![]() We have also created multipoint cases (Kenway & Martins, 2016) for the ADODG, and a full configuration case (Chen et al., 2016) where we look at the effect that trim has on the wing design. The initial and optimized geometries and meshes are provided on this page. (Lyu et al., 2015) solve the RANS-based wing optimization problem, try to find multiple local minima, and solve a number of related wing design optimization problems, including a multipoint optimization. The AIAA Aerodynamic Design Optimization Discussion Group developed a series of benchmark cases. (Martins & Hwang, 2013) present a broader overview of methods for computing derivatives, putting the adjoint method into context. (Martins et al., 2016) briefly describe other versions of the adjoint implementation that are more efficiently and are currently used in our aerodynamic shape optimization studies. This paper described an initial adjoint method that worked well but was not very efficient. The overall approach is to selectively use automatic differentiation on parts of the CFD code to compute the partial derivative terms in the discrete adjoint equations. ![]() The adjoint method and our implementation is explained by (Mader et al., 2008). Gradient-based optimization requires the derivatives of the objective function (e.g., drag) and constraint functions (e.g., lift, moment) with respect to all the design variables (e.g., angle of attack, shape variables). Note that the adjoint method itself is not an optimization strategy, it is just a way to compute the gradients and it is independent of the specific gradient-based optimization algorithm that is used. The key enabler in aerodynamic shape optimization is the combination of gradient-based optimization, which is necessary to handle the hundreds of shape variables involved, with an adjoint method that computes the required gradients efficiently. The adjoint approach for computing derivatives The process is fully automatic and the final result is the re-invention of a modern supercritical airfoil. In the video below, we start from a circle and minimize the drag with respect to the shape while enforcing constraints on the area and chord (He et al., 2019). Example: From a circle to a supercritical airfoil This is not intended to be a comprehensive literature review for such reviews, you can see the introductions of our papers and the works they cite. ![]() In this page we summarize the work our lab has done in aerodynamic shape optimization. The process is iterative: It starts with a given shape and then changes that shape to improve the performance while satisfying the specified constraints. The aerodynamic performance is usually evaluated using computer fluid dynamics (CFD) and the optimization can be done using a number of algorithms. Aerodynamic shape optimization, or aerodynamic design optimization consists in maximizing the performance of a given body (such as an airfoil or wing) by changing its shape. ![]()
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