Shape Optimization for the Mitigation of Coastal Erosion via Smoothed Particle Hydrodynamics
摘要
Adjoint-based shape optimization most often relies on Eulerian flow field formulations. However, given the suitability of Lagrangian particle methods for solving sedimentation problems in oceanography, extending optimization techniques to the Lagrangian framework is preferable. In our efforts to mitigate coastal erosion, we engage in shape optimization for fluid flows described by Lagrangian shallow water equations and discretized using smoothed particle hydrodynamics. We optimize the shape of obstacles based on a suitable cost function aimed at minimizing water wave heights along the shoreline. Theoretical findings will be validated through numerical simulations across various scenarios.