  We apply the cell merging method to a model shallow water problem with a
permeable boundary. We use a cut cell approach which is more easily and
systematically scalable with different shapes of boundaries. The novel cell
merging method presented in this paper uses both wave propagation algorithm and
gradient reconstruction for second order corrections, along with minmod and
Barth-Jespersen limiters. We observe second order convergence in two model
problems, one with a linear boundary and other with a composite, V-shaped
boundary. We assess the effectiveness of these two boundaries by doing a
realistic scenario including an island and observing inundation at the peak of
the island.
