  Coastal erosion describes the displacement of land caused by destructive sea
waves, currents or tides. Major efforts have been made to mitigate these
effects using groynes, breakwaters and various other structures. We address
this problem by applying shape optimization techniques on the obstacles. We
model the propagation of waves towards the coastline using two-dimensional
porous Shallow Water Equations with artificial viscosity. The obstacle's shape,
which is assumed to be permeable, is optimized over an appropriate cost
function to minimize the height and velocities of water waves along the shore,
without relying on a finite-dimensional design space, but based on shape
calculus.
