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Mathematical aspect of the stream-function equations of compressible turbomachinery flows and their finite element approximations using optimal control. (English) Zbl 0509.76071


MSC:

76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
76M99 Basic methods in fluid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
49K15 Optimality conditions for problems involving ordinary differential equations
65N15 Error bounds for boundary value problems involving PDEs
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References:

[1] Wu, C.-H., Three dimensional turbomachine flow equations expressed with respect to non-orthogonal curvilinear coordinates and methods of solution, (Paper presented at the 3rd International Symposium on Air Breathing Engines. Paper presented at the 3rd International Symposium on Air Breathing Engines, Munich (March 1976))
[2] Trans. ASME, 5 (1952)
[3] Li, K.-T., The mixed boundary value problem for the differential equations in semi-geodesic coordinates of the stream function on \(S_1\) and \(S_2\) flow surfaces of three dimensional flow in turbomachines and its finite element solution, J. Xi’an Jiaotong Univ., 12, 1, 31-60 (1978), NACA TN 2604, 1052.
[4] Li, K.-T.; Huang, A.-X., Solvability of the partial differential equation satisfied by the stream function in compressible flow and the error bound in the finite element solution, J. Xi’an Jiaotong Univ., 14, 4, 98-110 (1980)
[5] Hirsch, Ch.; Warzee, G., A finite element method for the axisymmetric flow computation in a turbomachine, Internal. J. Numer. Engrg., 10, 1, 193-213 (1976) · Zbl 0324.76046
[6] Hirsch, Ch.; Warzee, G., A finite element method for through flow calculations in turbomachines, ASME Paper 76-fe-12 (1976) · Zbl 0324.76046
[7] Alder, D.; Krimerman, Y., The numerical calculation of the meridional flow field in turbomachines using the finite element method, Israel J. Tech., 12, 3/4 (1974) · Zbl 0294.76005
[8] Alder, D.; Krimerman, Y., Calculation of the blade to blade compressible flow field in turbomachines using the finite element method, J. Mech. Engrg. Sci., 19, 3, 108-112 (1977)
[9] Bristeau, M. O.; Pironneau, O.; Glowinski, R.; Periaux, J.; Perrier, P., On the numerical solution of nonlinear problems in fluid dynamics by least square and finite element methods—Part I. Least square formulations and conjugate gradient solutions of the continuous problems, Comput. Meths. Appl. Mech. Engrg., 17/18, 619-657 (1979) · Zbl 0423.76047
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