This is more advice than a hard-and-fast answer, because there isn't a way to tell by RAW when exactly in a turn that something happens; if you knew for certain that, say, the barbarian lost their flight ability one second before the end of the turn, you could calculate it, but that "one second" figure really doesn't exist. So the final answer will have to be a DM call. I'd go one of two ways:

1. Say that a turn is a turn is a turn, is six seconds: the game is already several layers of abstraction, so precisely timing things in segments smaller than a six-second turn is more trouble than it's worth. Note that you also aren't calculating acceleration due to gravity with this plan already, and that would have a big impact on the distance traveled in the real world.
2. Being charitable without doing too much math, consider any "partial turn" durations to be halved, so three seconds. You're giving the barbarian player a bit of a break here while keeping the math simple. If they try to cut that down farther, just say no.

Both of these assume that the one making the call is the DM.

This method nets you more damage

Falling damage is dealt at the end of a fall.

PHB 183, Falling

At the end of a fall, a creature takes 1d6 bludgeoning damage for every 10 feet it fell, to a maximum of 20d6. The creature lands prone, unless it avoids taking damage from the fall.

So in order for Thunderwave to stop you from taking this damage, it has to end the fall first and then begin a new one, wherein you fall at a height of 15 ft or less. Furthermore, it must end the fall without dealing damage to you.

If you are falling and then are subjected to Thunderwave such that your fall stops and is reversed (ie, you are tossed upwards), you should take falling damage then. And now you begin a new fall from your new height.

For example: you fell from a height of 100 ft. After falling 90 ft, your Cleric (who is on the ground, right at the spot you are going to land on) casts Thunderwave, sending you back 15 ft upwards. Then, your fall must have ended at the moment you were 10 ft away from the ground when you were hit by Thunderwave.

You take 9d6 + 2d8 damage for this. Then you begin a new fall from a height of 25 ft (the 10 ft you were at, plus the 15 ft from TW), dealing you another 2d6 damage when you land.

All in all, this nets you extra damage equal to 1d6 bludgeoning, for the extra 15 ft fall, and 2d8 thunder, from the Thunderwave.

Response to Objections:

1. Thunderwave causes forced movement, and forced movement doesn't trigger damage effects. Is there a rule that Thunderwave must trigger the damage?

   • A spell does only what it states it does. Thunderwave does not say it prevents falling damage. Moreover, the saying goes "It's not the fall that hurts you; it’s the sudden stop" which I feel is applicable here. The rules for taking falling damage state that you take damage "at the end of the fall." If Thunderwave causes your fall to end, then you must take damage.

   • There is no rule that says forced movement never triggers damage.

2. Is there a rule that the falling counter isn't reset once pushed back up? Take Feather Fall -- you don't take fall damage by just waiting to cast it.

   • There are no rules about "resetting the counter of fall damage"; however, Feather Fall specifically negates fall damage.

3. So going by (2), then if you cast Fly on yourself while mid fall, do you take damage because your fall ended?

   • PHB 191, Flying Movement seems to suggest that if you are held aloft by magic, you are not considered falling. A non-falling creature does not take Fall damage. See this answer which discusses this specific objection in more depth.

4. "At the end of the a fall... the creature lands prone..." Thus the fall ends when the creature lands. That is not to say that the creature didn't fall 100', but that the thunderwave doesn't itself precipitate falling damage

   • These are two separate sentences with independent thoughts. More accurately, it's "At the end of the fall, you take damage equal to X" and "If you take damage after falling, you land prone." If Thunderwave causes the fall to end, damage is still taken. But landing becomes inapplicable as you do not land when hit by TW in this way.