Abstract
This paper presents a topology optimization method based on the level set method for design problem of flow channel using the lattice Boltzmann method (LBM). In the presented method, the optimization problems and their adjoint equations are formulated based on the original Boltzmann equation, and the design sensitivities are precisely obtained without the time-consuming numerical operations dealing with a large-scale asymmetric matrix, while the previous researches using the LBM use the lattice Boltzmann equation (LBE) for the formulations of optimization problems and the derivation of their adjoint equation. In addition, the Lattice kinetic scheme that has attract attention as a new type of the LBM, enables the reduction of memory usage in computing flow field is employed to reduce the computational cost in the computation of the state field. Based on the above formulations, we construct a level set-based topology optimization method incorporating fictitious interface energy for the design of fluid channel that minimizes pressure drop. Furthermore, two-and three-dimensional numerical examples are provided to confirm the validity and utility of the presented method.
