Is it necessary to watch "The Hobbit: An Unexpected Journey" in order to enjoy and understand "The Hobbit: The Desolation of Smaug"?

My answer is a clear (and honestly pretty obvious) Yes, definitely! It is one continuous story (which would not have needed to be turned into three movies at all, but that is a different question) and The Desolation of Smaug is a direct continuation of An Unexpected Journey, relying on characters and events introduced in that (they were even filmed as a whole, like the Lord of the Rings trilogy).

That being said, of course nothing stops you from reading a summary of the first part before watching the second (or just the book, though they made quite some many additions to the book's story). But this is clearly not the way I would suggest to follow.