The story of Noah's Ark was copied almost word for word from the much older Sumerian Epic of Atrahasis.
How did he stop the flying animals from flying away from the ark during the day or night? 

If the flood covered all the mountains on the planet, then the ark rose to such a level in the atmosphere that none of the animals on board could actually breathe. There are over 100 mountains over 23,622 feet high . The vast majority of ark dwellers would suffocate for the lack of oxygen.