A critical review of numerical solution of Navier-Stokes equations

  • Sin-I Cheng
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 41)


Flow Field Shock Front Truncation Error Mesh Point Difference Formulation 
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.

Specific references

  1. 1.
    Courant, R., Friedricks, K. O., and Levy, H., Über die Partiellen Differenzen gleichungen der Mathemetischen physik, Mathematics Annual, Vol. 100 (1928).Google Scholar
  2. 2.
    Fromm, J. E., “The Time Dependent Flow of An Incompressible Fluid” Methods in Computational Physics, Vol. 3, Academic Press, N. Y. (1964).Google Scholar
  3. 3.
    Cheng, S. I., “The Numerical Integration of Navier-Stokes Equations,” J. of American Institute of Aeronautical and Astronautics, Vol. 8, No. 12, (1970).Google Scholar
  4. 4.
    Hirt, C. W., “Heutristic Stability Theory for Finite Difference Equations,” J. of Computational Physics, Vol. 2, (1968).Google Scholar
  5. 5.
    Yanenko, N. N., The Method of Fractional Steps, English translation by M. Holt, Springer Verlag (1971).Google Scholar
  6. 6.
    Peaceman, D. W. and Rachford, H. H., Jr., “The Numerical Solution of Parabolic and Elliptic Differential Equations,” Journ, Soc. Industrial and Applied Mathematics, Vol. 3, (1955).Google Scholar
  7. 7.
    Douglas, J. and Gunn, J., “A General Formulation of Alternating Direction Methods,” Numerical Mathematics, Vol. 6, (1964).Google Scholar
  8. 8.
    Kreiss, H. O. and Oliger, J., “Comparison of Accurate Methods for the Integration of Hyperbolic Equations,” Tellus XXIV 3 (1972).Google Scholar
  9. 9.
    Fromm, J. E., “A Numerical Study of Buoyancy Driven Flows in Room Enclosures,” Proceedings of the 2nd International Conference on Numerical Methods in Fluid Dynamics, Berkeley, California, Sept. (1970), Springer Verlag.Google Scholar
  10. 10.
    Cheng, S. I., “Accuracy of Difference Formulation of Navier-Stokes Equations” The Physics of Fluids, Supplement II, Dec. 1969.Google Scholar
  11. 11.
    Fromm, J. E., “Practical Importance of Convective Difference Approximations of Reduced Dispersion,” The Physics of Fluids, Supplement II, Dec. 1969.Google Scholar
  12. 12.
    Moretti, G. and Bleich, G., “Three Dimensional Flow around Blunt Bodies,” Jour. of American Institute of Aeronautics and Astronautics, Vol. 5, No. 9, (1967).Google Scholar
  13. 13.
    v. Neumann, J. and Richtmeyer, R. D., “A Method for the Numerical Calculations of Hydrodynamic Shocks,” Jour. of Applied Physics, Vol. 21, (1950).Google Scholar
  14. 14.
    Lax, P. and Wendroff, B., “Systems of Conservations Laws,” Communications on Pure and Applied Mathematics, Vol. 13, (1960).Google Scholar
  15. 15.
    Thoman, D. C. and Szewczyk, A. A., “Time Dependent Viscous Flow over a Circular Cylinder,” The Physics of Fluids, Vol. 12, (1969).Google Scholar
  16. 16.
    Allen, J. and Cheng, S. I., “Numerical Solutions of the Compressible Navier-Stokes Equation for the Laminar Near Wake,” The Physics of Fluids, Vol. 13, No. 1, (1970).Google Scholar
  17. 17.
    Brailovskaya, I. Y., “A Difference Scheme for the Numerical Solution of the Two-Dimensional Unsteady Navier-Stokes Equations for a Compressible Gas,” Soviet Physics Doklady, Vol. 10, No. 2, Aug., (1965).Google Scholar
  18. 18.
    Cheng, S. I. and Chen, J. H., “Finite Difference Treatment of Strong Shock over a Sharp Leading Edge with Navier-Stokes Equations,” Proc. of 3rd International Conference on Numberical Methods in Fluid Mechanics, Vol II, held in Paris, France, July 1972, Springer-Verlag, Berlin.Google Scholar
  19. 19.
    Messina, N. A. and Cheng, S. I., “A Study of the Computation of Regular Shock Reflection with Navier-Stokes Equations,” presented at the Symposium on Application of Computers to Fluid Dynamics Analysis and Design, PolyTech. Institute of Brooklyn, Jan. 1973.Google Scholar
  20. 20.
    Jenson, V. G., “Viscous Flow Round a Sphere at Low Reynolds Number,” Proc. of Roy. Soc. London, A249, (1959).Google Scholar
  21. 21.
    Hamielec, A. E., Hoffman, T. W., and Ross, L. L., “Numerical Solution of the Navier-Stokes Equations for Flow Past Non-Solid Spheres,” Journal of American Institute of Chemical Engineers, Vol. 13, No. 2, March, 1967.Google Scholar
  22. 22.
    Rimon, Y. and Cheng, S. I., “Numerical Solution of a Uniform Flow over a Sphere at Intermediate Reynolds Numbers,” The Physics of Fluids, Vol. 12, No. 5, (1969).Google Scholar
  23. 23.
    Taneda, S., “Studies on Wake Vortices, Experimental Investigation of the Wake Behind a Sphere at Low Reynolds Numbers,” Journal of the Physical Society of Japan, Vol. 1, (1956).Google Scholar
  24. 24.
    Chorin, A. J., “Computational Aspects of the Turbulence Problem,” Proc. of the Second International Conference on Numerical Methods in Fluid Dynamics, held at Berkeley, California, U.S.A., Sept. 1970.Google Scholar
  25. 25.
    Daly, B. J. and Harlow, F. H., “Inclusion of Turbulence Effects in Numerical Fluid Dynamics,” Proc: of the Second International Conference on Numerical Methods in Fluid Dynamics, held at Berkeley, California, U.S.A. Sept. 1970.Google Scholar
  26. 26.
    Orzag, S., “Numerical Simulation of Turbulence,” (Fourier or Spectral Method), Proc. of Symposium on Statistical Models and Turbulence, held at San Diego, California, U.S.A., July 1971.Google Scholar
  27. 27.
    Ross, B. B. and Cheng, S. I., “PracticalA Numerical Solution of the Planar Supersonic Near Wake with its Error Analysis,” Proc. of the Second International Conference on Numerical Methods in Fluid Dynamics, held at Berkeley, California, Sept. 1970.Google Scholar
  28. 28.
    Carter, J. E., “The Navier-Stokes Equations for the Supersonic Laminar Flow over a Two-Dimensional Compression Corner,” NASA TR R385, July 1972.Google Scholar
  29. 29.
    Cheng, S. I. and Chen, J. H., “Slips, Friction, and Heat Transfer Laws in Merged Regimes,” to appear in The Physics of Fluids.Google Scholar

Copyright information

© Springer-Verlag 1975

Authors and Affiliations

  • Sin-I Cheng
    • 1
  1. 1.Department of Aerospace and Mechanical SciencesPrinceton UniversityUSA

Personalised recommendations