Application of a Parametric Level-Set Approach to Topology Optimization of Fluids with the Navier–Stokes and Lattice Boltzmann Equations

Abstract

Traditional material distribution based methods applied to the topology optimization of fluidic systems often suffer from rather slow convergence. The local influence of the design variables in the traditional material distribution based approaches is seen as the primary cause, leading to small gradients which cannot drive the optimization process sufficiently. The present work is an attempt to improve the rate of convergence of topology optimization methods of fluidic systems by employing a parametric level-set function coupled with a topology description approach. Using level-set methods, a global impact of design variables is achieved and the material description is decoupled from the flow field discretization. This promises to improve the gradients with respect to the design variables and can be applied to rather different types of fluid formulations and discretization methods. In the present work, a finite element method for solving the Navier-Stokes equations and a hydrodynamic finite difference lattice Boltzmann method are considered. Using a 2D example the parametric level-set approach is validated through comparison with traditional material distribution based methods. While the parametric level-set approach leads to the desired optimal designs and has advantages such as improved modularity and smoothness of design boundaries when compared to material distribution based methods, the present study does not reveal improvements for the convergence of the optimization problem.