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

TL;DR

This paper applies shape optimization to permeable obstacles using porous shallow water equations to effectively reduce coastal erosion by minimizing wave impact on shorelines.

Contribution

It introduces a novel shape optimization approach for permeable structures using shape calculus and porous shallow water equations.

Findings

Optimized obstacle shapes significantly reduce wave height and velocity near coastlines.

The method effectively minimizes shoreline wave impact without predefined shape constraints.

Shape calculus enables flexible and precise shape modifications for erosion mitigation.

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 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.