I would echo everything that the @TheCodeNovice said (I would upvote but I don't have enough reputation). When I was in graduate school I also found myself exploring many areas that were less familiar to my advisor. This tended to not cause me problems so long as I communicated clearly and frequently. However, I would say that you are much more likely to have publications come graduation if you work with techniques or on a problem that your advisor is familiar with. With that said, you should internally evaluate your career goals. Do you eventually want to pursue a career in academics? How much do you value your independence? Are you able to thrive while working independently?
If you want to pursue a career in academics then you will need publications. While you can collect more publications as a post-doc, it can be incredibly advantageous to publish 2-4 articles while in graduate school, and it is usually much easier to do this if you work on things that your advisor has expertise in. If you aren't locked in with your advisor decision (i.e. haven't gone through quals or candidacy) then you may want consider a different advisor.
Reflecting back on my experiences, I would say that my situation was not exactly "ideal".
However I did end up graduating with a fair amount of success. A large part of this success was me being mentored by a different faculty member that was more interested in my project. I initiated that connection after taking one of their classes. I would recommend that you also find a faculty member that is knowledgeable about FEA/SPH. You can develop a relationship with them, possibly publish with them, and they can be a powerful voice on your committee. These relationships can often be very productive since neither the student nor this second faculty member have direct skin in the game (i.e. they are not paying your stipend). If you do choose to use FEA/SPH then it is of paramount importance that the problem you are studying is very well defined. It is much harder to simultaneously learn about new computational methods and come up with an interesting research problem that the method can be used to solve. When I was working on things outside of my advisor's scope of expertise I often felt as though I didn't know how to progress the "field" that I was investigating. Part of this was because I didn't have a well defined research problem and so I spent lots of time trying to see if I could improve various computational methods. However part of this can also be the primary advisor's fault, as what is currently "state of the art" in a field is usually only learned by attending conferences. My advisor would not send me to conferences and so I had to rely on reading books and talking with other faculty to make progress.
(As an aside)
I studied similar things that you are talking about including SPH, DPD, SDPD, and FEM. When I was looking into SPH I found the book, "Fluid Mechanics and the SPH Method: Theory and Applications" to be helpful although it did contain a few errors in various places. I was working on a few different colloidal/active matter hydrodynamics problems and eventually settled on using the boundary element method (BEM) to simulate and explore several problems.