I checked the HSB values (using Photoshop Elements) of the same pixel before and after a saturation adjustment in Lightroom - here is the information:
Before Saturation: RGB: 159, 189, 233, Gray: 28% HSL: 216 degree, 32%, 91%
After Saturation: RGB: 99, 183, 255, Gray: 32% HSL: 208 degree, 61%, 100%
I don't know what algorithm Lightroom uses. It seems it doesn't simply increase S in HSL color space.
Does it use other color spaces, or use some functions to change all the 3 variables in HSL color space?
For saturation enhancement, one post talked about the way to do it in Gimp: Is there an equivalent to Adobe's "Vibrance" in Gimp? - the way to change saturation, while H and V remains the same (in Gimp the color space is HSV)