×

Finite element solution of flows through cascades of profiles in a layer of variable thickness. (English) Zbl 0641.76067

The concern of the paper is a numerical modelling of a subsonic irrotational inviscid flow past a cascade of profiles in a variable thickness fluid layer, mathematically speaking, a nonlinear two- dimensional elliptic problem with nonstandard nonhomogeneous boundary conditions. The authors have discretized the problem by means of finite element method, studied the convergence of the method, dealt with some aspects of algorithmizations, and finally presented some numerical results.
Reviewer: V.P.Tyagi

MSC:

76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
76B10 Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing
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: EuDML

References:

[1] I. Babuška M. Práger E. Vitásek: Numerical Processes in Differential Equations. SNTL Praha and John Wiley & Sons, 1966. · Zbl 0156.16003
[2] Ph. G. Ciarlet: The Finite Element Method for Elliptic Problems. Studies in Math. and its Appl. Vol. 4, North-Holland, Amsterdam-New York-Oxford, 1979.
[3] M. Feistauer: Mathematical study of rotational incompressible non-viscous flows through multiply connected domains. Apl. mat. 26 (1981), No. 5, 345-364. · Zbl 0486.76025
[4] M. Feistauer: Numerical solution of non-viscous axially symmetric channel flows. Proc. of the conf. ”Mathematical Methods in Fluids Mechanics”, Oberwolfach 1981, Methoden und Verfahren der Math. Physik, Band 24, P. Lang, Frankfurt am Main, 1982.
[5] M. Feistauer: On irrotational flows through cascades of profiles in a layer of variable thickness. Apl. mat. 29 (1984), No. 6, 423-458. · Zbl 0598.76061
[6] M. Feistauer: Finite element solution of non-viscous flows in cascades of blades. ZAMM 65 (1985) 4, T 191 - T 194. · Zbl 0605.76068
[7] M. Feistauer: Mathematical and numerical study of flows through cascades of profiles. Proc. of ”International Conference on Numerical Methods and Applications” held in Sofia, August 27-September 2, 1984, 271-278.
[8] M. Feistauer: On the finite element approximation of a cascade flow problem. · Zbl 0646.76085
[9] M. Feistauer: Finite element solution of flow problems with trailing conditions. · Zbl 0766.76049
[10] M. Feistauer J. Felcman: Numerical solution of an incompressible flow past a cascade of profiles in a layer of variable thickness by the finite element method. Proc. of the conf. ”HYDROTURBO 1985” held in Olomouc, September 11-13, 1985.
[11] M. Feistauer J. Felcman Z. Vlášek: Finite element solution of flows in elements of blade machines. Proc. of ”Eight Int. Conf. on Steam Turbines with Large Output” held in Karlovy Vary, October 30-November 1, 1984.
[12] M. Feistauer J. Felcman Z. Vlášek: Calculation of irrotational flows through cascades of blades in a layer of variable thickness. Research report, ŠKODA Plzeň, 1983
[13] M. Feistauer Z. Vlášek: Irrotational steady subsonic flow of an ideal fluid - Theory and finite element solution. Research report, ŠKODA Plzeň, 1981
[14] J. Felcman: Flow past a rotating cascade of blades in a layer of variable thickness. Research report, ČKD Praha, 1984
[15] J. Felcman: Finite element solution of cascade flows. Thesis. Faculty of Mathematics and Physics, Prague, 1986 · Zbl 0638.76074
[16] S. Fučík A. Kufner: Nonlinear Differential Equations. Studies in Applied Mechanics 2, Elsevier, Amsterdam-Oxford -New York, 1980.
[17] R. Glowinski: Numerical Methods for Nonlinear Variational Problems. Springer-Verlag, New York-Berlin-Heidelberg-Tokyo, 1984. · Zbl 0536.65054
[18] A. Kufner O. John S. Fučík: Function Spaces. Academia, Prague, 1977.
[19] E. Martensen: Berechnung der Druckverteilung an Gitterprofilen in ebener Potentialströmung mit einen Fredholmschen Integralgleichung. Arch. Rat. Mech. Anal. 3 (1959), 253-270. · Zbl 0204.25603
[20] J. Nečas: Les Méthodes Directes en Théories des Equations Elliptiques. Academia, Prague, 1967. · Zbl 1225.35003
[21] J. Nečas: Introduction to the Theory of Nonlinear Elliptic Equations. Teubner-Texte zur Mathematik, Band 52, Leipzig, 1983. · Zbl 0526.35003
[22] M. Rokyta: Numerical solution of strongly nonlinear elliptic problems. Thesis. Faculty of Mathematics and Physics, Prague, 1985
[23] G. Strang G. J. Fix: An Analysis of the Finite Element Method. Prentice Hall, Inc. 1974. · Zbl 0278.65116
[24] Z. Vlášek: Integral equation method in a plane flow past profiles and cascades of profiles. Acta Polytechnica, 3 (IV, 1, 1977), 63-69.
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.