to attack someone in a violent way:
Two men assaulted him after he left the bar.
He was found guilty of indecently assaulting a student.
if a feeling, sound, smell etc assaults you, it affects you in a way that makes you uncomfortable or upset:
The noises and smells of the market assaulted her senses.
to strongly criticize someone's ideas, plans etc
to try to do something very difficult:
a task force to assault the problems