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On the finite element approximation of a cascade flow problem

  • Convergence of the SSOR Method for Nonlinear Systems of Simultaneous Equations
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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.

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References

  1. Babuška, I.: Approximation by hill functions. Comment. Math. Univ. Carolinae11, 787–811 (1970)

    Google Scholar 

  2. Babuška, I.: Approximation by hill functions II. Comment. Math. Univ. Carolinae13, 1–22 (1972)

    Google Scholar 

  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)

    Google Scholar 

  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

    Google Scholar 

  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)

    Google Scholar 

  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

    Google Scholar 

  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)

    Google Scholar 

  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 Plzeň, 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)

    Google Scholar 

  11. Feistauer, M.: Finite element solution of non-viscous flows in cascades of blades. ZAMM65, 191–194 (1985)

    Google Scholar 

  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., Vlášek, 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., Nečas, J.: Entropy regularization of the transonic potential flow problem. CMUC,25, 431–443 (1984)

    Google Scholar 

  16. Feistauer, M., Nečas, J.: On the solvability of transonic potential flow problems. Z. für Analysis und ihre Anwendungen,4, 305–329 (1985)

    Google Scholar 

  17. Fučík, S., Kufner, A.: Nonlinear Differential Equations. Studies in Applied Mechanics 2. Amsterdam, Oxford, New York: Elsevier 1980

    Google Scholar 

  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

  20. Kratochvíl, J., Ženíšek, A.: The algorithm of the solution of the two-dimensional potential flow of compressible fluid by the finite element method. Vodohosp. Čas.25, 357–379 (1977)

    Google Scholar 

  21. Kufner, A., John, O., Fučík, S.: Function Spaces. Academia, Prague, 1977

    Google Scholar 

  22. Lions, J.L.: Quelques méthodes de résolution des problémes aux limites non linéaires. Paris: Dunod, Gauthier-Villars 1969

    Google Scholar 

  23. Martensen, E.: Berechnung der Druckverteilung an Gitterprofilen in ebener Potentialströmung mit einer Fredholmschen Integralgleichung. Arch. Ration. Mech. Anal.3, 253–270 (1959)

    Article  Google Scholar 

  24. Nečas, J.: Les méthodes directes en théories des equations elliptiques. Academia, Prague, 1967

  25. Nečas, J.: Introduction to the Theory of Nonlinear Elliptic Equations. Teubner Texte zur Mathematik, Bd. 52, Leipzig, 1983

  26. Norrie, D.H., de Vries, G.: The Finite Element Method. London: Academic Press 1973

    Google Scholar 

  27. Strang, G., Fix, G.J.: An Analysis of the Finite Element Method. Englewood Cliffs, New Jersey: Prentice Hall 1973

    Google Scholar 

  28. Zlámal, M.: The finite element method in domains with curved boundaries. Int. J. Numer. Meth. Enger.5, 367–373 (1973)

    Google Scholar 

  29. Ženíšek, A.: Discrete forms of Friedrichs' inequalities in the finite element method. RAIRO Analyse numérique/Anal. Numer.15, 265–286 (1981)

    Google Scholar 

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Feistauer, M. On the finite element approximation of a cascade flow problem. Numer. Math. 50, 655–684 (1986). https://doi.org/10.1007/BF01398378

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