Aerodynamic Design Optimization on Unstructured Meshes Using the Navier-Stokes Equations

TLDR

The study uses 3‑D Reynolds‑averaged Navier–Stokes equations with a one‑equation turbulence model. The paper develops and demonstrates a discrete adjoint method for aerodynamic design optimization on unstructured grids. The authors implement the flow and adjoint equations on unstructured meshes, differentiate compressible and incompressible solvers, verify sensitivity derivatives against finite‑difference gradients, and examine simplifying approximations to the residual linearization. The method accurately predicts sensitivity derivatives and yields successful optimization results for both compressible and incompressible flows.

Abstract

A discrete adjoint method is developed and demonstrated for aerodynamic design optimization on unstructured grids. The governing equations are the three-dimensional Reynolds-averaged Navier-Stokes equations coupled with a one-equation turbulence model. A discussion of the numerical implementation of the flow and adjoint equations is presented. Both compressible and incompressible solvers are differentiated and the accuracy of the sensitivity derivatives is verified by comparing with gradients obtained using finite differences. Several simplyfying approximations to the complete linearization of the residual are also presented, and the resulting accuracy of the derivatives is examined. Demonstration optimizations for both compressible and incompressible flows are given.