×

zbMATH — the first resource for mathematics

Minimum drag shape in two-dimensional viscous flow. (English) Zbl 0840.76079
Summary: The problem of finding the shape of a body with smallest drag in a flow governed by the two-dimensional steady Navier-Stokes equations is considered. The flow is expressed in terms of a streamfunction which satisfies a fourth-order partial differential equation with the biharmonic operator as principal part. Using the adjoint variable approach, both the first- and second-order necessary conditions for the shape with smallest drag are obtained. An algorithm for the calculation of the optimal shape is proposed in which the first variations of solutions of the direct and adjoint problems are incorporated. Numerical examples show that the algorithm can produce the optimal shape successfully.

MSC:
76M30 Variational methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
76M20 Finite difference methods applied to problems in fluid mechanics
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Kwak, J. Struct. Mech. Earthq. Eng. 483/I-26 pp 159– (1994)
[2] Pironneau, J. Fluid Mech. 59 pp 117– (1973)
[3] Pironneau, J. Fluid Mech. 64 pp 97– (1974)
[4] Mironov, J. Appl. Math. Mech. (PMM) 39 pp 103– (1974)
[5] Glowinski, J. Fluid Mech. 72 pp 385– (1975)
[6] Cabuk, J. Fluid Mech. 237 pp 373– (1992)
[7] Perturbation Methods in Fluid Mechanics, Parabolic, Stanford, CA, 1975.
[8] Fujii, SIAM J. Control Optim. 24 pp 346– (1986)
[9] Fujii, J. Optim. Theory Appl. 65 pp 223– (1990)
[10] Fujii, J. Optim. Theory Appl. 65 pp 431– (1990)
[11] Moretti, AIAA J. 30 pp 933– (1992)
[12] and , Methods of Mathematical Physics, Vol. 2, Interscience, New York, 1962, pp. 240-261.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.