Concurrent hpk-Mesh Adaptation and Shape Optimization of Complex Geometries through an Adjoint-Based Discontinuous Petrov-Galerkin Isogeometric Analysis

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The past decade has seen the application of adjoint-based optimization frameworks for the multidisciplinary design of aerodynamic surfaces as well as mesh adaptation to increase the accuracy of integrated functions such as lift and drag coefficients. Both adjoint-based design optimization and mesh adaptation have been advanced independently but not investigated concurrently. Aerodynamic shape optimization algorithms must facilitate the design of the next generation of commercial aircraft to meet future global standards on the environmental impact of aviation. The European Union's Clean Sky and NASA's Environmentally Responsible Aviation (ERA) Project have placed benchmarks on the type of performance improvements that are expected on future aircraft designs. The community, therefore, is at a critical juncture to innovate and develop radically new aircraft designs. Computational tools that allow airframe manufacturers to both design aircraft with superior high-lift aerodynamic performance and accurately resolve far-field acoustic signatures within a single numerical framework are invaluable. Such capabilities are unlike the current practice of employing multiple numerical tools that only prolong the design cycle and arrive at sub-optimal designs. Thus, the long-term vision of the research program is to establish a common framework using a high-order discontinuous Petrov-Galerkin scheme for the concurrent mesh adaptation and shape optimization to increase the performance of aerodynamic surfaces. The research program has the potential to make a transformative impact on the design of the next generation of commercial aircraft. The research training will provide graduate students an enriching environment to contribute and define an emerging field. Scholars will graduate with skills in formulating research questions, communicating their ideas, receiving critiques, and being trained on the next-generation of high-performance computing. The long-term impact of this research program will produce highly skilled personnel and enable Canada to remain a leader in current aircraft technology.