Full-Space Approach to Aerodynamic Shape Optimization

TL;DR

This paper introduces a full-space Lagrange-Newton-Krylov-Schur approach for aerodynamic shape optimization that couples design and flow computations, reducing iterations and improving efficiency over traditional reduced-space methods.

Contribution

The paper presents a novel full-space optimization framework for ASO that leverages second-order information and couples PDE constraints directly, enhancing computational efficiency.

Findings

LNKS reduces the number of forward problem iterations.

The approach outperforms reduced-space methods on benchmark tests.

High-order discretization improves solution accuracy.

Abstract

Aerodynamic shape optimization (ASO) involves finding an optimal surface while constraining a set of nonlinear partial differential equations (PDE). The conventional approaches use quasi-Newton methods operating in the reduced-space, where the PDE constraints are eliminated at each design step by decoupling the flow solver from the optimizer. Conversely, the full-space Lagrange-Newton-Krylov-Schur (LNKS) approach couples the design and flow iteration by simultaneously minimizing the objective function and improving feasibility of the PDE constraints, which requires less iterations of the forward problem. Additionally, the use of second-order information leads to a number of design iterations independent of the number of control variables. We discuss the necessary ingredients to build an efficient LNKS ASO framework as well as the intricacies of their implementation. The LNKS approach is then compared to reduced-space approaches on a benchmark two-dimensional test case using a high-order discontinuous Galerkin method to discretize the PDE constraint.