Shape Optimization for the Mitigation of Coastal Erosion via Shallow Water Equations

TL;DR

This paper applies shape optimization to design obstacles that mitigate coastal erosion by modeling wave propagation with shallow water equations, aiming to minimize wave impact on the shoreline.

Contribution

It introduces a shape optimization framework using shape calculus for designing coastal structures to reduce erosion, without relying on finite-dimensional design spaces.

Findings

Optimized obstacle shapes effectively reduce wave height and velocity near the coast.

The method demonstrates potential for practical coastal erosion mitigation.

Shape calculus enables flexible and precise obstacle design.

Abstract

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 groins, breakwaters and various other structures. We try to address this problem by applying shape optimization techniques to the obstacles. We model the propagation of waves towards the coastline, using two-dimensional shallow water equations. The obstacle's shape 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.