How to handle advection-term involving two unknows?

General Discussion
1

Hello All,

I am trying to implement a temperature equation in the fluid system. I have a term (u \dot \nabla T) that couples velocity and temperature in the temperature equation. How can I handle such a term? Any help or direction would be greatly appreciated. Thank you so much!

2

You can solve NS equation first, then the u is known. Or you can use newton method to solve the coupled u-T problem

3

what is Newton method ?
could you share a reference to simply explain