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I'm reading an old paper (from the 1980s) where someone solved the vorticity equation to get streamlines for flow. This is probably a silly question, but I'd be interested to know why he may have used this method instead of solving for the x and y (it's a 2-D set-up) components of flow.

Might it have been because of the more limited computational facilities back then, or could there be another advantage to using the vorticity method?

I'd like to know because I want to write some code for calculating fluid parcel trajectories over time. And I'm wondering where to start--which governing equations to use, etc. If anyone has any general advice, I'd love to hear it. Thanks.