A Discrete Adjoint Gas-Kinetic Scheme for Aerodynamic Shape Optimization in Turbulent Continuum Flows

TL;DR

This paper introduces an efficient discrete adjoint gas-kinetic scheme for aerodynamic shape optimization in turbulent flows, verified against linearized solvers and demonstrated on complex benchmark cases.

Contribution

The study develops a robust, accurate adjoint GKS using algorithmic differentiation, validated through benchmark cases and turbulent flow optimizations.

Findings

Excellent agreement between adjoint and linearized solvers in sensitivity predictions.

Targeted design objectives achieved within few optimization cycles.

Demonstrated effectiveness in complex turbulent aerodynamic shape optimization.

Abstract

This study presents an efficient and accurate discrete adjoint gas-kinetic scheme (GKS) for sensitivity analysis and aerodynamic shape optimization in continuum flow regimes. Developed using the backward mode of algorithmic differentiation (AD), the adjoint solver is rigorously verified against a duality-preserving linearized GKS solver generated via forward-mode AD. The robustness and practical effectiveness of the solver are evaluated through three benchmark cases: the inverse design of turbine blades, lift-to-drag ratio enhancement, and shock-strength reduction for a NACA 0012 airfoil. To capture realistic flow physics, fully turbulent optimizations are conducted using the one-equation Spalart--Allmaras (SA) model. Numerical results demonstrate excellent agreement between the discrete adjoint and linearized solvers, exhibiting matching sensitivity convergence behaviors, identical asymptotic residual decay rates, and negligible discrepancies in final sensitivity predictions. Furthermore, the optimization studies confirm that targeted design objectives are consistently achieved within a limited number of design cycles, highlighting the solver's computational efficiency, accuracy, and suitability for complex aerodynamic geometries.