Ask HN: How to start an open source project/organization

I'm thinking of starting an open source project. The project would entail creating and maintaing numerical models used in process engineering. Users of this would either be researchers or engineers in industry.

Currently there is a single commercial library of these models (even though the models are written out in research papers). Since I work in this industry, I know that there would be interest among companies to move towards open source. This means that companies maybe willing to sponsor the development in one way or another (engineers contributing during work hours, supply data, potentially funds).

What would be the best way to start this? The obvious way would be to just setup a public repository and go at it, but I think that some sort of (non-profit) organization behind the entire thing may give it more traction.

Does anyone have experience with this and can offer any advice?