Come up.

I meant sort of approaching.

What I am looking for understanding is extracting image of a verb in the mind of a native.
I know the meaning of come up, but I am trying to understand when would you say, for instance, "she come up to me."
You know what I mean?

However, here an example:
A young girl came up to me and asked for money.

English is full of phrasal verbs that it is possible to find synonyms. But what I am seeking is what you would use to describe a situation. I believe "UP" in a phrasal verb recalls a meaning in the mind of a native, and of course he/she have learnt exceptions as well, by growing up.

Hi,

However, here an example:
A young girl came up to me and asked for money.

Here are nuances I feel about this.

She approached me unexpectedly.
She was probably not close to me before she came up to me.

come up: "He came up to me and introduced himself." This means he approached me close. So "up" creates the verb "to come close."

run up: "He ran up to me and said he was scared." This means he approached me fast and stopped close to me. So "up" creates the verb "to run until you're close to someone/something and stop."