its weird, you just kinda have to practie getting it. If you kinda smile, but keep the corners of your mouth relaxed you should get it. I know that sounds weird, but that's what my private teacher told me and it works.
Keep your hole a little bigger blow down and use slow air. And which low D are you talking about the one on the staff or below the staff. If it is the one on the staff I dont think it can go as high as the two-figher D. If it is the one below the staff just dont think about the note you are playing just play it. It gets easier once you know the note and how low you need to play it. Just get used to it and it will get better!
For Low C,,,you have to hook your upper lip over the emboucher and blow down into the HJ start with E then to D then C in one breath,,,once you get the vibration going you'll get it,,,,,,do it 10 min/day
I have to pull my lips into a fairly tight smile embouchure to get good low tones, and adjust my jaw so that the air stream is closer to the sound hold edge. Furthermore, sometimes when I find that I am having difficulty it's because I am unconsciously rolling the flute in to try and get the notes. If I raise my head it usually fixes the problem.
It may sound counterintuitive, but I often find that practicing the third register helps my low notes. I think it makes the lips stronger.