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.