shallow water and simple scheme

AO

when we apply the simple scheme to solve incompressible N-S equation, we could derive the relationship between pressure and velocity and use simple scheme to solve it. But speaking about shallow water equation which is depth-averaged, the relationship is about depth and velocity, obviously the continutiy eq is for h (water depth). my question is do i have to change something for simple scheme? Or someone could help me by giving some references. thanks a lot