I had a cavernularia obesa for several years. In my experience it requires a really deep sand bed, is NOT photosynthetic, requires a massive waterflow, and lots of both zooplankton and phytoplankton. I used cryopaste phytoplankton, prawn eggs, and oyster eggs and that seemed to work. Decapsulate brine shrimp eggs would probably work better than live brine shrimp but it probably won't survive without a varied diet. The sand bed it was in was about 8 inches deep but it probably could get by with 6 inches. I would not recommend this animal to the average hobbyist.
I'll try to find a picture of mine.