I follow a mixture of advise offered by various experts and have acheieved a measure of success. I measure the success by not being exhausted upon arrival in Europe and being sharp (awake) enough to deal with adventures: such as making connections or finding a B&B/hotel I have never seen before.
#1. The AMA advises during a flight drink lots of liquid, NON ALCOHOLIC, nothing challenging, ie. no games, interesting motion pictures, etc. short naps if unable to sleep, do not overeat, except for a hot fudge sundae.
#2. A number of years ago a Surgeon General advised that in order to adjust the body clock, one should be exposed to daylight for approximately 2 hours at your destination after crossing several time zones. A simple in the outdoors solves this one.
#3. The Discovery Channel had an interesting piece regarding a natural supplement called NADH, available in most health food stores. It does not help keep you awake, but, heightens the senses considerably. It was not rejected by the FDA and is safe to use.

The above combination has worked for us for some time.
Hope it helps,
L