In my plugin code I would like to perform a WP_Query (or similar) which returns all posts matching a given query string, as if the user typed that same string into the WordPress search form. Perhaps I'm just being dense, but I cannot seem to find a way to do so. I would expect to have a special parameter for WP_Query, such as matching, but I see no evidence of one.

I'll start going through the WordPress codebase to see how it's done internally, and I'll post the answer here if I find it. I just thought someone might happen to know offhand.