I am a Master student and I am doing a research internship now. I do not have to defend the results of my research at the end of the internship so I am not required to actually get any meaningful result. However, it is in my interest to get a good result and, ideally, a publication. I have always been a good student and ranked high in my program this year. Also, while I am not an expert in the field I am doing an internship in, I believe that I have a reasonable background (if judged by the classes I took) and definitely can learn whatever pieces missing down the road.
I am working under a supervision of a professor who is well-reputed in my field of applied mathematics. It was my intention to get an internship with him since the beginning of the academic year so when the prof suggested me a research topic I quickly agreed. When we had a discussion about the topic several months before the internship started I found the topic a little bit strange and uninteresting, however I thought that I didn't understand it well. Also, during that first discussion it appeared to me that the prof had not thought about the topic a lot, however he seemed enthusiastic about it.
During the time since our first meeting with the prof I studied relevant papers yet my impression of the topic didn't change (it still seemed not enough novel from theoretical point of view and not practical from applied point of view). Also I found something which makes the whole idea which is at the core of the research kind of useless. I reported my findings to the prof and he seemed to agree with me. Yet he would suggest me to perform several numeric experiments to further investigate the problem.
I have carried several of such experiments yet they do not produce any definitive results. Moreover, to my knowledge, in the general setting, the problems I am experimenting with have been studied extensively before yet the special case I am working with is lacking a particular structure which would suggest something interesting. My supervisor already mentioned several times through our meetings that if the experiments failed then we would change the topic. The experiments doesn't provide favorable results however he keeps suggesting new ones.
I do not like the topic and would like to change it as quickly as possible. However, I do not want to be seen as one who just jumps from topic to topic when something doesn't work. During our last meeting I attempted to "corner" the professor, asking for the interpretation of the possible outcome of the experiment in advance. Also, I was seemingly displeased by the idea of more experiments because I was arguing about their meaninglessness. The supervisor throw a phrase which goes like "you seem to be looking for the excuse to not do the job". I have definitely no interest in avoiding work as I want to get some results. Yet, my understanding is that our current efforts will be fruitless.
What should I do in this situation?