Topology optimization using the lattice Boltzmann method for unsteady natural convection problems

Abstract

This paper proposes a density-based topology optimization method for natural convection problems using the lattice Boltzmann method (LBM). As the LBM can be developed as a completely explicit scheme, its attractive features over the traditional ones, such as the finite element method, are (1) suitability for solving unsteady flow problems and (2) scalability for large-scale parallel computing. We develop an LBM code for solving unsteady natural convection problems and provide its sensitivity analysis based on the so-called adjoint lattice Boltzmann method. Notably, the adjoint equation is derived from the discrete particle velocity Boltzmann equation and can be solved similarly to the original LBM concerning unsteady natural convection problems.