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MTech(Res): Adjoint-Based Aerodynamic Shape and Mesh Optimization with High-order Discontinuous Galerkin Methods
November 29 @ 3:00 PM - 5:00 PM
The aerodynamic shape of an aircraft plays a critical role in its performance. Aerodynamic Shape Optimization (ASO) modifies the shape to achieve desired performance metrics, such as reduced drag or increased lift. ASO integrates numerical optimization techniques with Computational Fluid Dynamics (CFD). Gradient-based optimization techniques are widely employed for ASO. The adjoint solution enables the accurate and efficient computation of the gradients of the performance metrics with respect to the shape parameters. Performance metrics are derived from CFD solutions, which inherently contain inaccuracies. These inaccuracies can affect the reliability of the optimization process. High-order methods, like Discontinuous Galerkin (DG), offer improved accuracy for a computational cost comparable to Finite Volume methods in compressible flows, making them well-suited for ASO. Adaptive mesh refinement can further improve the accuracy of simulations. The adjoint solution used for computing gradients also finds application in mesh adaptation. Combining adjoint-based mesh adaptation with gradient-based ASO provides better control over the inaccuracies during optimization.
Towards this, the present work performs ASO using high-order DG methods and devises strategies for incorporating adaptive mesh refinement. The shape is defined using smooth splines, and the Free Form Deformation (FFD) method controls shape changes. With changes in the geometry, the mesh needs to move to be consistent with the modified shape. A mesh deformation strategy ensures that the mesh evolves smoothly with geometry. A gradient-based method employing the Sequential Quadratic Programming (SQP) algorithm is used for optimization. The adjoint solution computes the gradients and passes them to the optimization algorithm. Optimization for a set of drag minimization problems, including benchmark Aerodynamic Design Optimization Discussion Group (ADODG) test case 1 and inverse design problems, is performed on non-adapted meshes.
Furthermore, a strategy is formulated to incorporate adjoint-based mesh adaptation within the optimization process. Based on the value of adjoint-based error estimates, the strategy decides on instances of the optimization process that require control of the errors and, thus, mesh adaptation. Such a strategy leads to automated control of errors in the performance metrics, thus improving the reliability and efficiency of the optimization process.
Speaker: Pandya Kush Tusharbhai
Research Supervisor: Aravind Balan