Open Access

ARTICLE

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

by Peng Wei¹, Zirun Jiang¹, Weipeng Xu¹, Zhenyu Liu², Yongbo Deng^2,3, Minqiang Pan^4,*

1 State Key Laboratory of Subtropical Building Science, School of Civil Engineering and Transportation, South China University of Technology, Guangzhou, 510641, China
2 State Key Laboratory of Applied Optics (SKLAO), Changchun Institute of Optics, Fine Mechanics and Physics (CIOMP), Chinese Academy of Sciences, Changchun, 130033, China
3 Institute of Microstructure Technology (IMT), Karlsruhe Institute of Technology (KIT), Eggenstein-Leopoldshafen, 76344, Germany
4 School of Mechanical and Automotive Engineering, South China University of Technology, Guangzhou, 510641, China

* Corresponding Author: Minqiang Pan. Email:

(This article belongs to the Special Issue: New Trends in Structural Optimization)

Computer Modeling in Engineering & Sciences 2023, 136(1), 593-619. https://doi.org/10.32604/cmes.2023.023978

Received 20 May 2022; Accepted 13 September 2022; Issue published 05 January 2023

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.

---

Keywords

---