A Panel-Free Aeroelastic Solver with Adjoint Sensitivities

ifasd2024 Tracking Number 138

The conventional approach to aeroelastic analysis with a panel method involves constructing a panel mesh of external surfaces and their wakes to estimate lifting pressures, constructing a finite-element mesh of the substructure to estimate deformations, and implementing a consistent and conservative interpolation scheme to simultaneously resolve the coupled state equations. Both the structural and the aero meshes are typically constructed from an explicit geometry that does not readily accommodate topological changes. When used in an optimization, the conventional approach requires an expensive re-meshing step for both analyses upon changes in the design, and expensive re-evaluation of topological operations like intersections, unions and subtractions. In recent years, feature-mapping methods have been applied to solve structural displacements by mapping the geometric components in the design to an implicit field-representation (circumventing the need to re-mesh upon design changes). The implicit representation naturally and robustly transforms topological operations into inexpensive arithmetic operations. In contrast to conventional free-form topology optimization methods, the feature-based approach parameterizes the design in terms of high-level geometric features, resulting in optimized designs that are directly compatible with existing parametric CAD systems. We present a novel panel-free approach to solve potential-based lifting pressures that is inspired by the feature-mapping approach used in structural topology optimization. The lifting surfaces and their wakes are mapped to a fixed analysis domain wherein an efficient multi-grid solver resolves the lifting pressures. In addition, we present a natural method to consistently and conservatively transfer loads and displacements between disciplines. Since all of the mappings are differentiable, we present an algorithm to adjointly compute the design-sensitivity of quantities depending on the coupled aeroelastic state, facilitating efficient gradient-based optimization. The computational efficiency gained by circumventing the need to re-build and re-mesh the explicit geometry for each analysis, the topological design flexibility gained by mapping to an implicit representation, and the efficient adjoint computation of design-sensitivities make the proposed aeroelastic solver an attractive alternative to the conventional approach.