When someone is lying down, you say *sit **up****.<br>
When someone is standing in an upright position, you say *sit **down***.

What in the situation when you want to ask a very small kid to sit down to a chair, but the chair is too high for him so he has to *climb **up*** the chair to *sit down* on it? See a [picture][1]. *Sit down* sounds like not matching the context. Would you still use *sit down*? 

(I believe this is not a duplicate of http://english.stackexchange.com/questions/122019/lying-down-and-then-sit-up-down)


  [1]: http://voiceboks.com/products/wp-content/uploads/2013/10/Going-up-Abiie-group-4.jpg