Topology optimization for unsteady flow problems using lattice Boltzmann method incorporating level set method

Abstract

This paper presents a topology optimization method for unsteady incompressible flow problems using the lattice Boltzmann method (LBM) and level set boundary expressions. In this research, the optimization problem was formulated, the adjoint function and design sensitivety were derived based on the lattice Boltzmann equation. The level set function, a scalar function, was employed to express the material distribution in the design domain. The optimal structure of flow field was obtained with the updating of level set function during the optimization process. Numerical examples to maximize the dissipation kinetic energy were implemented to confirm the validity of the presented method.