Topology optimization method for interior flow based on transient information of the lattice Boltzmann method with a level-set function

We propose a topology optimization method for a flow field using transient information. The optimization algorithm of many conventional methods use the fully converged information of a flow field. In contrast, our approach uses the transient information of an unsteady flow field and update the design domain while solving the unsteady flow field, thereby greatly reducing the computational cost. The fluid and solid regions are clearly distinguished by a level-set function. Consequently, the boundary is concretely represented, and precise boundary conditions are applied on the wall boundary. The lattice Boltzmann method is employed as a fluid computation method. To implement the non-slip boundary conditions at the fluid-solid boundary, we apply bounce-back conditions. We update the domain according to a sensitivity analysis. A sensitivity is formulated based on the lattice Boltzmann equations without adjoint equations for self-adjoint flow. We approximately use the sensitivity for non-self-adjoint equations, i.e. lattice Boltzmann equations, and discuss the optimality and limitations. The approximated sensitivity also considers the bounce-back boundary conditions at the wall separating the fluid and solid regions.