Thanks a lot.
Could you please explain, how it becomes an adverb?
The meaning of 'down' in 'sit down' is something along the lines of 'to a lower position'. Constituents that convey such meaning are called adverbials. What grammatical units can realize an adverbial?
1. nouns (adverbial objective)
2. prepositional phrases
By process of elimination, you will probably arrive at adverbs. Why can we rule out 'down' being a PP? Because there is either no prep or there is no complement. How about the noun interpretation?
i. I am going home.
ii. I am sitting down.
As you can see, your question is not as simple as it may seem at face value.
In i, the way I see the sentence, there is an omitted preposition:
I am going (to) home.
In ii, however, I can't imagine a preposition inserted like this:
I am siting (to) down.
Adverb is my answer to 'down' regarding its form. It is important to bear in mind that adverb is a notion related to form. Adverbial is the name for the functional counterpart.