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Adaptive projection-grid methods and their application

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Fifteenth International Conference on Numerical Methods in Fluid Dynamics

Part of the book series: Lecture Notes in Physics ((LNP,volume 490))

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Abstract

Effective projection-grid method on adaptive grid for solution of stationary 2-D incompressible Navier-Stokes equations is presented. The method implies obtaining the solution in the form of piecewise polynomial functions on arbitrary regular grid with triangular cells. The grids are adapted to the singularities of the solution as well to the domain geometry. The suggested method assumes the appearance of cells with arbitrarily small angles which does not significantly affect the accuracy of the approximated solution. Some numerical results are presented and discussed.

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References

  1. A.G. Sleptsov: Russian J. Numer. Anal. Mathem. Modeling, 8 501 (1993)

    MathSciNet  Google Scholar 

  2. Yu. I. Shokin, A.G. Sleptsov: Russian J. Numer. Anal. Mathem. Modelling, 10 449 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  3. A.G. Sleptsov, Yu.I. Shokin: Adaptive Projection-Grid method for Elliptic Problems, J. Comput. Mathem. and Mathem. Phys. (in appear).

    Google Scholar 

  4. J.T. Oden, L. Demkowicz: Comput. Math. Appl. Mech. and Engng, 91 11 (1991)

    Article  MathSciNet  Google Scholar 

  5. G. Strang, G.J. Fix: An Analysis of the Finite Element Method, Prentice-Hall, Ink, Englewood Cliffs, NJ, (1973)

    MATH  Google Scholar 

  6. P. Ciarlet: The Finite Element Method for Elliptic Problems, Studies in Mathematics and Its Applications, 4, North-Holland Publishing Company, Amsterdam, New-York, Oxford (1978)

    Google Scholar 

  7. A.G. Sleptsov: Russian J. Theor. and Applied Mech. 1 74 (1991)

    Google Scholar 

  8. A.G. Sleptsov: Russian J. Thear. and Applied Mech. 1 213 (1991)

    Google Scholar 

  9. V.B. Karamyshev, V.M. Kovenya, A.G. Sleptsov and S.G. Cherny: Variational Method of Accelerating Linear Iterations, Computers and Fluids (in appear)

    Google Scholar 

  10. Y. Saad: Mathematics of Computation 37 105 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  11. V.B. Karamyshev, V.M. Kovenya, S.G. Cherny: 14-th ICNMFD, Bangalore, India (1994)

    Google Scholar 

  12. V. Karamyshev, V.M. Kovenya, A.G. Sleptsov, S. Cherny: Sixth International Symposium on CFD, Nevada, USA (1995)

    Google Scholar 

  13. I.P. Mysovskikh: Interpolation Qubature Formulas, Moscow: Nauka (1979)

    Google Scholar 

  14. B.-N. Jiang, G.F. Carey: J. Numeric. Meth. Engng 24 569 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  15. V.B. Karamyshev, V.M. Kovenya, A.G. Sleptsov: ECCOMAS'96, Paris, France (1996)

    Google Scholar 

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Paul Kutler Jolen Flores Jean-Jacques Chattot

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© 1997 Springer-Verlag

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Karamyshev, V., Kovenya, V., Sleptsov, A. (1997). Adaptive projection-grid methods and their application. In: Kutler, P., Flores, J., Chattot, JJ. (eds) Fifteenth International Conference on Numerical Methods in Fluid Dynamics. Lecture Notes in Physics, vol 490. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0107153

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  • DOI: https://doi.org/10.1007/BFb0107153

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63054-8

  • Online ISBN: 978-3-540-69120-4

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