Output-Based Adaptive Methods for Steady & Unsteady Aerodynamics
By Prof. Krzysztof Fidkowski, Assistant Professor of Aerospace Engineering at the University of Michigan
Friday, January 10, 2013: 4:00 to 5:00 PM EST
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.
Krzysztof Fidkowski is an assistant professor in the Aerospace Engineering Department at the University of Michigan. His research interests include development of robust solution techniques for computational fluid dynamics, error estimation, computational geometry management, parallel computation, large-scale model reduction, and design under uncertainty. His teaching interests are in undergraduate aerodynamics and numerical methods, and in graduate computational fluid dynamics.
Ph.D. (Aerospace Engineering) 2007, Massachusetts Institute of Technology
S.M. (Aerospace Engineering) 2004, Massachusetts Institute of Technology
S.B. (Aerospace Engineering) 2003, Massachusetts Institute of Technology
S.B. (Physics) 2003, Massachusetts Institute of Technology