I will leave her alone for now so that she can process things up.
I think for a sentence like this one, "process up" makes a suitable fit. I assume it means "absorb", but I didn't find it used according to my research, nor I found its meaning. And although Ngram shows some results for "process up", I didn't find it used as a whole phrase in Google Books.
Does process up exist in English? And can it convey the meaning of "absorb" which is to take something in, especially gradually?
The sentence is said by A to herself in an informal writing story. B has talked harshly to C and told C things that would change C's life to the worse. Then, B leaves A and C alone in the room, and that's when A says the sentence to herself intending C in her speech.