Adjoint lattice kinetic scheme for topology optimization in fluid problems

TL;DR

This paper introduces the Adjoint Lattice Kinetic Scheme (ALKS), a memory-efficient topology optimization method for fluid problems based on Lattice Kinetic Scheme, with successful numerical validation on thermal and non-thermal flows.

Contribution

It develops an adjoint-based topology optimization method using LKS, including an approximate boundary condition treatment, reducing memory use significantly compared to LBM.

Findings

Reduces memory usage by up to 75% in unsteady thermal fluid problems.

Produces physically meaningful and consistent results with previous research.

Demonstrates effectiveness for both steady and unsteady thermal and non-thermal fluid problems.

Abstract

This paper proposes a topology optimization method for non-thermal and thermal fluid problems using the Lattice Kinetic Scheme (LKS).LKS, which is derived from the Lattice Boltzmann Method (LBM), requires only macroscopic values, such as fluid velocity and pressure, whereas LBM requires velocity distribution functions, thereby reducing memory requirements. The proposed method computes design sensitivities based on the adjoint variable method, and the adjoint equation is solved in the same manner as LKS; thus, we refer to it as the Adjoint Lattice Kinetic Scheme (ALKS). A key contribution of this method is the proposed approximate treatment of boundary conditions for the adjoint equation, which is challenging to apply directly due to the characteristics of LKS boundary conditions. We demonstrate numerical examples for steady and unsteady problems involving non-thermal and thermal fluids, and the results are physically meaningful and consistent with previous research, exhibiting similar trends in parameter dependencies, such as the Reynolds number. Furthermore, the proposed method reduces memory usage by up to 75% compared to the conventional LBM in an unsteady thermal fluid problem.