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?