I definitely fall into the discovery writer category, but I do have a process of development that can be fairly rigorous in a way.
I start off by developing the initial starting point for my story very carefully. I need a goal, motivation, and conflict for each of my main characters, and also for my villain. I've learned that without those three elements, any story idea will fail. You either develop them through improvisation, or you get them before you start. Experience has taught me that it is better, for me, to figure them out before I start.
Then I spend some time daydreaming, writing down random notes and ideas, until I begin to get a vague sense for all the different kinds of events that might take place in the first act of my story. This isn't so much a specific plan of action. Instead it's more of a dreamy, multiverse blob of possibilities that lives in my head. If I spend enough time daydreaming, I might also start to get glimpses of the second act. (I think in terms of 4 act structure--basically 3-act structure with the second act broken into two pieces.)
Then I develop a few random scene ideas, usually no more than five or six. Most of the time these are not really planned scenes in the typical fashion of an outline. Instead they tend to be open-ended what-if scenarios, like "what if Joe got attacked by an alien while he was filling his car with gas?", or "What if Linda saw a flying saucer through her kitchen window?"
These initial scenes will all be based on my premise, and designed to serve my concept for the story setup, but won't be created in any particular chronological order. Usually I only have a vague sense of where I'll put them in the actual story before I start writing them. Most of the initial material is intended to fit somewhere in Act 1, but that's about all I know for sure. I write these first few scenes (or at least a couple of them) to see what will happen. For example, with Joe and the aliens--maybe he will survive, maybe he'll get abducted, maybe he'll kill an alien. I'm not really sure till I put him in the situation and try it out. Some of these scene ideas end up being duds, and don't make it into the story at all. Others get cast aside as soon as the writing starts because it becomes obvious that they won't actually work.
While I'm working on the initial scenes, a bunch of other random scene ideas will occur to me, still mostly open-ended. Some are inspired by very small things that occur to me--character moments, images, snatches of dialogue--and some are not necessarily connected to specific cause and effect elements in other parts of the story. Some will be obvious followups to scenes I've already written, others will be speculative ideas for things that might happen further along, or even things that might've happened earlier: setup scenes, character development scenes. I'll make notes about these, and sometimes I will open a document and conduct little conversations with myself on the page about possible plot elements (something I learned from a writing book by David Morrell).
Eventually, I pick a few more of my scene ideas or images, and write them to see what happens.
During all this, I continue day-dreaming, and making notes, and expanding the multiverse story-blob in my head. At some point I start to have a good grasp of the basic nature of Act 2--not necessarily all the specific plot twists and turns, but a strong sense of the pressures that will come to bear on my characters, and the sorts of scenes that are likely to be needed. At this point I will also begin to get glimpses of things that could happen in act 3 and 4. I'll make notes, and eventually start writing scenes that occur much later in the story, just to test out the ideas. Writing these scenes helps me solidify my feeling for the later acts, and allows me to plant more foreshadowing into the early material.
Eventually, writing all these bits and fragments out of order allows me to see a clear framework for the shape of my story from beginning to end, and the scenes I've already written become a flagpole outline. Then I just have to fill in the gaps.