zbMATH — the first resource for mathematics

Sensitivities, adjoints and flow optimization. (English) Zbl 0962.76030
Summary: We consider several issues related to the calculation of flow sensitivities and to the solution of flow optimization problems. For the latter, one-shot Lagrange multiplier methods are presented, as well as sensitivity- and adjoint-based iterative algorithms. A sample application of each method to a specific flow optimization problem is provided. Then we discuss difficulties associated with the practical implementation of methods. Particular emphasis is placed on the effect of flow discontinuities on approximate sensitivities and adjoints. A discussion of these issues is given in the context of the Riemann problem for which exact solution is known.

76D55 Flow control and optimization for incompressible viscous fluids
Full Text: DOI
[1] Joslin, AIAA J. 35 pp 816– (1997)
[2] Streett, Appl. Numer. Math. 6 pp 123– (1989)
[3] Hou, SIAM J. Cont. Optim., , -1885 35 pp 1997– (1847)
[4] Gunzburger, SIAM J. Numer. Anal.
[5] ’Sensitivity calculations for conservation laws with application to discontinuous fluid flows’, Ph.D. Thesis, Virginia Technical, Blacksburg, 1997.
[6] , and , Optimization-based design in high-speed flows, CFD for Design and Optimization, Vol. FED-232, ASME, New York, 1995, pp. 61-68.
[7] ’The sensitivity equation method for optimal design’, Ph.D. Thesis, Virginia Technical, Blacksburg, 1994.
[8] , and , ’Sensitivity calculations of a 2D, inviscid, supersonic forebody problem’, in and (eds.), Identification and Control of Systems Governed by Partial Differential Equations, SIAM, Philadelphia, 1993.
[9] Gay, ACM Trans. Math. Soft. 9 pp 503– (1983)
[10] and , ’UCFD, an unstructured computational fluid dynamics package’, Technical Report, Dept. of Aerospace Engng., Virginia Tech., Blacksburg, 1995.
[11] and , Sensitivity discrepancy for geometric parameters, CFD for Design and Optmization, Vol. FED-232, ASME, New York, 1995, pp. 9-15.
[12] and , ’Discretization of cost and sensitivities in shape optimization’, Computation and Control IV, Birkhaüser, Boston, 1995, pp. 43-56.
[13] , , and , ’ADIFOR 2.0 users guide’, Technical Report CRPC-95516-S, Center for Research on Parallel Computation, 1995.
[14] Bischof, Comp. Sci. Eng. 3 pp 18– (1996)
[15] , and , Application of automatic differentiation to 3D volume grid generation software, CFD for Design and Optimization, Vol. FED-232, ASME, New York, 1995, pp. 17-22.
[16] Numerical Methods for Conservation Laws, Birkhaüser, Basel, 1991.
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.