No 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 toward 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.

No abstract

Adjoint-based shape optimization most often relies on Eulerian flow field formulations. However, since Lagrangian particle methods are the natural choice for solving sedimentation problems in oceanography, extensions to the Lagrangian framework are desirable. For the mitigation of coastal erosion, we perform shape optimization for fluid flows, that are described by incompressible Navier-Stokes equations and discretized via Smoothed Particle Hydrodynamics. The obstacle's shape is hereby optimized over an appropriate cost function to minimize the height of water waves along the shoreline based on shape calculus. Theoretical results will be numerically verified exploring different scenarios.