A flow topology optimization method for steady state flow using transient information of flow field solved by lattice Boltzmann method

A topology optimization method for fluid flow using transient information is proposed. In many conventional methods, the design domain is updated using steady state information which is obtained after solving the flow field equations completely. Hence we must solve the flow field at each iterative which leads to high computational cost. In contrast, the proposed method updates the design domain using transient information of flow field. Hence the flow field is solved only once. The flow field is solved by lattice Boltzmann method (LBM). It is found that, by using LBM, the flow field is stably computed even though the design domain drastically changes during the computation. The design domain is updated according to sensitivity analysis. In many conventional methods, the sensitivity of objective functionals under lattice Boltzmann equations is obtained using additional adjoint equations. However, in the proposed method, the sensitivity is explicitly formulated and computed without using adjoint variables. In this paper, we show some numerical examples for low Reynolds number flows. The results demonstrate good convergence property in small computation time.