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Let's say I managed to compute a velocity field that is divergence-free. How do I integrate it over time? meaning, I created a potential function, set v to be curl of potential function, so I have now a velocity filed. My question then: How do I animate/move particles in that field? Is is possible to have an analytical function that is like position(t) given that velocity field? [simplest and dumb analogy, position(t)=sin(t) i + cos(t) j].

I work in visual effects, so I am not looking for something accurate, just to give an illusion of turbulence without simulation (there are plenty of fluid sims that can do the job, but I am not interested in simulation, just need something fast...]

PS. I am calculating a velocity field from this paper https://www.cs.ubc.ca/~rbridson/docs/bridson-siggraph2007-curlnoise.pdf

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  • $\begingroup$ Minor comment to the post (v2): Please consider to mention explicitly author, title, etc. of link, so it is possible to reconstruct link in case of link rot. $\endgroup$
    – Qmechanic
    Mar 19, 2019 at 5:26

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Okay, I watched some tutorials today, in summary, the goal of the paper (mentioned in the previous post) is to compute a velocity flow that satisfies div(v) = 0 (this makes velocity field looks like a fluid). Anyways, after computing that velocity field, I "think" the only way to use it is just by simple sim loop, i.e. p(n)= p(n-1)+v(n)*dt. I don't see any analytical forms such to compute p(n)=fun(t)...

Cheers Ps. The paper is: "Curl-Noise for Procedural Fluid Flow", by: Robert Bridson ,Jim Hourihan, Marcus Nordenstam current active link : https://www.cs.ubc.ca/~rbridson/docs/bridson-siggraph2007-curlnoise.pdf

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