Numerical Analysis

  • Demetri P. Telionis
Part of the Springer Series in Computational Physics book series (SCIENTCOMP)


This monograph is addressed to physicists and engineers with background in fluid mechanics and some familiarity with numerical analysis. No special sections are included to introduce the reader to basic concepts of fluid mechanics. However, since the monograph appears as a volume of a series in Computational Physics, it is perhaps pertinent here to include some fundamental concepts, formulas, and theorems on numerical methods.


Truncation Error Discretization Error Implicit Scheme Time Plane Rectangular Mesh 
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  1. Belcher, B. J., Burggraf, O. R., Cooke, J. C., Robins, A. J., and Stewartson, K., 1972. In Recent Research of Unsteady Boundary Layers, ed. Eichelbrenner, E. A., 1444–1465.Google Scholar
  2. Brown, S. N., and Stewartson, K., 1969. In Annual Review of Fluid Mechanics, ed. Sears, W. R., Annual Reviews, Inc., 1, 45–72.Google Scholar
  3. Carnahan, B., Luther, H. A., and Wilkes, J. O., 1969. Applied Numerical Methods, Wiley, New York.zbMATHGoogle Scholar
  4. Carter, J. E., 1974. AIAA Paper No. 74–583.Google Scholar
  5. Catherall, D., and Mangier, K. W., 1966. J. Fluid Mech., 26, 163–182.ADSCrossRefGoogle Scholar
  6. Cebeci, T., 1977. Proc. R. Soc. Lond., A355, 225–238MathSciNetADSGoogle Scholar
  7. Courant, R., Friedrichs, K. O., and Lewy, H., 1928. Math. Annalen., 100, 32–74.MathSciNetADSzbMATHCrossRefGoogle Scholar
  8. Davis, R. T., Whitehead, R. E., and Wornom, S. F., 1970. “The Development of an Incompressible Boundary-Layer Theory Valid to Second Order,” Va. Poly. Inst. & State Univ. Eng. Report, VPI-E-70–1.Google Scholar
  9. Davis, R. T., 1974. “A Study of the Use of Optimal Coordinates in the Solution of the Navier-Stokes Equations,” Univ. of Cincinnati, Report No. AFL 74–12–14.Google Scholar
  10. Dean, W. R., 1950. Proc. Cambridge Philos. Soc., 46, 293–306.MathSciNetADSzbMATHCrossRefGoogle Scholar
  11. Dwyer, H. A., 1968. AIAA J., 6, 2447–2448.ADSCrossRefGoogle Scholar
  12. Eddy, E. P., 1949, “Stability in the Numerical Solution of Initial Value Problems in Partial Differential Equations,” NOLM 10232, Naval Ordinace Laboratory, White Oak, Silver Spring, Maryland.Google Scholar
  13. Farn, C. L. S., and Arpaci, V. S., 1966. AIAA J., 4 730–732.CrossRefGoogle Scholar
  14. Fromm, J. E., 1964. Meth. Comp. Physics, 3, 345–382.Google Scholar
  15. Ghia, U., and Davis, R. T., 1974. AIAA J., 12, 1659–1665.ADSzbMATHCrossRefGoogle Scholar
  16. Guirand, J. P., 1969. C R. Acad. Sci. Paris, 268, 239–241.Google Scholar
  17. Hall, M. G., 1969. Proc Roy. Soc. Lond. A310, 401–414.ADSGoogle Scholar
  18. Hirt, C. W., 1965. AIAA Paper No. 65–3.Google Scholar
  19. Isaacson, E., and Keller, H. B., 1966. Analysis of Numerical Methods, Wiley, New York.zbMATHGoogle Scholar
  20. Kaplun, S., 1954. ZAMP 5, 111–135.MathSciNetADSzbMATHCrossRefGoogle Scholar
  21. Keller, H. B., 1969. SIAM J. Num. Anal., 6, 8–30.ADSzbMATHCrossRefGoogle Scholar
  22. Keller, H. B., 1971. In Numerical Solution of Partial Differential Equations, ed. Hubbard, B., 2, 327–350.Google Scholar
  23. Keller, H. B., 1975. In Lecture Notes in Physics, Proceedings of Fourth International Conference on Numerical Methods in Fluid Dynamics, 1–21, Springer, Colorado.CrossRefGoogle Scholar
  24. Keller, H. B. 1978. Ann. Rev. Fluid. Mech., 10, 417–433.ADSCrossRefGoogle Scholar
  25. Keller, H. B., and Cebeci, T., 1971. In Lecture Notes in Physics, Proceedings of Second International Conference on Numerical Methods in Fluid Dynamics, Springer, Berlin.Google Scholar
  26. Klemp, J. B., and Acrivos, A., 1971. J. Fluid Mech., 53, 177–191.ADSCrossRefGoogle Scholar
  27. Klineberg, J. M., and Steger, J. L., 1974. AIAA Paper No. 74–94.Google Scholar
  28. Lax, P. D., and Richtmyer, R. D., 1956. Comm. Pure Appl Math., 9, 267–293.MathSciNetzbMATHCrossRefGoogle Scholar
  29. Mehta, U. B., 1972. “Starting Vortex, Separation Bubbles and Stall-0 Numerical Study of Laminar Unsteady Flow Around an Airfoil,” Ph.D. Thesis, Illinois Institute of Technology.Google Scholar
  30. Mehta, U. B., and Lavan, Z., 1975. J. Fluid Mech., 67, 227–256.ADSzbMATHCrossRefGoogle Scholar
  31. Moore, F. K., 1957. In Boundary Layer Research, ed. Görtier, H., 296–311, Springer, Berlin.Google Scholar
  32. Nash, J. F., Carr, L. W., and Singleton, R. E., 1975. AIAA J., 13, 167–172.ADSCrossRefGoogle Scholar
  33. Nickel, K., 1958. Arch. Rat. Mech Anal., 2, 1–31.MathSciNetzbMATHCrossRefGoogle Scholar
  34. O’Brien, G. G., Hyman, M. A., and Kaplan, S., 1951. J. Math. Physics, 29, 223–251.MathSciNetzbMATHGoogle Scholar
  35. Phillips, J. H., and Ackerberg, R. C., 1973. J. Fluid Mech., 58, 561–579.ADSzbMATHCrossRefGoogle Scholar
  36. Robins, A. J., 1970. Ph.D. Thesis, Bristol University.Google Scholar
  37. Richtmyer, R. D., 1957. Difference Methods for Initial-Value Problems, Interscience, New York.zbMATHGoogle Scholar
  38. Richtmyer, R. D., and Morton, K. W., 1967. Difference Methods for Initial Value Problems, second edition, Wiley, New York.zbMATHGoogle Scholar
  39. Roache, P. J., 1972. Computational Fluid Dynamics, Hermosa Publishers, Albuquerque.zbMATHGoogle Scholar
  40. Rott, N., 1956. Q. Appl Math., 13, 444–451.MathSciNetzbMATHGoogle Scholar
  41. Sears, W. R., 1956. J. Aerosol Sci., 23, 490–499.MathSciNetzbMATHGoogle Scholar
  42. Shen, S. F., 1978. Adv. Appl. Mech., 18, 177–220.ADSzbMATHCrossRefGoogle Scholar
  43. Shen, S. F., and Nenni, J. P., 1975. In Unsteady Aerodynamics, ed. Kinney, R. B., 1, 245–259.Google Scholar
  44. Smith, G. D., 1965. Numerical Solution of Partial Differential Equations, Oxford Univ. Press, New York and London.zbMATHGoogle Scholar
  45. Stewartson, K., 1960. In Advances in Applied Mechanics, eds. Dryden, H. L., and Von Karman, T., 6, 1–37, Academic Press, New York.Google Scholar
  46. Telionis, D. P., and Werle, M. J., 1973. J. Appl. Mech., 95, 369–374.CrossRefGoogle Scholar
  47. Telionis, D. P., and Tsahalis, D. Th., 1974a. AIAA J., 12, 1469–1476.ADSzbMATHCrossRefGoogle Scholar
  48. Telionis, D. P., and Tsahalis, D. Th. 1974b. Acta Astron., 1, 1487–1505.zbMATHCrossRefGoogle Scholar
  49. Telionis, D. P., Tsahalis, D. Th., and Werle, M. J., 1973. Phys. Fluids, 16, 968–973.ADSzbMATHCrossRefGoogle Scholar
  50. Thorn, A., and Apelt, C. J., 1961. Field Computations in Engineering and Physics, C. Van Nostrand, Princeton, New Jersey.Google Scholar
  51. Thoman, D. C., and Szewczyk, A. A., 1969. Phys. Fluids, Suppl. II, 76–86.ADSGoogle Scholar
  52. Thompson, R. J., 1964. J. Soc. Indust. Appl. Math., 12, 189.MathSciNetzbMATHCrossRefGoogle Scholar
  53. Wang, K. C., 1975. Phys. Fluids, 18, 951–955.ADSzbMATHCrossRefGoogle Scholar
  54. Werle, M. J., and Bertke, S. D., 1972. AIAA J., 10, 1250–1252.ADSzbMATHCrossRefGoogle Scholar
  55. Werle, M. J., and Davis, R. T., 1972. J. Appl. Mech., 39, 7–12.ADSzbMATHCrossRefGoogle Scholar
  56. Williams, J. C., and Johnson, W. D., 1974a. AIAA J., 12, 1388–1393.ADSzbMATHCrossRefGoogle Scholar
  57. Williams, J. C., and Johnson, W. D., 1974b. AIAA J., 12, 1427–1429.ADSzbMATHCrossRefGoogle Scholar
  58. Wirz, H. J., 1975. In Progress in Numerical Fluid Dynamics, Lecture Notes in Physics, ed. Wirz, H. J., 41, 442–476, Springer, New York.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag New York Inc. 1981

Authors and Affiliations

  • Demetri P. Telionis
    • 1
  1. 1.Department of Engineering Science and MechanicsVirginia Polytechnic Institute and State UniversityBlacksburgUSA

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