gradient calculation of cell vertex finite volume method
 

I am solving shallow water equations using cell vertex finite volume method.
The computational domain is discretized into a triangular mesh.
I need to calculate the flow variable gradient at vertex of each triangular.
I used least-square method but it wasn't accurate. maybe I didn't calculate properly at boundary!?
I'm considering using Green-Guass method but I don't know how to calculate the gradient at vertex which are on boundary, such as solid wall, inflow or outflow boundary.

Any one can give some suggestion.
Thanks in advance.