Topology optimization for rarefied gas flow problems using density method and adjoint IP-DSMC

Abstract

In this paper, a topology optimization method based on direct simulation Monte Carlo (DSMC) is presented for rarefied gas flows. Distribution of fluid and solid in the design domain is characterized by a pseudo density. The traditional DSMC algorithm is extended to include the pseudo density by interpreting solid as an imaginary gas with fixed temperature and zero macroscopic velocity. Treating the pseudo density as the design variable, design sensitivity is obtained through the Lagrangian multiplier method and the adjoint state method. A discrete version of the adjoint equations is used, so that the adjoint variables can be evaluated using the information stored during the forward DSMC process. The information preservation (IP) method for subsonic flow is also considered in order to reduce random noise and simplify the discrete adjoint equations. The extended DSMC algorithm is verified by numerical examples, and optimized design for bent pipe is also included.