Skip to main content
SpringerLink
Log in

Solving the problem of Bingham fluid flow in cylindrical pipeline

  • Published:
Russian Mathematics Aims and scope Submit manuscript

Abstract

We consider an elliptic variational inequality in a circular domain, which simulates viscoplastic Bingham flow in a pipe. This variational inequality is approximated by finite-difference scheme on a grid in polar coordinates. To solve the finite-dimensional problem we propose a generalized Uzawa-type iterative method. We prove the convergence of the iterative method.

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. Mosolov, P. P., Myasnikov V. P. “Variational Methods in the Theory of the Fluidity of a Viscous-Plastic Medium,” J. Mech. Appl. Math. 29, 545–577 (1965).

    Article  MATH  Google Scholar 

  2. Mosolov, P. P., Myasnikov, V. P. “On Qualitative Singularities of the Flow of a Viscoplastic Mediumin Pipes,” J. Mech. Appl. Math. 31, 609–613 (1967).

    Article  MATH  Google Scholar 

  3. Duvaut G., Lions J.-L. Inequalities in Mechanics and Physics (Springer-Verlag, N. Y., 1976; Nauka, Moscow, 1980).

    Book  MATH  Google Scholar 

  4. Glowinski, R., Lions, J.-L., Tremolieres, R. Numerical Analysis of Variational Inequalities (Dunod, Paris, 1976; Mir, Moscow, 1979).

    Google Scholar 

  5. Glowinski, R. Numerical Methods for Nonlinear Variational Problems (Springer-Verlag, N. Y., 1984).

    Book  MATH  Google Scholar 

  6. Dean, E. J., Glowinski, R., Guidoboni, G. “On the Numerical Simulation of Bingham Visco-Plastic Flow: Old and New results,” J. Non-Newtonian Fluid Mech., No. 142, 36–62 (2007).

    Google Scholar 

  7. Muravleva, E. A., Ol’shanskii, M. A. “Two Finite-Difference Schemes for Calculation of Bingham Fluid Flows in a Cavity,” Rus. J. Num. Anal. Math. Model. 23(6), 615–634 (2008).

    MATH  MathSciNet  Google Scholar 

  8. Muravleva, E. A. “Finite-Difference Schemes for the Computation of Viscoplastic Medium Flows in a Channel,” Mathematical Models and Computer Simulations 1(6), 768–779 (2009).

    Article  MathSciNet  Google Scholar 

  9. Fortin, M., Glowinski, R. Augmented Lagrangian Methods (North-Holland, Amsterdam, N. Y., 1983).

    MATH  Google Scholar 

  10. Glowinski, R., LeTallec, P. Augmented Lagrangian and Operator-Splitting Methods in Nonlinear Mechanics (SIAM Studies in Applied Mathematics, PA, 1989).

    Book  MATH  Google Scholar 

  11. Lapin, A. “Preconditioned Uzawa-Type Methods for Finite-Dimensional Constrained Saddle Point Problems,” Lobachevskii J. Math. 31(4), 309–322 (2010).

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Kazan (Volga Region) Federal University, ul. Kremlyovskaya 18, Kazan, 420008, Russia

    A. V. Lapin & A. D. Romanenko

Authors
  1. A. V. Lapin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. D. Romanenko
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. V. Lapin.

Additional information

Original Russian Text © A.V. Lapin, A.D. Romanenko, 2015, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2015, No. 2, pp. 82–86.

Submitted by R.Z. Dautov

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lapin, A.V., Romanenko, A.D. Solving the problem of Bingham fluid flow in cylindrical pipeline. Russ Math. 59, 67–70 (2015). https://doi.org/10.3103/S1066369X15020103

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1066369X15020103

Keywords

Search

Navigation