HI! My major is computer graphics. I have read many papers, but some basic concepts are missing in computer graphics papers on fluid animation.

I have two questions. 1. Is is possible to use 'semi-lagrangian method' on staggered grid system for advecting facial velocities? I think that it is understandable to advect 'sclar' by means of the semi-lagrangian method. But, the velocities are defined on the faces in the staggered grid, and they have only normal portion of each face. Can I advect the facial velocities by means of the semi-lagrangian method?

2. What's the reason they use the staggered grid system for liquid animation? for example, front tracking for multiphase flows and 'free surface' simulation. Can I define only one vector velocity at the center of a cell with a scalar pressure?

Thank you for reading. Any comments can be very helpful to me.

I can answer your second question.

the closeness rule:

in the differential equation sense, a point is more influenced by closer points.

now, if you put velocity and pressure at the same point, you may suppose the pressure at this point has most influence on the velocity at the same point.

however, in many schemes, the most influential one is simply skipped due to technical reasons.

then the staggered grid came to this world.