Topology optimization method for unsteady state incompressible viscous flow based on a level set immersed boundary method

Abstract

This paper proposes a novel topology optimization method for unsteady state incompressible Navier-Stokes flow. Many methods of topology optimization for steady state flow have been proposed, whereas most fluid flow problems should be considered as unsteady state. Therefore, a topology optimization method focusing on unsteady state fluid flow governed by the incompressible Navier-Stokes equation is considered in this paper. In addition, the defined boundary condition on the wall of an optimized structure should be precisely evaluated because it describes the specific fluid flow profile, such as velocity and pressure, on the wall that the fluid contacts. In order to solve flow profile near walls, an immersed boundary method is applied in the proposed method. The finite volume method is adopted to discretize primal and adjoint problems. These problems are solved using the Pressure-Implicit with Splitting of Operators (PISO) method. In this study, sensitivity analysis based on a topological derivative is applied. The update scheme for the design variable uses a reaction-diffusion equation. Some examples are shown and the effectiveness of our method is discussed in this paper.

Keywords

• topology optimization
• unsteady-state flow
• topological derivative
• immersed boundary method
• level set method