Topology optimization of incompressible Navier–Stokes problem by level set based adaptive mesh method

This paper presents a level set based adaptive mesh method for solving the topology optimization of incompressible Navier–Stokes problem. The objective is to minimize the dissipated power in the fluid, subject to the Navier–Stokes problem as state equations with a fluid volume constraint. The material distribution information that implicitly represented via level set function is considered as the design variable, which provides an easy way to construct the refinement indicator. Shape and topology sensitivity analysis suggest the steepest descent direction. By the proposed method, the computational expense is mainly focused near the interfaces, which lead to a significant reduction of the computational cost. Although illustrated by the Navier–Stokes problem, we would like to emphasize that our method is not restricted to this particular situation, it can be applied to a wide range of shape or topology optimization problems arising from the fluid dynamics.