Topology Optimization for Steady-State Navier-Stokes Flow Based on Parameterized Level Set Based Method

Abstract

In this paper, we consider solving the topology optimization for steady-state incompressible Navier-Stokes problems via a new topology optimization method called parameterized level set method, which can maintain a relatively smooth level set function with a local optimality condition. The objective of topology optimization is to find an optimal configuration of the fluid and solid materials that minimizes power dissipation under a prescribed fluid volume fraction constraint. An artificial friction force is added to the Navier-Stokes equations to apply the no-slip boundary condition. Although a great deal of work has been carried out for topology optimization of fluid flow in recent years, there are few researches on the topology optimization of fluid flow with physical body forces. To simulate the fluid flow in reality, the constant body force (e.g., gravity) is considered in this paper. Several 2D numerical examples are presented to discuss the relationships between the proposed method with Reynolds number and initial design, and demonstrate the feasibility and superiority of the proposed method in dealing with unstructured mesh problems. Three 3D numerical examples demonstrate the proposed method is feasible in three-dimensional.