What is name of this card game?
The descriptions sound a little like a game I played at school and was know by us (possible as local dialect) as Slam.

Doing a google search I've found [double patience] which matched your description.1

28 cards are played out in 7 piles with 1-7 in each (if you recalled 21 then then would work as 6 piles 1-6 in each)

The object is to get rid of your cards onto central piles.

It's possible to play with multiple players if each player has their own deck.