Yup, I do this as part of tai chi and qi gong (referred to as 'dan tian' breathing).

Seems to be a thing of the west to take elements of yoga, tai chi, daoism et al, and distill them - mindfulness comes to mind - and as devices they're good, but together they amount to so much more than the sum of their parts, hence the eastern penchant for a 'holistic' approach.