Shape Optimization for the Mitigation of Coastal Erosion via Smoothed Particle Hydrodynamics

TL;DR

This paper introduces a novel Lagrangian-based shape optimization method using smoothed particle hydrodynamics to mitigate coastal erosion by minimizing wave heights along shorelines.

Contribution

It extends shape optimization techniques to Lagrangian particle methods for sedimentation problems, specifically applying it to coastal erosion mitigation.

Findings

Successful numerical verification of theoretical results

Effective shape optimization reduces wave heights

Demonstrates applicability of Lagrangian methods in coastal engineering

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 Lagrangian shallow water 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 by exploring different scenarios.