4 Years in PhD. No publications and adviser keep changing my research First of all, I need to apologize for writing a really long description. 

I started my PhD in Mechanical Engineering 4 years ago and working with a professor, who has no idea on what we are doing and keep changing research area based on the funding possibilities irrespective of our capabilities. He is holding an administrative position as an associate dean and he has no idea on latest methods. He always refer to the methods published in 1980's.  

First, I worked on an experimental research and had to stop after 1.5 years due to lack of funding to continue that. Then, I moved to a numerical research and used an open source software as my adviser didn't have money to buy a commercial software. Even though I had some experience in numerical work it took sometime to learn an opensource software. 

After spending so much time, I finally managed to develop a new solver to simulate my problem. 

I didn't get any input from my adviser as he didn't even want to listen to my research issues. The only thing he ask whenever I met him is do you have results to publish and when you are going to write a paper. Whenever I explain a technical issue he get furious and blame me. Then he doesn't talk to me for at least a month and he forgets what happened. Most of the time, I have to explain what's the problem I'm working on. 

Last year he asked me to change my research, as my problem takes at least 2 days to run one simulation, which is normal in similar simulations. He told me that my solver is useless and there is no point of having a such code if it takes more than 4 hours. I was explaining why it takes long time and it's normal in such simulations even with a commercial software. But he got really angry and scolded me. Finally, I had no option other than changing my research because, I'm funded from his TA position (though the funding coming from the department).  

Now, I have worked on this research for 6 months and he is still complaining about the simulation time. Now he wants me to abandon my work again as one of his friends found a paper (which is published in 1975) on a different method that claims it can solve similar problems faster. However, that method is based on many assumptions and no one has used that method after 1985 due to its limitations. 

And my problem has completely different physics and cannot be used at all. I showed him some of the review papers which explain why that method is wrong and why no one uses it. But, he doesn't believe it and told me don't trust all the papers you read because most of the review papers are wrong as different authors interpret things in different ways. And he scold me saying there is no error in that method and it's me who try to find excuses not to change it. 

I have tried to change my PI several times, but no other professor wants to take me as they don't want to make any problem with associate dean. I tried to apply other universities and they are expecting a recommendation from my adviser. I know clearly that my professor will never give me a recommendation to leave the group. He once told me and our lab mates, it won't be easy to leave this group even if you want. 

No one in this university will dare to take my student. and he once told me that he cannot see me graduating at least in 2020. I don't really know what I should do. 

I'm an international student and my I-20 will expire in 2 months and I need his authorization to extend it. I'm 29 years old and I'm actually not in a position to take a risk.
Change your adviser. Probably time to cut your losses and leave, your time is more valuable