Hi all! New to this forum, signed up for the specific purpose of getting some help with this problem.

In general, I need to solve this:

u . grad (phi) = 0

I know the form of u, and so I need to solve for phi. Is there a general method of solution to such a problem? In some simple cases I can solve relatively easily by inspection/ trial and error, and there can be many different solutions. But for more complicated forms, it becomes too difficult.

I'm only working in two dimensions, and so I could perhaps simplify it as:

(d phi / dx) + f(x,y) (d phi /dy) = 0

Hopefully someone can help me!

Many thanks