This is from a native speaker My house is leaking (see:3:02-3:05) who is checking around his basement after heavy rain and sees some damp corner. He touches it and says:
"Oh, that is wet. We have been having water come through here."
I would, as a non-native speaker, never be able to make up such a sentence, because I think we as learners are not made to acquire such a natural level thinking in English. I would probably say:
"Oh it is wet. There seems to be water. It must be coming through here."
Anyway, I thought about the structure of the sentence, because it seemed long and complex to me. Firstly, I thought it might be a causative sentence "have water come through", but it did not make sense.
Then I thought it might be shortened relative clause "...water which come through here.", But then it did not make sense either.
Then I made some more research and came to conclusion that the structure of the sentence seems very much like this sentence I have found:
"We had a strange woman come to the door selling pictures."
So, am I right in my final conclusion?