Green Ampt: Infiltration

Water infiltrates into the ground from a pressurised (p = 1) semi-circular pipe.
The objective is to, assumming no unsaturated zone, track the satration front.
This is essentially a filling problem but the potential on the front is a function of space and time.

• p is pressure,
• h = p/rg + z is the head (length),
• n is the outward normal on the saturation front,
• v_n is the velocity of the front,