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Simulating water over terrain
If you don't want a long an boring introduction, skip directly to the virtual pipes method description. I will get a little bit sad if you do this, though x) I'm somewhat obsessed with terrain generation, grid-based games, simulations, and stuff like that.
Even those that do can often get away with some simplistic approach: I can easily imagine being able to fill up a hill in a game like Civilization (though it would probably break a lot of stuff gameplay-wise), and it doesn't interact with water in any way. The paper recommends using a factor of pow(friction,dt) to make it dt-independent (which is closely related to exponential smoothing I've explained in another article). If we look at Red Blob Games' amazing article on hexagonal grids, what I'm using is basically the axial coordinate system on a dual to a pointy-top hex orientation.
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