I get sleepy every day after lunch. What do you do to stay productive throughout the late afternoon, or when your body is tired but you need to work?
I think many people, after their midday meal, tend to sit still afterwards to "digest". This can cause sleepiness.
If you have extra time on your lunch break after finishing your food, take a walk. Whether it's around the building, or outside for some fresh air, moving around a bit can do you a world of good. You could even get up and stretch your legs anytime you start to feel your brain shutting down (i.e. sleepy).
Common practice in some Asian countries (Taiwan, at least) since lunch breaks tend to be longer there, is to take a short nap after lunch. Literally, lay your head on your desk and nap. I suppose this can help to restore some energy and get rid of sleepiness. Never really picked up the habit while I was there.
Lastly, though my comment was joking in nature, caffeine might actually be a doable option. Coffee, soda, whatever. It may give you just what you need.