Skip to main content
SpringerLink
Log in

A factorization method for numerical solution of the Navier–Stokes equations for a viscous incompressible liquid

  • Published:
Journal of Applied and Industrial Mathematics Aims and scope Submit manuscript

Abstract

Some implicit difference scheme of approximate factorization is proposed for numerical solution of the Navier–Stokes equations for an incompressible liquid in curvilinear coordinates. Testing of the algorithm is carried out on the solution of the problems concerning the Couette and Poiseuille flows; and the results are presented of numerical simulation of a flow between the rotating cylinders with covers.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. L. G. Loitsyanskii, Mechanics of Liquids and Gases (Nauka, Moscow, 1978; Pergamon Press, Oxford, 1966).

    MATH  Google Scholar 

  2. O. A. Ladyzhenskaya, TheMathematical Theory of Viscous Incompressible Flow (Nauka, Moscow, 1970; Gordon and Breach, New York, 1969).

    MATH  Google Scholar 

  3. N. N. Yanenko, The Method of Fractional Steps. The Solution of Problems of Mathematical Physics in Several Variables (Nauka, Novosibirsk, 1967; Springer, Berlin, 1971).

    MATH  Google Scholar 

  4. A. Chorin, “Numerical Solution of Navier–Stokes Equations,” Math. Comp. 22 (7), 745–762 (1968).

    Article  MathSciNet  MATH  Google Scholar 

  5. P. J. Roache, Computational Fluid Dynamics (Hermosa, Albuquerque, NM, 1982; Mir, Moscow, 1980).

    MATH  Google Scholar 

  6. R. Peyret and Th. D. Taylor, Computational Methods for Fluid Flow (Springer, Berlin, 1983; Gidrometeoizdat, Leningrad, 1986).

    MATH  Google Scholar 

  7. A. A. Amsden and F. N. Harlow, The SMACMethod, Rep. NLA–4370 (Los Alamos Sci. Lab., Los Alamos, 1970).

    Google Scholar 

  8. E. L. Tarunin, Nonlinear Problems of Heat Convection. Selected Works (Izd. Perm. Gos. Univ., Perm’, 2002) [in Russian].

    Google Scholar 

  9. A. A. Tolstykh, Compact Difference Schemes and Their Applications in Hydrodynamics Problems (Nauka, Moscow, 1996) [in Russian].

    Google Scholar 

  10. O. M. Belotserkovskii, V. A. Gushchin, V. V. Shchennikov, “Use of the Splitting Method to Solve Problems of the Dynamics of a Viscous Incompressible Fluid,” Zh. Vychisl. Mat. i Mat. Fiz. 15 (1), 197–207 (1975) [USSR Comput. Math. and Math. Phys. 15 (1), 190–200 (1975)].

    Google Scholar 

  11. A. A. Samarskii and P. N. Vabishchevich, Additive Schemes for Problems of Mathematical Physics (Nauka, Moscow, 1999) [in Russian].

    MATH  Google Scholar 

  12. Ch H. Bruneau and C. Jouron, “An Efficient Scheme for Solving Steady Incompressible Navier–Stokes Equations,” J. Comput. Phys. 89 (2), 389–413 (1990).

    Article  MATH  Google Scholar 

  13. T. Kavamura, H. Takami, and K. Kuwahara, New Higher-Order Upwind Scheme for Incompressible Navier–Stokes Equations (Springer, New York, 1985).

    MATH  Google Scholar 

  14. P. N. Vabishchevich, “Additive Schemes for Some Differential-Operator Equations,” Zh. Vychisl. Mat. iMat. Fiz. 50 (12), 2144–2154 (2010) [Comput. Math. and Math. Phys. 50 (12), 2033–2043 (2010)].

    MathSciNet  MATH  Google Scholar 

  15. S. G. Chernyi, D. V. Chirkov, V. N. Lapin, V. A. Skorospelov, and S. V. Sharov, Computational Modeling of Flows in Turbomachines (Nauka, Novosibirsk, 2006) [in Russian].

    Google Scholar 

  16. V. M. Kovenya and N. N. Yanenko, Splitting Method in Problems of Gas Dynamics (Nauka, Novosibirsk, 1981) [in Russian].

    MATH  Google Scholar 

  17. V. M. Kovenya, “An Algorithm for Solution of the Navier–Stokes Equations for Viscous Incompressible Fluid,” Vychisl. Tekhnol. 11 (2), 39–51 (2006).

    MathSciNet  MATH  Google Scholar 

  18. A. V. Bazovkin, V. M. Kovenya, and O. M. Vavilova, “Factorization Method for Numerical Solution of the Navier-Stokes Equations for Viscous Incompressible Fluid,” Vychisl. Tekhnol. 14 (2), 13–31 (2009).

    MATH  Google Scholar 

  19. V. M. Kovenya, Splitting Algorithms for Solving the Aerohydrodynamic Problems of High Dimension (Izd. Sibir. Otdel. Ross. Akad. Nauk, Novosibirsk, 2014) [in Russian].

    Google Scholar 

  20. V. M. Kovenya and A. S. Lebedev, “Modifications of the Splitting Method for Constructing Economical Difference Schemes,” Zh. Vychisl. Mat. i Mat. Fiz. 34 (6), 886–897 (1994) [Comput. Math. and Math. Phys. 34 (6), 763–773 (1994)].

    MathSciNet  MATH  Google Scholar 

  21. G. I. Marchuk, Methods of Numerical Mathematics (Izd. Novosib. Gos. Univ., Novosibirsk, 1972; Springer, New York, 1982; Nauka, Moscow, 1989).

    MATH  Google Scholar 

  22. G. I. Taylor, “Stability of a Viscous Liquid Contained Between Two Rotating Cylinders,” Philos. Trans. Roy. Soc. London. Ser. A 223, 289–343 (1923).

    Article  MATH  Google Scholar 

  23. J. Abshagen, K. A. Cliffe, J. Langenberg, G. Pfister, T. Mullin, and S. J. Tavener, “Taylor–Couette Flows with Independently Rotating End Plates,” Theor. Comput. Fluid Dynamics 18 (2–4), 129–136 (2004).

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Computational Technologies, pr. Akad. Lavrent’eva 6, Novosibirsk, 630090, Russia

    V. M. Kovenya

  2. Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia

    A. S. Kudryashov

Authors
  1. V. M. Kovenya
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. S. Kudryashov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. M. Kovenya.

Additional information

Original Russian Text © V.M. Kovenya, A.S. Kudryashov, 2016, published in Sibirskii Zhurnal Industrial’noi Matematiki, 2016, Vol. XIX, No. 2, pp. 61–73.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kovenya, V.M., Kudryashov, A.S. A factorization method for numerical solution of the Navier–Stokes equations for a viscous incompressible liquid. J. Appl. Ind. Math. 10, 232–242 (2016). https://doi.org/10.1134/S1990478916020083

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1990478916020083

Keywords

Search

Navigation