How do I react if I bump into my ex or his new girl?

I look up articles on what to do when you bump into your ex, but most seem to imply that the break up didn’t go as bad as it could. Mine did, and he was abusive, and he begged for me to come back to him and found someone new in a snap.

I just want to be able to prepare myself for IF he tries to talk to me again, or if I bump into them. What should I do? Act cordial? What if he tries to speak with me?