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Output-based hp Adaptive Methods for Steady and Unsteady Aerodynamics

Thursday, September 27, 3:30PM – 5PM
ACE 6.304

Krzysztof Fidkowski

This talk presents recent advances in output-based solution strategies for steady and unsteady aerodynamics simulations. The target discretization is the discontinuous Galerkin finite element method for the compressible Euler and Navier-Stokes equations. Adaptation is output-based; that is, driven by the solution of a discrete adjoint problem specific to a chosen scalar output. The adjoint-weighted residual yields an error estimate that corrects the output for effects of numerical error and at the same time provides an adaptive indicator for reducing the error through targeted refinement. For steady-state problems, we consider both mesh subdivision and approximation order increase as refinement options, and we tailor the adaptation to choose the most efficient of these options. For unsteady problems, we employ dynamic order refinement on a fixed unstructured tessellation of the spatial domain, combined with time-step optimization. We furthermore study the effects of the geometric conservation law on error estimates in unsteady simulations involving mesh motion. Results for the compressible Navier-Stokes simulations in two and three dimensions demonstrate the accuracy of the error estimates and the efficiency of the proposed output-based adaptation approach. We show that for these problems output error estimation and adaptation can have a significant impact on robustness and efficiency of the solution algorithm.

Bio: Krzysztof Fidkowski is an Assistant Professor in the Aerospace Engineering department at the University of Michigan. Prior to this appointment, he was a post-doctoral associate in the Department of Aeronautics and Astronautics at the Massachusetts Institute of Technology, where he received his doctorate, master's, and bachelor's degrees. His research interests lie in algorithm development for computational fluid dynamics, with a focus on error estimation and adaptive meshing for high-order discretizations. He teaches graduate computational fluid dynamics and undergraduate aerodynamics.

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