Skip to main content
SpringerLink
Log in

Numerical solution of stationary viscous incompressible fluid problems by the method of fictitious domains

  • V. Numerical Methods in the Mechanics of Continuous Media
  • Published:
Computational Mathematics and Modeling Aims and scope Submit manuscript

Abstract

We consider some issues of numerical implementation of the fictitious domain method for viscous incompressible fluid problems. Plane stationary problems are solved by successive approximations in the nonlinearity. Plane heat convection problems in the Boussinesq approximation are also considered. Solution examples of some specimen problems are presented.

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

Literature Cited

  1. P. Roache, Computational Fluid Dynamics, Hermosa Publishers, Albuquerque, New Mexico (1976).

    Google Scholar 

  2. T. D. Mueller, "Application of numerical methods to investigation of physiological flows," in: Numerical Methods in Fluid Dynamics [Russian translation], Mir, Moscow (1981), pp. 80–151.

    Google Scholar 

  3. V. I. Polezhaev and A. I. Fedoseev, Finite Element Method in Problems of Fluid Mechanics and Heat and Mass Exchange [in Russian], Preprint No. 160, IPMekh AN SSSR (1980).

  4. I. V. Starshinova and I. V. Fryazinov, Numerical Analysis of Hydrodynamic and Heat Processes of Single-Crystal Growing by the Czochralski Method [in Russian], Preprint No. 52, IPMat AN SSSR (1982).

  5. I. F. Thompson, Z. U. A. Warsi, and C. W. Mastin, "Boundary-fitted coordinate systems for numerical solution of partial differential equations — a review," J. Comp. Phys.,47, No. 1, 1–108 (1982).

    Google Scholar 

  6. A. N. Bugrov, The Method of Fictitious Domains in the Equations for the Stream Function of a Viscous Incompressible Fluid [in Russian], Preprint, IM Sib. Otd. Akad. Nauk SSSR, Novosibirsk (1977).

    Google Scholar 

  7. Sh. Smagulov and M. K. Orunkhanov, "An approximate solution method for the equations of hydrodynamics in multiply connected domains," Dokl. Akad. Nauk SSSR,260, No. 5, 1078–1082 (1981).

    Google Scholar 

  8. B. I. Myznikova and E. L. Tarunin, "Application of the method of fictitious domains to solve Navier-Stokes equations in the variables stream function and vorticity," in: Investigation of Thermal Convection and Heat Transfer [in Russian], Izd. UNTs AN SSSR, Sverdlovsk (1981), pp. 45–57.

    Google Scholar 

  9. A. A. Samarskii and E. S. Nikolaev, Methods of Solution of Grid Equations [in Russian], Nauka, Moscow (1978).

    Google Scholar 

  10. A. K. Nikitin, K. S. Akhverdiev, and B. I. Ostroukhov, Hydrodynamic Theory of Lubrication and Computation of Sliding Bearings Under Stationary Operating Conditions [in Russian], Nauka, Moscow (1981).

    Google Scholar 

  11. P. N. Vabishchevich and T. N. Vabishchevich, Direct Problems of Numerical Solution of Plane Stationary Problems of Viscous Incompressible Fluid [in Russian], Preprint No. 111, IPMat AN SSSR (1982).

  12. A. N. Bugrov, "The method of fictitious domains in the problem of transverse bending of a thin plate," Chislennye Metody Mekhaniki Sploshnoi Sredy,8, No. 4, 45–58 (1977).

    Google Scholar 

  13. P. N. Vabishchevich, Numerical Solution of the Problem of MHD Equilibrium in a Shell of Arbitrary Shape [in Russian], Preprint No. 121, IPMat AN SSSR (1979).

Download references

Authors
  1. P. N. Vabishchevich
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. T. N. Vabishchevich
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Vychislitel'naya Matematika i Matematicheskoe Obespechenie EVM, pp. 255–262, 1985.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Vabishchevich, P.N., Vabishchevich, T.N. Numerical solution of stationary viscous incompressible fluid problems by the method of fictitious domains. Comput Math Model 1, 123–128 (1990). https://doi.org/10.1007/BF01128324

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01128324

Keywords

Search

Navigation