I'm still a bit confused about what exactly was going on here.
From what I can recall, it's due to the fact that the simulation modeled incompressible fluid which have the property that (div/curl) (?) wouldn't be a physically accurate behavior to simulate, so they basically subtracted out that part of the gradient?
motoole2
The right image (and corresponding video) assumes that air-pressure is negligible when solving for fluid flow (referred to as the single-phase case for fluid simulation). A goal of this fluid simulation paper is to consider how to solve the two-phase fluid flow problem, where air pressure is non-negligible. As for the technical details and your actual question.. Jim can probably give you a better answer. ;-)
jmccann
Attempting a more complete answer:
In fluid simulation, you model incompressible fluids. "Divergence" measures local compression. So a typical fluid simulation approach is to:
Come up with a velocity field (generally by "advecting" == "moving" the old velocity field through itself) that may have some compression.
Remove the compression (divergence) from the field.
Repeat.
The typical approach to step 2 is to compute a divergence-free field by solving for a scalar function whose gradient is as close as possible to the velocity field, then subtracting this gradient. (This takes advantage of the fact that the gradient of a scalar field is always curl-free -- that is, it contains only divergence.)
This paper, instead, solves directly for the new velocity by solving for a vector field whose curl is as close as possible to the velocity and then setting the corrected velocity to this curl.
The reason it does this is so that it can weight the "closeness" by the density of the fluid (making it free to have mis-matches in the air, but expensive to have mis-matches in the liquid).
I'm still a bit confused about what exactly was going on here. From what I can recall, it's due to the fact that the simulation modeled incompressible fluid which have the property that (div/curl) (?) wouldn't be a physically accurate behavior to simulate, so they basically subtracted out that part of the gradient?
The right image (and corresponding video) assumes that air-pressure is negligible when solving for fluid flow (referred to as the single-phase case for fluid simulation). A goal of this fluid simulation paper is to consider how to solve the two-phase fluid flow problem, where air pressure is non-negligible. As for the technical details and your actual question.. Jim can probably give you a better answer. ;-)
Attempting a more complete answer:
In fluid simulation, you model incompressible fluids. "Divergence" measures local compression. So a typical fluid simulation approach is to:
The typical approach to step 2 is to compute a divergence-free field by solving for a scalar function whose gradient is as close as possible to the velocity field, then subtracting this gradient. (This takes advantage of the fact that the gradient of a scalar field is always curl-free -- that is, it contains only divergence.)
This paper, instead, solves directly for the new velocity by solving for a vector field whose curl is as close as possible to the velocity and then setting the corrected velocity to this curl.
The reason it does this is so that it can weight the "closeness" by the density of the fluid (making it free to have mis-matches in the air, but expensive to have mis-matches in the liquid).