Topological Derivative‐Based Topology Optimization of Linearized Viscous Shallow Water Equation

In this paper, we focus on the derivation of the topological derivative of shallow water equations. We consider two‐dimensional viscous shallow‐water equations linearized around a constant velocity. While these equations are commonly used to model various hydrodynamic phenomena such as waves and tsunamis, their study in a topology optimization framework remains rare. This work thus constitutes an original contribution, by proposing a formal derivation of the topological derivative associated with these equations. This approach opens the way to new optimal design methods for systems governed by shallow water equations.