Adjoint shape optimization from the continuum to free-molecular gas flows

TL;DR

This paper introduces an adjoint-based shape optimization method for solid bodies in multiscale gas flows, efficiently handling both rarefied and continuum regimes with high accuracy and rapid convergence.

Contribution

It develops a multiscale adjoint sensitivity analysis framework integrated with a quasi-Newton optimizer for rapid shape optimization across flow regimes.

Findings

Achieves optimal airfoil shapes in 12 iterations

Optimization completes within 5 to 20 minutes using parallel computing

Effectively eliminates sensitivity oscillations through boundary parameterization

Abstract

An adjoint-based shape optimization method for solid bodies subjected to both rarefied and continuum gas flows is proposed. The gas-kinetic BGK equation with the diffuse-reflection boundary condition is used to describe the multiscale gas flows. In the vicinity of the gas-solid interface, a body-fitted mesh is utilized, and the sensitivity with respect to the boundary geometry is analyzed through a combined continuous and discrete adjoint methods. The primal and adjoint governing equations are resolved using efficient multiscale numerical schemes, ensuring the precision of the sensitivity analysis in all flow regimes. The sensitivity data is subsequently integrated into a quasi-Newton optimization algorithm to facilitate rapid convergence towards the optimal solution. Numerical experiments reveal that the discretization of the molecular velocity space can induce sensitivity oscillations; however, these can be effectively eliminated by employing appropriate parameterization of the boundary geometry. In optimizing 2D airfoils for drag reduction under varying degrees of gas rarefaction, our method achieves the optimal solution in just a dozen optimization iterations and within a time frame of 5 to 20 minutes (utilizing parallel computation with 40 to 160 cores), thereby underscoring its exceptional performance and efficiency.