Hostname: page-component-7dd5485656-glrdx Total loading time: 0 Render date: 2025-10-29T11:36:50.389Z Has data issue: false hasContentIssue false
  • English
  • Français

Optimal control of stationary, low Mach number, highly nonisothermal, viscous flows

Published online by Cambridge University Press:  15 August 2002

Max D. Gunzburger  and
O. Yu. Imanuvilov
Max D. Gunzburger
Affiliation:
Department of Mathematics, Iowa State University, Ames IA 50011-2064, U.S.A.; gunzburg@iastate.edu.
O. Yu. Imanuvilov
Affiliation:
Department of Mathematics, Iowa State University, Ames IA 50011-2064, U.S.A.; vika@iastate.edu.
Get access

Abstract

An optimal control problem for a model for stationary, low Machnumber, highly nonisothermal, viscous flows is considered.The control problem involves the minimization of a measure ofthe distance between the velocity field and a given targetvelocity field. The existence of solutions of a boundary valueproblem for the model equations is established as is theexistence of solutions of the optimal control problem. Then, aderivation of an optimality system, i.e., a boundary valueproblem from which the optimal control and state may bedetermined, is given.

Keywords

Optimal controlcompressible flowsviscous flowslow Machnumber flows.

Information

Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 5 , 2000 , pp. 477 - 500
Copyright
© EDP Sciences, SMAI, 2000

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

F. Durst, A. Galjukov, Y. Makarov, M. Shafer, P. Voinovich and A. Zhmakin, Efficient 3D unstructured grid algorithms for modelling of chemical vapour deposition in horizontal reactors, in Simulation of Semiconductor Devices and Processes, Vol. 6, edited by H. Ryssel and P. Pichler (1995) 258-261.
Efimov, N. and Stechkin, S., Approximative compactness and Tchebycheff sets. Soviet Math. 2 (1961) 1226-1228.
Einset, E. and Jensen, K., Finite element solution of three-dimensional mixed convection gas flows in horizontal channels using preconditioned iterative methods. Int. J. Numer. Meth. Engrg. 14 (1992) 817-841. CrossRef
Forester, C. and Emery, A., A computational method for low Mach number unsteady compressible free convective flows. J. Comput. Phys. 10 (1972) 487-502. CrossRef
J.-L. Lions and E. Magenes, Non-homogeneous Boundary Value Problems and Applications 1. Springer, New York (1972).
Makarov, Y. and Zhmakin, A., On the flow regimes in VPE reactors. J. Cryst. Growth 94 (1989) 537-550. CrossRef
J. Serrin, Mathematical priciples of classical fluid mechanics, in Handbuch der Physik VIII/1, edited by S. Flügge and C. Truesdell. Springer (1959) 1-125.
R. Temam, Navier-Stokes Equations. North-Holland, Amsterdam (1979).
Vlasov, L., Approximate properties of sets in normed linear spaces. Russian Math. Surveys 28 (1973) 1-66. CrossRef