not applicable or very inefficient for most simulations of this type and for the few simulations, for which this approach is applicable and efficient, there are much better specific approaches available. Consequently, in pratice, nobody uses this general approach over better specific approaches. Besides this fundamental flaw, there are other issues bothering me about this approach and my work, like being pretty much implementation focused, not offering much room for interesting optimizations and that I have to work pretty much alone.

While I have realized all this even before accepting this position, I've been telling my self that all of this will somehow work out. However, as things are now, it's quite the contrary: I've resigned a long time ago and lost pretty much all interest in CS. I've been thinking about quitting this position for a long time, but I do not want to disappoint my supervisor, whom I like very much, and I also do not know where else to work. I'm also afraid of throwing away 2 1/4 years of work on a PhD. What would you advise me to do?
In general, a proof or demonstration that something does not work for a particular application can be as valuable as proving that something does work. This is especially true if a priori, the thing should seem to work. 

You might explore with your advisor whether this is a viable direction for your work to take. I can't predict what he/she would say, but it is worth spending some time in the exploration before you bail out. You probably have some deep insights into the problem that you can bring to bear. 

Again, research is about knowledge, not about doing some inappropriate thing just to "force" it to kind of work. Extract the knowledge from the project. 

But your advisor is likely the final judge here.