Methods of Computational Gasdynamics

  • O. M. Belotserkovskii
Part of the International Centre for Mechanical Sciences book series (CISM, volume 40)


At present, specialists of applied sciences are confronted with various kinds of practical problems whose successful and accurate solution, in most cases, may be attained only by numerical methods with the aid of computers. Certainly, it does not mean that analytical methods which permit us to find the solution in the “closed” form will not be developed. Nevertheless, it is absolutely clear that the range of problems permitting such an approach to their solution is rather narrow, therefore, the development of general numerical algorithms for the investigation of problems of mathematical physics is important.


Shock Wave Mach Number Difference Scheme Supersonic Flow Shock Layer 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    R. Courant, K.O. Friedrichs, H. Levy; Über die partiellen Differenzengleichungen der matematischen, Physik. Math. Ann., 100, 32, (1928).CrossRefzbMATHGoogle Scholar
  2. [2]
    K.J. Babenko, G.P. Voskresenskii; A numerical calculation method of a space supersonic gas flow around a body, Zh. Vychisl. Matem. i Matem. Fiz., v. 1, N. 6, (1961), 1051–1060.Google Scholar
  3. [3]
    D.E. Okhotsimskii, J.L. Kondrasheva, Z.P. Vlasova, R.K. Kazakova; Point explosion calculation with opposite pressure taken into account, Tr. Matem. Inst. AN SSSR, v. 50, (1957).Google Scholar
  4. [4]
    D.E. Okhotsimskii, Z.P. Vlasova; On shock wave behaviour at a great distance from an explosion site, Zh. Vychisl. Matem, i Matem. Fizz, v. 2, N. 1, (1962), 107–124.Google Scholar
  5. [5]
    S.K. Godunov; A numerical calculation difference method for hydrodynamics discontinuous solutions, Matem. sb., Ir. 47 (89), N.3, (1959), 271–306;MathSciNetGoogle Scholar
  6. [6]
    S.G. Godunov, A.V. Zabrodin, G.P. Prokopov; A difference scheme for two-dimensional nonstationary gas dynamics problems and flow calculation with a detached shock wave, Zh. Vychisl. Matem. i Matem. Fiz., v. 1, N. 6, (1961), 1020–1050.MathSciNetGoogle Scholar
  7. [7]
    V.V. Rusanov; Calculation of nonstationary shock wave inter action with obstacles, Zh. Vychisl. Matem, i Matem. Fiz., v. 1, N. 2, (1961), 267–279.MathSciNetGoogle Scholar
  8. [8]
    A.A. Dorodnitsyn; On one method of numerical solution of some nonlinear aerohydrodynamics problems, Tr. III Vses. Matem. Siezd., 1956, v. III, Moscow, Izd. AN SSSR, (1958), 447–453.Google Scholar
  9. [9]
    O.M. Belotserkovskii, P.I. Chushkin; A numerical method of integral relations, Zh. Vychisl. Matem. i Matem. Fiz., v. 2, N. 5, (1962), 731–759.Google Scholar
  10. [10]
    P.I. Chushkin; A subsonic gas flow around ellipses and ellipsoids, Sb. “Vychisl. Matem.”, N. 2, Izd. AN SSSR, (1957), 20–44.Google Scholar
  11. [11]
    P.I. Chushkin; Subsonic gas flow calculation around an Arbitrary-shape profile and a body of revolution (a symmetrical case) - Sb. “Vychisl. Matem.”, N.3, Izd. AN SSSR, (1958), 99–110.Google Scholar
  12. [12]
    P.I. Chushkin; Calculation of some subsonic gas flows - Prikl. Matem. i Mekhan., v. 21, N. 3, (1957), 353–360.Google Scholar
  13. [13]
    O.M. Belotserkovskii; A flow with a detached shock wave around a circular cylinder - Dokl. AN SSSR,v.113, N.3, (1957), 509–512.Google Scholar
  14. [14]
    O.M. Belotserkovskii; A flow with a detached shock wave around a symmetrical profile - Prikl. Matem. i Mekhan., v.22, N.2, (1958), 206–219.MathSciNetGoogle Scholar
  15. [15]
    O.M. Belotserkovskii; On calculation of a flow with a detached shock wave around axisymmetrical bodies performed on a computer — Prikl. Matem. i Mekhan., v.24, N.3, (1960), 511–517.Google Scholar
  16. [16]
    A.A. Dorodnitsyn; On one method of the equation solution of a laminar boundary layer — Zh. Prikl. Mekhan. i Tekhn. Fiz., v. 1, N.3, (1960), 111–118.Google Scholar
  17. [17]
    Yu. N. Pavlovskii; Numerical calculation of a laminar bound ary layer in a compressible gas — Zh. Vychisl. Matem i Matem. Fiz., v.2, N.5, (1962), 884–901.MathSciNetGoogle Scholar
  18. [18]
    O.N. Katskova, A.N. Kraiko; Calculation of plane and axisymmetric supersonic flows with irreversible processes — Moscow, (1964), Vych. Ts. AN SSSR.Google Scholar
  19. [19]
    O.N. Katskova, I.N. Naumova, Y.D. Shmyglevskii, N.P. Shulishnina, Experience in the calculation of plane and axisymmetric supersonic flows by the method of characteristics — Moscow, (1961), Vych. Ts. AN SSSR.Google Scholar
  20. [20]
    O.N. Katskova, P.I. Chushkin; On one scheme of a numerical method of characteristics — Dokl. AN SSSR, v.154, N.1, (1964), 26–29.Google Scholar
  21. [21]
    O.M. Belotserkovskii, A. Bulekbayev, V.G. Grudnitskii; Algorithms for schemes of the method of integral re lations applied to the calculations of mixed gas flows — Zh. Vych. Mat. i Mat., Fiz., v.6, N.6, (1966), 1064–1081.zbMATHGoogle Scholar
  22. [22]
    O.M. Belotserkovskii, A. Bulekbayev, M.M. Golomazov, V.G. Grudnitskii, V.K. Bushin, V.F. Ivanov, Y.P. Lunkin, F.D. Popov, G.M. Ryabinkov, T.Y. Timofeeva, A.I. Tolstikh, V.N. Fomin, F.V. Shugayev; Flow past blunt bodies in supersonic flow: theoretic al and experimental results — Edited by O.M. Belotserkovskii, Trudy Vych. Ts. AN SSSR, published by Computing Center, AN SSSR, 1966 (1st edition), 1967 (2nd edition, revised and extended).Google Scholar
  23. [23]
    P.I. Chushkin, Blunt bodies of simple form in supersonic gas flow — Prikl. Mat. i Mech., v.24, N.5, (1960), 927–930.Google Scholar
  24. [24]
    P.I. Chushkin; Method of characteristics for three—dimensional supersonic flow — Trudy Vych. Ts. AN SSSR, Moscow, (1968).Google Scholar
  25. [25]
    K.M. Magomedov, A.S. Kholodov; On the construction of difference schemes for equations of hyperbolic type based on characteristic coordinates — Zh. Vych. Mat. i Fiz., v.9, N.2, (1969), 373–368.zbMATHGoogle Scholar
  26. [26]
    F.H. Harlow; The particle—in-Cell Computing Method for Fluid Dynamics — Methods in Computational Physics, v.3, edited by Berni Alder, Sidney Fernbach, Manuel Rotenberg, Academic Press, N.Y., (1964).Google Scholar
  27. [27]
    M. Rich; A method for Eulerian Fluid Dynamics — Los Alamos Scientific Laboratory, New Mexico, Lab. Rep. LAMS — 2826, (1963).Google Scholar
  28. [28]
    O.M. Belotserkovskii, Y.M. Davidov; The use of unsteady methods of “large particle” for problems of external aerodynamics — Vych. Ts. AN SSSR, (1970), 85 p.Google Scholar
  29. [29]
    O.M. Belotserkovskii, E.S. Sedova, F.V. Shugaev; Supersonic Flow Around Blunt Bodies of Revolution with a sur face Discontinuity — Zh. Vychisl. Matem. i Matem. Fiz., v.6, N.5, (1966), 930–934.Google Scholar
  30. [30]
    Aerophysical Investigations of Supersonic Flows. Edited by Dunaev Yu. A., Izd. “Nauka”, Moscow — Leningrad, (1967).Google Scholar
  31. [31]
    O.M. Belotserkovskii, E.G. Shifrin; Transonic flows behind a detached shock wave — Zh. Vychisl. Matem. i Matem. Fiz., V.9, N.4, (1969), 908–931.Google Scholar
  32. [32]
    O.M. Belotserkovskii et. al.; Numerical investigation of modern problems in gas dynamics Izd. “Nauka”, Moscow, (1974).Google Scholar
  33. [33]
    V.F. Diachenko; On one new method of the numerical solution of nonstationary gas dynamics problems with two space variables — Zh. Vychisl. Matem. i Matem. Fiz., v.5, N.4, (1965), 680–688.Google Scholar
  34. [34]
    O.M. Belotserkovskii, Y.M. Davidov; A non—stationary “coarse particle” method for gas—dynamical computations — Zh. Vychisl. Matem. i Matem. Fiz., v.11, N.1, (1971), 182–207.Google Scholar
  35. [35]
    R.A. Gentry, R.E. Martin, J. Daly; An eulerian differencing method for insteady compressible flow problem — J. Comput. Phys., v.1, (1966), 87–118.CrossRefGoogle Scholar
  36. [36]
    O.M. Belotserkovskii, Y.M. Davidov; Computation of trans—sonic “supercritical” flows by the “coarse particle” method — Zh. Vychisl. Matem. i Matem. Fiz., v.13, N.1, (1973), 147–171.Google Scholar
  37. [37]
    O.M. Belotserkovskii; Numerical methods of some transonic aerodynamics problems — J. Comput. Phys., v.5, N.3, (1970), 587–611.CrossRefMathSciNetGoogle Scholar
  38. [38]
    O.M. Belotserkovskii; Numerical experiment in gas dynamics — Lecture Notes in Physics, Springer Verlag, N.35, (1975), 79–84.Google Scholar

Copyright information

© Springer-Verlag Wien 1975

Authors and Affiliations

  • O. M. Belotserkovskii
    • 1
  1. 1.Computing CenterAcademy of SciencesMoscowUSSR

Personalised recommendations