Topology optimization for incompressible viscous fluid flow using the lattice kinetic scheme

Abstract This paper presents a topology optimization method for flow channel design using the lattice kinetic scheme (LKS). LKS is a numerical scheme merging the lattice Boltzmann method with the kinetic scheme for solving the incompressible Navier-Stokes equations. In the lattice Boltzmann method, the discrete distribution functions for every grid in the analysis domain need to be stored to compute the flow field, while in the LKS, only the flow velocities and the densities are stored, and thus requiring less storage. Moreover, in the LKS, the macroscopic boundary conditions in terms of the velocity and the pressure can be imposed directly rather than considering the bounce-back boundary condition against the distribution function. In this study, the optimization is performed based on the gradient of the objective functional with respect to the design variables and the design sensitivity is computed by the adjoint variable method. Both the forward and the adjoint problems are solved using the LKS. The validity of the design sensitivity is verified by comparing it with the finite difference approximation of objective functional. Numerical examples of solving two-dimensional flow channel design problems are presented to demonstrate the proposed method.