Aerodynamic Shape Optimization with Discretization Error Control

Abstract

Based on higher order adaptive Discontinuous Galerkin (DG) methods available in the DLR PADGE solver, the present thesis aims to demonstrate the capability of performing aerodynamic shape optimization with discretization error control. Such an optimization process is based on flow solutions which are computed on adaptively h-refined (mesh element subdivision) or hp-refined (combination of mesh element subdivision and various polynomial degrees and thus various discretization orders) meshes targeted at the accurate and efficient evaluation of a given quantity (e.g., drag, lift or moment coefficient) until the associated error estimation indicates that the corresponding discretization error is below a prescribed error tolerance. This allows to "optimize physics rather than numerical errors" by error estimation and to improve the efficiency ot the optimization by mesh adaption. Efficient adjoint-based gradient evaluation of the objective function with respect to the design variables is employed and extended to include a target lift constraint. The current work takes sufficient advantage ot the adjoint solution for not only the mesh refinement and gradient evaluation in optimization but also for error estimation in some of the test cases. The developed optimization chain with discretization error control is then applied to three aerodynamic shape optimization test cases including two inviscid flows and one transonic viscous flow. For a more complex viscous test case the optimization is performed on adaptively refined meshes not with error control but with a prescribed fixed number of refinement steps due to limitations of the current version of the PADGE solver. All results show that the quality (aerodynamic performance) of the optimized shapes improves as the accuracy of the underlying flow solutions increases. Furthermore, they show that using h- and hp-refinement with discretization error control leads to a same level of the cost function reduction with much fewer degrees of freedom and also less computational cost than refining the mesh globally with no consideration of the discretization error. In particular, the hp-refinement offers the best efficiency in optimization.