Problem is, there is no server. All client side. So the tab on which you click "run simulation" is effectively the "server", except it stops running when the user switches tabs.

Put two of them in two iframes on the same page? No code changes should be needed

The fact that you don't have a backend is the limiting factor here.

There are perfectly legitimate reasons to not have a backend. In fact, if something can be accomplished without user sending his data to some remote server (as opposed to just fetching data from the server), I believe it should be done this way.

In some ways it's limiting, but overall it's a good thing. Less complexity, less network transfer, works offline, etc. It's just more challenging to do in JS/HTML than in your choice of traditional desktop app dev tools.

GMail and Google Docs work offline too. Surely with things like Firebase it's less complex than inter-tab communication?

Oh, you’re volunteering to pay for it? How nice of you!

</sarcasm>

Cost is a real concern for these things. The tradeoff is running things on client or expensive backend or spending ages building a custom, efficient backend.