When simulating fluids with calculus, do we consider each pixel in terms of (x,y) and then apply the functions?

In general, what sort of mathematical/physical considerations do we have to make when simulating the motion of fluids?

When simulating fluids with calculus, do we consider each pixel in terms of (x,y) and then apply the functions?

In general, what sort of mathematical/physical considerations do we have to make when simulating the motion of fluids?