Topological Derivative for Shallow Water Equations

Coastal erosion is a major and growing environmental problem describing the movement of sand caused by tides, waves or currents. Several phenomena contribute to the significant advance of the sea. These include climate change, with rising sea levels due to the melting of ice at the Earth's poles, the amplification of the tidal effect, leading to the transport of large masses of sand, storms, etc. We contribute to this problem by using topological shape optimization techniques applied to an PDE describing coastal erosion. We use Shallow water equations as a model.