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Finite difference methods for the steady-state navier-stokes equations

  • Fundamental Numerical Techniques
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Proceedings of the Third International Conference on Numerical Methods in Fluid Mechanics

Part of the book series: Lecture Notes in Physics ((LNP,volume 18))

Abstract

Two iterative methods for numerically solving the incompressible 2D steady-state Navier-Stokes equation are presented. These are the Numerical Oseen (NOS) method and the Laplacian Driver (LAD) method. Unlike most methods, these are not time-dependent or even time-like in their iterations. The methods make use of recent advances in numerically solving 2D linear second-order partial differential equations with methods which are direct (i.e., non-iterative).

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References

  • Briley, W. R. (1970). "A Numerical Study of Laminar Separation Bubbles Using the Navier-Stokes Equations," Report J110614-1, United Aircraft Research Laboratories, East Hartford, Connecticut, U.S.A.

    Google Scholar 

  • Buneman, O. (1969), "A Compact Non-Iterative Poisson Solver," SUIPR Report No. 294, Stanford University, Stanford, California, May 1969.

    Google Scholar 

  • Davis, R. T. (1972). "Numerical Solution of the Navier-Stokes Equations for Laminar Incompressible Flow Past a Parabola," J. Fluid Mechanics, Vol. 51, Part 3, pp. 417–433.

    Article  MATH  ADS  Google Scholar 

  • Dorr, F. W. (1970), "The Direct Solution of the Discrete Poisson Equation on a Rectangle," SIAM Review, Vol. 12, No. 2, pp. 248–263, March 1970.

    Article  MATH  MathSciNet  Google Scholar 

  • Roache, P. J., (1970), "Sufficiency Conditions for a Commonly Use Downstream Boundary Condition on Stream Function," J. Computational Physics, Vol. 6, No. 2, pp. 317–321.

    Article  MATH  ADS  Google Scholar 

  • Roache, P. J. (1971), "A Direct Method for the Discretized Poisson Equation," SC-RR-70-579, Sandia Laboratories, Albuquerque, New Mexico, February 1971. See also Proc. Second Intn'l Conf. on Numerical Methods in Fluid Mechanics, M. Holt, ed., Springer-Verlag, 1971.

    Google Scholar 

  • Roache, P. J. (1972a), "Finite Difference Methods for the Steady-State Navier-Stokes Equations," SC-RR-72-0419, Sandia Laboratories, Albuquerque, New Mexico, August 1972.

    Google Scholar 

  • Roache, P. J. (1972b), Computational Fluid Dynamics, to be published.

    Google Scholar 

  • Roache, P. J. (1972c), "On Artificial Viscosity," to be published in J. Computational Physics.

    Google Scholar 

  • Schlichting, H., (1968), Boundary Layer Theory, 6th Edition, McGraw-Hill Book Co., Inc., New York.

    Google Scholar 

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Henri Cabannes Roger Temam

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© 1973 Springer Verlag

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Roache, P.J. (1973). Finite difference methods for the steady-state navier-stokes equations. In: Cabannes, H., Temam, R. (eds) Proceedings of the Third International Conference on Numerical Methods in Fluid Mechanics. Lecture Notes in Physics, vol 18. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0118670

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  • DOI: https://doi.org/10.1007/BFb0118670

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06170-0

  • Online ISBN: 978-3-540-38377-2

  • eBook Packages: Springer Book Archive

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