Approximate methods for equations of incompressible fluid



Approximate methods on the basis of sequential approximations in the theory of functional solutions to systems of conservation laws is considered, including the model of dynamics of incompressible fluid. Test calculations are performed, and a comparison with exact solutions is carried out.


functional solutions to systems of conservation laws convergence of approximate methods equations of incompressible fluid exact solutions 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    V. A. Galkin, “Metric theory of functional solutions of the cauchy problem for a system of conservation laws,” Dokl. Math. 81 (2), 219–221 (2010).MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    S. N. Kruzhkov, “Methods for constructing generalized solutions of the Cauchy problem for a first-order quasilinear equation,” Usp. Mat. Nauk 20 (6), 112–118 (1965).Google Scholar
  3. 3.
    S. N. Kruzhkov, “First-order quasilinear equations in several independent variables,” Math. USSR-Sb. 10 (2), 217–243 (1970).CrossRefMATHGoogle Scholar
  4. 4.
    S. N. Kruzhkov, Works, Ed. by N. S. Bakhvalov, V. A. Galkin, and Yu. A. Dubinskii (Fizmatlit, Moscow, 2000) [in Russian].Google Scholar
  5. 5.
    R. J. DiPerna, “Measure-valued solutions of conservation laws,” Arch. Ration. Mech. Anal. 88, 223–270 (1985).MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    V. A. Galkin and V. A. Tupchiev, “On the solvability in the mean of a system of quasi-linear conservation laws,” Dokl. Akad. Nauk SSSR 300 (6), 1300–1304 (1988).Google Scholar
  7. 7.
    V. A. Galkin, “Functional solutions of conservation laws,” Dokl. Akad. Nauk SSSR 310 (4), 834–839 (1990).MathSciNetMATHGoogle Scholar
  8. 8.
    V. A. Galkin, “Theory of functional solutions to systems of conservation laws and its applications,” Tr. Semin. im. I.G. Petrovskogo 20, 81–120 (2000).MathSciNetGoogle Scholar
  9. 9.
    V. A. Galkin and V. V. Russkikh, “Convergence of approximate methods for incompressible fluid equations,” Mat. Model., No. 3, 101–113 (1994).MATHGoogle Scholar
  10. 10.
    L. D. Landau and E. M. Lifshitz, Fluid Mechanics (Nauka, Moscow, 1986; Butterworth-Heinemann, Oxford, 1987).MATHGoogle Scholar
  11. 11.
    A. S. Monin and A. M. Yaglom, Statistical Fluid Mechanics (MIT Press, Cambridge, Mass., 1971; Nauka, Moscow, 1986), Vol.1.Google Scholar
  12. 12.
    S. V. Vallander, Lectures on Aeromechanics (Leningr. Gos. Univ., Leningrad, 1978) [in Russian].Google Scholar
  13. 13.
    V. B. Betelin and V. A. Galkin, “Control of incompressible fluid parameters in the case of time-varying flow geometry,” Dokl. Math. 92 (1), 511–513 (2015).MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    V. A. Galkin and A. O. Dubovik, “On the control of heat release in viscous incompressible flow by moving the flow boundary,” Vestn. Kibern. Elektr. Zh. 19 (3), 136–140 (2015).Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  • V. A. Galkin
    • 1
  • A. O. Dubovik
    • 1
  • A. A. Epifanov
    • 2
  1. 1.Surgut State UniversitySurgut, Khanty-Mansiysk avtonomnyi okrugRussia
  2. 2.Motorola Solutions, SurgutMoscowRussia

Personalised recommendations