Monolithic p-Adaptive High-Order Aerodynamic Shape Optimization

Abstract

Aerodynamic shape optimization requires a robust, accurate, and efficient flow solver. However, during aerodynamic shape optimization, large geometry and flow solution changes may decrease solution accuracy and efficiency on fixed meshes. The optimizer may converge to a spurious optimum if the solution loses accuracy. We use the discontinuous Galerkin (DG) method to tackle this problem because it yields high-order-accurate solutions that often have less error per degree of freedom compared to second-order finite-volume methods. Because DG degrees of freedom often incur a higher computational cost, we take advantage of local adaptation to maximize accuracy at a given cost. However, during optimization, it is not clear when to adapt to avoid overoptimizing initial designs and to avoid errors polluting the optimal solution. We develop an adaptation strategy that reaches a target error at the end of a single optimization loop. Finally, we present results for two airfoil optimization test cases. Our results show that this adaptation procedure outperforms optimization using fixed-fidelity DG and second-order finite volume on a per-degree-of-freedom basis.