Abstract
Flow optimization and control problems have the typical structure of all such problems. Their description involves
state variables: ø=velocity, pressure, density, internal energy, temperature, etc.;
control variables or design parameters: g = velocity on the boundary, heat flux on the boundary, parameters that determine the shape of the boundary, etc.;
objective,or cost,functional: J(ø,g); and
constraints: F(ø,g)=0, i.e., the flow equations; \( \wedge (\emptyset ) = 0 \) side constraints.
This research was partially supported by the Air Force Office of Scientific Research under AFOSR/DARPA MURI Grant Number F49620–95–1–0407.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
J. Appel. Sensitivity Calculations for Conservation Laws with Application to Discontinuous Fluid Flows, Ph.D. Thesis, Virginia Tech, Blacksburg, 1997.
J. Appel, A. Godfrey, M. Gunzburger and E. Cliff. Optimization-based design in high-speed flows, CFD for Design and Optimization,FED-232, 6168, ASME, New York, 1995.
M. Applebaum and R. Walters. UCFD, An Unstructured Computational Fluid Dynamics Package, Virginia Tech, Blacksburg, 1995.
C. Bischof, A. Carle, P. Khademi, A. Mauer and P. Hovland. ADIFOR 2.0 User’s Guide, Center for Research on Parallel Computation, Technical Report CRPC-95516-S, August, 1995.
C. Bischof, P. Khademi, A. Mauer and A.Carle. Adifor 2.0: automatic differentiation of Fortran 77 programs, Computational Science and Engineering 3:18–32, 1996.
C. Bischof, W. Jones, A. Mauer, and J. Samareh. Application of automatic differentiation to 3-D volume grid generation software, CFD for Design and Opti mization,FED-232, 17–22, ASME, New York, 1995.
J. Borggaard. The Sensitivity Equation Method for Optimal Design, Ph.D. Thesis, Virginia Tech, Blacksburg, 1994.
J. Borggaard, J. Burns, E. Cliff and M. Gunzburger. Sensitivity calculations for a 2D, inviscid, supersonic forebody problem, Identification and Control of Systems Governed by Partial Differential Equations, Ed. by H. T. Banks, et al., SIAM. Philadelphia, PA, 1993.
J. Dennis and R. Schnabel. Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice Hall, Englewood Cliffs, 1983.
J. Dongarra and E. Grosse. Distribution of mathematical software via electronic mail, Comm. ACM, 30:403–407, 1987.
D. Gay. Algorithm 611 subroutines for unconstrained minimization using a model/ trust-region approach, ACM Trans. Math. Soft. 9:503–524, 1983.
R. LeVeque. Numerical Methods for Conservation Laws, Birkhäuser, Basel, 1991.
R. LeVeque and C. Zhang. The immersed interface method for acoustic wave equations with discontinuous coefficients, to appear in Wave Motion.
H. Liepmann and A. Roshko. Elements of Gas Dynamics, Wiley, New York, 1965.
G. Sod. A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws, J. Comp. Phys., 27:1–31, 1978.
G. Strang. On the construction and comparison of difference schemes, SIAM J. Numer. Anal., 5:506–517, 1968.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer Science+Business Media New York
About this chapter
Cite this chapter
Gunzburger, M. (1998). Sensitivities in Computational Methods for Optimal Flow Control. In: Borggaard, J., Burns, J., Cliff, E., Schreck, S. (eds) Computational Methods for Optimal Design and Control. Progress in Systems and Control Theory, vol 24. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1780-0_12
Download citation
DOI: https://doi.org/10.1007/978-1-4612-1780-0_12
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-7279-3
Online ISBN: 978-1-4612-1780-0
eBook Packages: Springer Book Archive