We present an approach to aerodynamic optimization in which the shape control is adaptively parameterized. Starting from a coarse set of design variables, a sequence of higher-dimensional nested search spaces is automatically generated. Refinement can be either uniform or adaptive, in which case only the most important shape control is added. The relative importance of candidate design variables is determined by comparing objective and constraint gradients, computed at low cost via adjoint solutions. A search procedure for finding an effective ensemble of shape parameters is also given. We first demonstrate this system on a multipoint drag miminization problem in 2D with many constraints, showing that an adaptive parameterization approach consistently achieves smoother, more robust, and faster design improvement than fixed parameterizations. We also establish a 3D shapematching benchmark, where we demonstrate that our approach automatically discovers the necessary parameters to match a target shape. By largely automating shape parameterization, this work also aims to remove a time-consuming aspect of shape optimization.

Results are presented for four optimization benchmark problems posed by the AIAA Aerodynamic Design Optimization Discussion Group. The benchmarks are intended to exercise optimization frameworks on representative airfoil and wing design problems. All problems involve drag minimization subject to geometric and aerodynamic constraints. Our design approach involves two forms of adaptation. First, the shape parameterization is gradually and automatically enriched from an initially coarse search space. Second, adjoint solutions are used to drive adaptive mesh refinement to control discretization error. The error threshold is tailored so that the finest meshes, with the greatest accuracy, are used only when nearing the optimum. On the inviscid airfoil design problem, while reducing the drag by a factor of 10, we show how the combination of progressive parameterization and tiered discretization error control can dramatically accelerate the optimization. On the viscous airfoil design problem, we use inviscid analysis-driven optimization to reduce the total drag by a factor of two. Next, we improve the span efficiency factor of a wing by performing twist optimization. Finally, we optimize the Common Research Model wing, managing to hold drag roughly fixed, while targeting an initially-violated pitching moment constraint. Our approach aims to introduce greater complexity and accuracy only when necessary to improve the design, and also support a greater degree of automation.

We present a versatile geometry platform for shape optimization of aerospace vehicles. The platform deforms discrete surface meshes using the computational geometry kernel of an open-source modeling tool called Blender. Several parametric deformation techniques are available, including lattice and cage-based deformation, as well as more intuitive skeletal and direct-manipulation techniques. Deformations are invoked through a back-end scripting interface, which we also use to implement custom deformation algorithms as plugins. Surface sensitivities are provided to support gradient-based optimization. The platform can be used in sequence with other geometry tools to enable flexible manipulation that a single constructive modeler (e.g. CAD) cannot always achieve alone. We also present an intuitive constraint-based deformation technique in which a sparse set of surface points serve as design variables. We test our platform on several standard aerodynamic design problems, including inverse airfoil design, shape-matching, and lift-constrained drag minimization for an airfoil with thickness constraints. A wing-fuselage integration problem demonstrates the approach in 3D. In a final example, our platform is pipelined with a constructive modeler to parabolically sweep a wingtip while applying a 1-G loading shape along the wingspan. This work is part of our larger goal of improving the flexibility and usability of discrete aerospace geometry tools by capitalizing on the computer graphics industry's sustained investment in geometry processing techniques.

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Simulation results are presented for all test cases prescribed in the Second AIAA Sonic Boom Prediction Workshop. For each of the four nearfield test cases, we compute pressure signatures at specified distances and o↵-track angles, using an inviscid, embedded-boundary Cartesian-mesh flow solver with output-based mesh adaptation. The cases range in complexity from an axisymmetric body to a full low-boom aircraft configuration with a powered nacelle. For e ciency, boom carpets are decomposed into sets of independent meshes and computed in parallel. This also facilitates the use of more e↵ective meshing strategieseach o↵-track angle is computed on a mesh with good azimuthal alignment, higher aspect ratio cells, and more tailored adaptation. The nearfield signatures generally exhibit good convergence with mesh refinement. We introduce a local error estimation procedure to highlight regions of the signatures most sensitive to mesh refinement. Results are also presented for the two propagation test cases, which investigate the e↵ects of atmopsheric profiles on ground noise. Propagation is handled with an augmented Burgers' equation method (NASA's sBOOM), and ground noise metrics are computed with LCASB. NomenclatureA ref Reference area C D/L/M Drag/lift/pitching moment coe cients C p Local pressure coe cient e Integrated signature di↵erences E Local error estimate J Aerodynamic output functional Distance along signature L Reference length for propagation M Mach number p Static pressure p Order of convergence r Distance from flight path T Temperature w Weight in functional ↵ Angle of attack p M 2 1 1 ✓ O↵set angle to avoid sonic glitch µ Mach angle = sin 1 (1/M 1 ) ⇢ Density ⌧ Normalized x-distance from nose Mach cone O↵-track/Azimuthal angle Subscripts (•) 1 Freestream value (•) t Stagnation value (•) c Coarse (•) f Fine (•) m Medium Abbreviations asel/csel A-/C-weighted sound exposure level axie Axisymmetric body (Case I) axie-prop Axisymmetric body (Prop. Case I) c25f C25d with flow-through nacelle (Case III) c25p C25d with powered nacelle (Case IV) jwb jaxa wing-body (Case II) lcasb Loudness Code for Asymmetric Sonic Booms lm-1021 Lockheed Martin 1021 (Prop. Case II) pl Perceived level of noise sbpw Sonic Boom Prediction Workshop