Topology optimization in thermal-fluid flow using the lattice Boltzmann method

This paper proposes a topology optimization method for thermal-fluid flow problems using the lattice Boltzmann method (LBM). The design sensitivities are derived based on the adjoint lattice Boltzmann method (ALBM), whose basic idea is that the adjoint problem is first formulated using a continuous adjoint approach, and the adjoint problem is then solved using the LBM. In this paper, the discrete velocity Boltzmann equation, in which only the particle velocities are discretized, is introduced to the ALBM to deal with the various boundary conditions in the LBM. The novel sensitivity analysis is applied in two flow channel topology optimization problems: 1) a pressure drop minimization problem, and 2) a heat exchange maximization problem. Several numerical examples are provided to confirm the utility of the proposed method.