Adjoint-Based Methods in Aerodynamic Design-Optimization
Eugene M. Cliff
Interdisciplinary Cetner for Applied Mathematics
Virginia Polytechnic Institute and State University
Matthias Heinkenschloss
Department of Computational and Applied Mathematics
Rice University
Ajit Shenoy
Interdisciplinary Cetner for Applied Mathematics
Virginia Polytechnic Institute and State University
In: J. Borggaard, J. Burns, E. Cliff and S. Schreck (eds.),
Computational Methods for Optimal Design.
Proceedings of the AFSOR Workshop on Optimal Design
and Control, Arlington, VA, 30. September - 3. October 1997.
Birkhäuser Verlag, Progress in Systems and Control Theory,
Basel, Boston, Berlin, 1998.
Abstract
In this paper we study the use of adjoints in the calculation of
design gradients for cost and constraint functionals in
optimization-based aerodynamic design. While there is an extensive
literature on numerical implementation of these ideas, the
underlying mathematical treatment is usually quite formal. Here we
focus on rigorous justification of the approach and on careful
characterization of the underlying function spaces. One practical
result is the demonstration that just as the flow variables may have
internal jumps, so do the associated adjoints. For a particular
flow-matching problem we are able to characterize the jump by a
transversality condition.