Article
Full entry |
PDF
(3.7 MB)
Feedback
PDF
(3.7 MB)
Feedback
Keywords:
numerical modelling; subsonic irrotational inviscid flow; cascade of profiles; variable thickness fluid layer; nonlinear two-dimensional elliptic problem; nonhomogeneous boundary conditions; finite element method; convergence; algorithmizations; stream function
numerical modelling; subsonic irrotational inviscid flow; cascade of profiles; variable thickness fluid layer; nonlinear two-dimensional elliptic problem; nonhomogeneous boundary conditions; finite element method; convergence; algorithmizations; stream function
Summary:
The paper is devoted to the numerical modelling of a subsonic irrotational nonviscous flow past a cascade of profiles in a variable thickness fluid layer. It leads to a nonlinear two-dimensional elliptic problem with nonstandard nonhomogeneous boundary conditions. The problem is discretized by the finite element method. Both theoretical and practical questions of the finite element implementation are studied; convergence of the method, numerical integration, iterative methods for the solution of the discrete problem and the algorithmization of the finite element solution. Some numerical results obtained by a multi-purpose program written by authors are presented.
References:
[1] I. Babuška M. Práger E. Vitásek: Numerical Processes in Differential Equations. SNTL Praha and John Wiley & Sons, 1966. MR 0223101
[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. MR 0520174
[3] M. Feistauer: Mathematical study of rotational incompressible non-viscous flows through multiply connected domains. Apl. mat. 26 (1981), No. 5, 345-364. MR 0631753 | Zbl 0486.76025
[4] M. Feistauer: Numerical solution of non-viscous axially symmetric channel flows. In: 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. MR 0767495 | 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. In: 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. (to appear in Numer. Math.). MR 0884294 | Zbl 0646.76085
[9] M. Feistauer: Finite element solution of flow problems with trailing conditions. (to appear). 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. In: 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. In: 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 (in Czech).
[13] M. Feistauer Z. Vlášek: Irrotational steady subsonic flow of an ideal fluid - Theory and finite element solution. Research report, ŠKODA Plzeň, 1981 (in Czech).
[14] J. Felcman: Flow past a rotating cascade of blades in a layer of variable thickness. Research report, ČKD Praha, 1984 (in Czech).
[15] J. Felcman: Finite element solution of cascade flows. Thesis. Faculty of Mathematics and Physics, Prague, 1986 (in Czech).
[16] S. Fučík A. Kufner: Nonlinear Differential Equations. Studies in Applied Mechanics 2, Elsevier, Amsterdam-Oxford -New York, 1980. MR 0558764
[17] R. Glowinski: Numerical Methods for Nonlinear Variational Problems. Springer-Verlag, New York-Berlin-Heidelberg-Tokyo, 1984. MR 0737005 | Zbl 0536.65054
[18] A. Kufner O. John S. Fučík: Function Spaces. Academia, Prague, 1977. MR 0482102
[19] E. Martensen: Berechnung der Druckverteilung an Gitterprofilen in ebener Potentialströmung mit einen Fredholmschen Integralgleichung. Arch. Rat. Mech. Anal. 3 (1959), 253-270. DOI 10.1007/BF00284179 | MR 0114431
[20] J. Nečas: Les Méthodes Directes en Théories des Equations Elliptiques. Academia, Prague, 1967. MR 0227584
[21] J. Nečas: Introduction to the Theory of Nonlinear Elliptic Equations. Teubner-Texte zur Mathematik, Band 52, Leipzig, 1983. MR 0731261
[22] M. Rokyta: Numerical solution of strongly nonlinear elliptic problems. Thesis. Faculty of Mathematics and Physics, Prague, 1985 (in Czech).
[23] G. Strang G. J. Fix: An Analysis of the Finite Element Method. Prentice Hall, Inc. 1974. MR 0443377
[24] Z. Vlášek: Integral equation method in a plane flow past profiles and cascades of profiles. Acta Polytechnica, 3 (IV, 1, 1977), 63-69.
Search
Partner of
