×

zbMATH — the first resource for mathematics

On the finite element approximation of a cascade flow problem. (English) Zbl 0646.76085
Summary: The finite element analysis of a cascade flow problem with a given velocity circulation round profiles is presented. The nonlinear problem for the stream function with nonstandard boundary conditions is discretized by conforming linear triangular elements. We deal with the properties of the discrete problem and study the convergence of the method both for polygonal and nonpolygonal domains, including the effect of numerical integration.

MSC:
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
76G25 General aerodynamics and subsonic flows
76M99 Basic methods in fluid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
PDF BibTeX XML Cite
Full Text: DOI EuDML
References:
[1] Babu?ka, I.: Approximation by hill functions. Comment. Math. Univ. Carolinae11, 787-811 (1970) · Zbl 0215.46404
[2] Babu?ka, I.: Approximation by hill functions II. Comment. Math. Univ. Carolinae13, 1-22 (1972) · Zbl 0244.41005
[3] Benda, J.: Application of the finite element method to the calculation of an ideal fluid flow in a plane cascade of blades. Ph. D. Thesis, Faculty of Mechanical Engineering, Technical University, Prague 1984 (in Czech)
[4] Ciarlet, Ph.G.: The Finite Element Method for Elliptic Problems. Studies in Math. and its Appl. Vol.4. Amsterdam, New York, Oxford: North-Holland 1979
[5] Ciavaldini, J.F., Pogu, M., Tournemine, G.: Existence and regularity of stream functions for subsonic flows past profiles with a sharp trailing edge. Arch. Ration. Mech. Anal. 93, 1-14 (1986) · Zbl 0621.76067
[6] Deconinck, H., Hirsch, Ch.: Finite element method for transonic blade-to-blade calculation in turbomachines. Transactions of ASME, J. Engerg. Power, October 1981,103, 665-677
[7] Deconinck, H., Hirsch, Ch.: A finite element method solving the full potential equation with boundary layer interaction in transonic cascade flow. AIAA Paper 79-0132 (1979)
[8] Feistauer, M.: On non-viscous flows in cascades of blades. ZAMM64, 186-188 (1984)
[9] Feistauer, M.: Solution of some nonlinear problems in mechanics of non-viscous fluids. In: Proc. of 5th Summer School ?Software and Algorithms of Numerical Mathematics 83?, Faculty of Mathematics and Physics in Prague-Technical University in Plze?, 1984 (in Czech)
[10] Feistauer, M.: On irrotational flows through cascades of profiles in a layer of variable thickness. Appl. Mat.29, 423-458 (1984) · Zbl 0598.76061
[11] Feistauer, M.: Finite element solution of non-viscous flows in cascades of blades. ZAMM65, 191-194 (1985) · Zbl 0605.76068
[12] Feistauer, M.: Mathematical and numerical study of flows through cascades of profiles. In: Proc. of ?International Conference on Numerical Methods and Applications? held in Sofia, August 27, September 2, 271-278 (1984)
[13] Feistauer, M., Felcman, J.: Numerical solution of an incompressible flow past a cascade of profiles in a layer of variable thickness. In: Proc. of the conf. HYDROTURBO 85 held in Olomouc, September 11-13, Vol. I, 1-10 (1985)
[14] Feistauer, M., Felcman, J., Vl??ek, Z.: Finite element solution of flows in elements of blade machines. In: Proc. of ?Eighth Int. Conf. on Steam Turbines with Large Output? held in Karlovy Vary, October 30, November 1, 204-210 (1984)
[15] Feistauer, M., Mandel, J., Ne?as, J.: Entropy regularization of the transonic potential flow problem. CMUC,25, 431-443 (1984) · Zbl 0563.35006
[16] Feistauer, M., Ne?as, J.: On the solvability of transonic potential flow problems. Z. f?r Analysis und ihre Anwendungen,4, 305-329 (1985) · Zbl 0621.76069
[17] Fu??k, S., Kufner, A.: Nonlinear Differential Equations. Studies in Applied Mechanics 2. Amsterdam, Oxford, New York: Elsevier 1980 · Zbl 0426.35001
[18] Hamina, M., Saranen, J.: On the numerical solution of the compressible subsonic gas flow. Mathematics University of Oulu, No.1, August 1984 0736 0939 V 3
[19] Hirsch, Ch., Warzee, G.: Finite element computation of subsonic cascade flows. Proc. of 6th Canadien Congress on Appl. Mech., Vancouver 1977 · Zbl 0324.76046
[20] Kratochv?l, J., ?en??ek, A.: The algorithm of the solution of the two-dimensional potential flow of compressible fluid by the finite element method. Vodohosp. ?as.25, 357-379 (1977)
[21] Kufner, A., John, O., Fu??k, S.: Function Spaces. Academia, Prague, 1977
[22] Lions, J.L.: Quelques m?thodes de r?solution des probl?mes aux limites non lin?aires. Paris: Dunod, Gauthier-Villars 1969 · Zbl 0189.40603
[23] Martensen, E.: Berechnung der Druckverteilung an Gitterprofilen in ebener Potentialstr?mung mit einer Fredholmschen Integralgleichung. Arch. Ration. Mech. Anal.3, 253-270 (1959) · Zbl 0204.25603
[24] Ne?as, J.: Les m?thodes directes en th?ories des equations elliptiques. Academia, Prague, 1967
[25] Ne?as, J.: Introduction to the Theory of Nonlinear Elliptic Equations. Teubner Texte zur Mathematik, Bd. 52, Leipzig, 1983 · Zbl 0526.35003
[26] Norrie, D.H., de Vries, G.: The Finite Element Method. London: Academic Press 1973 · Zbl 0293.65087
[27] Strang, G., Fix, G.J.: An Analysis of the Finite Element Method. Englewood Cliffs, New Jersey: Prentice Hall 1973 · Zbl 0356.65096
[28] Zl?mal, M.: The finite element method in domains with curved boundaries. Int. J. Numer. Meth. Enger.5, 367-373 (1973) · Zbl 0254.65073
[29] ?en??ek, A.: Discrete forms of Friedrichs’ inequalities in the finite element method. RAIRO Analyse num?rique/Anal. Numer.15, 265-286 (1981)
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.