Fast local convergence for flow topology optimization using the lattice Boltzmann method with a modified Newton method

Abstract

We propose a Newton-gradient-hybrid optimization method for fluid topology optimization. The method accelerates convergence and reduces computation time. In addition, the fluid-solid boundaries are clearly distinguished. In the method, the optimization process and flow computation are executed concurrently. The flow computation utilizes the lattice Boltzmann method (LBM), and the optimization algorithm partly utilizes a Hessian matrix. Due to the formulation of LBM and the optimization algorithm, the Hessian matrix is a diagonal matrix. Since the optimization problem is nonconvex problem, the Hessian matrix is not generally positive semidefinite. Hence, we employ a gradient method for a component whose corresponding Hessian matrix elements are negative. We compare the optimization results with those of conventional gradient method and show that the convergence is accelerated and the fluid-solid boundaries are clearly distinguished.