Topology optimization method for incompressible viscous flow applying an immersed boundary method

Abstract

This paper proposes a new topology optimization method for steady state incompressible viscous flow. Since fluid flow profiles, such as velocity and pressure profiles, describe specific behavior on walls that fluid contacts, defined boundary conditions in such profiles should be precisely evaluated. The immersed boundary method is implemented here to represent fluid flow profiles, and enhanced accuracy is obtained through their rigorous use during optimization. The topological derivative is derived for the sensitivity analysis and the finite volume method is used for numerical analysis during the optimization process. Several numerical examples are provided to confirm that the optimal configurations accurately represent flow distributions, in contrast to previous research in which a specific treatment for internal wall boundaries was not considered.

Keywords

• topology optimization
• sensitivity analysis
• topological derivative
• immersed boundary method
• level set method