Without knowing more specifics about your situation and whether or not this will help, I will say that I have a child (now 6.5) who is very intelligent, very verbal and very articulate when reasonably calm, can engage in some very deep conversations about interesting topics, can think about and solve a lot of "problems" creatively-and yet for some reason when she's upset (and she gets very upset very quickly) she is unable to articulate herself, unable to problem-solve, and just falls apart crying. At age 3.5, when she'd fall apart it was screaming, wailing, falling to the ground, and becoming aggressive and it could last up to an hour (eta this happened daily, often multiple times, and was (is) very stressful-and was the reason I decided not to homeschool my child


.
What I found was that the key was to prevent these episodes as much as possible. That meant becoming very observant about what factors were involved. Yes, she fell apart (and often still does, but it's different now) whenever things didn't go her way. But why? I finally figured out (wish I'd figured it out earlier) that in those moments, she was unable to handle her strong emotions in another way. It could be because she was tired, hungry, ate foods with dyes, was going through a stressful time, etc. The larger, more general and overarching, issue was (and to a degree still is) that she lacked some basic skills that are needed in order to handle frustration more effectively-and some were skills I could teach, and some were skills that would come with maturity and support and role-modeling. She lacks some ability to modulate her emotions-for her it's calm to very upset in very little time (think 0 to 60 in .5 seconds). This is a really big part of handling frustration, the ability to remain calm enough to problem-solve and talk about it. She lacks some ability to identify and name her emotions, despite a large vocabulary otherwise. She can be very rigid in her thinking at times, which also adds to her frustration. And so on.
So for us it's all about prevention and remaining calm, and helping her learn how to handle frustration more effectively. It's about letting some stuff go altogether. It's about respecting and valuing her needs and feelings and working through things with her before she gets to that point of melting down-with empathy, helping her identify the problem, problem-solving with her to find a solution that works for
both of us (so not always just sticking to my original idea of what should happen, or just going along with what she wants, but finding something that meets both our needs-this helps her learn to think, to problem solve, to identify her emotions, to communicate). We are totally still just muddling through trying to figure out how to do this, but it has been helping. I recommend the book
The Explosive Child, which describes this process very well. Also, the book
Raising A Thinking Child is all about how to teach children how to think through problems, to problem-solve.
Some would recommend simply ignoring the screaming, and that may work for you. It never did work for us, as ignoring the screaming
alonedidn't help our dd learn the skills she needed to handle things differently and did not help our home become more peaceful. (We did ignore the screaming once it really got going b/c what else can you do when they're shrieking and you can't soothe them and any interaction makes it worse? So we just stayed near and available until it began to subside.)
Once my daughter has begun melting down, there's very little we can actually do to stop it-this is why prevention is so important. Once she has begun melting down we might decide the issue isn't worth the meltdown and it's impact on the family and just let it go, let things happen the way she wants and learn from it so we can approach the same or similar issues differently in the future. But this might not help, and in some cases isn't possible. We might be able to soothe her with a backrub or cuddles, but often she rejects this until she's calmer. Most often, we can only ride it out and keep everyone safe.