Chances at computational science grad schools

[creepypasta13]

I'm about to apply to grad programs in AE/ME and computational science right now. I have a general interest in doing numerical and computational work on physical problems. So that's why I'm considering computational science but not applied math programs. For now, the main area of interest I have is computational fluid dynamics.

I got my BS degrees in physics and applied math last year. I ultimately want to do research in my career, so I'm pretty sure I want the phD, but I'm not 100% sure

GRE: 800Q, 470V, 5.0 W. I may have to take the GRE math subject as a lot of the computational science programs recommend but don't require it
GPA: 3.77 overall and major. But I only took 2 engineering courses: A in heat transfer and B- in fluid mechanics.
Research experience: An REU in solid-state physics, and 2 quarters of research with an applied math prof doing research in materials modeling. No publications
Work experience: Two different internships in industry, including one that just ended last week

LORs: One from REU prof. Another from the prof I did research with in math (but he's a post-doc). My guess is that these LORs will be good but not great. I've heard various opinions for who to choose for my last LOR. I could choose a physics prof I took a class with 3 years ago, my heat transfer prof I got an A with 6 months ago (but he also works at a company, so he might not even have a phD), or my two different hiring managers at my internships (one has a phD in applied math in CFD)

Because I plan on applying to 4-8 grad schools in AE/ME also, I've only listed these schools as possible choices for computational science programs:

texas-austin, MIT, stanford (website says RAship only given to MS students with firm commitment to pHd - does that mean chances are really slim?), maryland, minnesota

I would appreciate any comments. Thanks

 

[sweetpotato]

I would maybe suggest applying to more schools. MIT, Stanford, and U of Texas at Austin (especially the first two) are extremely hard to get into even for the most qualified applicants. I don't know anything about Maryland and Minnesota, but I would assume they are less competitive. Maybe add some more schools of that sort.

 

[creepypasta13]

so Texas-Austin isn't within my reach? Anyways, there just aren't many programs in computational science, so the only other school I've seen that's in the same range as Maryland and Minnesota is Purdue. Unless someone here can suggest other schools within my reach