Incompressible Viscous Flow

  • Clive A. J. Fletcher
Chapter
Part of the Springer Series in Computational Physics book series

Abstract

In this chapter no assumption is made about the relative magnitude of the velocity components, consequently, reduced forms of the Navier-Stokes equations (Chap. 16) are not available. Instead the full Navier-Stokes equations must be considered; however, it will be assumed that the flow is incompressible.

Keywords

Stream Function Poisson Equation Unsteady Flow Neumann Boundary Condition Discrete Form 
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.
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Amsden, A.A., Harlow, F.H. (1970): J. Comput. Phys. 6, 322–325MATHADSGoogle Scholar
  2. Aregbesola, Y.A.S., Burley, D.M. (1977): J. Comput. Phys. 24, 398MATHADSGoogle Scholar
  3. Aziz, K., Heliums, J.D. (1967): Phys. Fluids 10, 314–324MATHADSGoogle Scholar
  4. Baker, A.J. (1983): Finite Element Computational Fluid Mechanics (McGraw-Hill, New York)MATHGoogle Scholar
  5. Baker, A.J., Kim, J.W., Freels, J.D., Orzechowski, J.A. (1987): Int. J. Numer. Methods Fluids 7, 1235–1260MATHADSGoogle Scholar
  6. Brachet, M.E., Meiron, D.I., Orszag, S.A., Nickel, B.G., Morf, R.H., Frisch, U. (1983): J. Fluid Mech. 130, 411–452MATHADSGoogle Scholar
  7. Briley, W.R. (1974): J. Comput. Phys. 14, 8–28MATHADSGoogle Scholar
  8. Briley, W.R., McDonald, H. (1984): J. Fluid Mech. 144, 47–77MATHADSGoogle Scholar
  9. Brooks, A.N., Hughes, T.J.R. (1982): Comput. Methods Appl. Mech. Eng. 30, 199–259ADSMathSciNetGoogle Scholar
  10. Campion-Renson, A., Crochet, M.J. (1978): Int. J. Numer. Methods Eng., 12, 1809–1818MATHGoogle Scholar
  11. Castro, I.P., Cliffe, K.A., Norgett, M.J. (1982): Int. J. Numer. Methods Fluids 2, 61–88ADSGoogle Scholar
  12. Cazalbou, J.B., Braza, M., HaMinh, H. (1983): In Proc. 3rd Int. Conf. Numer. Methods Laminar and Turbulent Flow, Seattle (Pineridge Press, Swansea) pp. 786–797Google Scholar
  13. Chorin, A.J. (1967): J. Comput. Phys. 2, 12–26MATHADSGoogle Scholar
  14. Chorin, A.J. (1968): Math. Comput. 22, 745–762MATHMathSciNetGoogle Scholar
  15. Connell, S.D., Stow, P. (1986): Comput. Fluids 14, 1–10MATHADSGoogle Scholar
  16. Davis, R.W., Moore, E.F. (1982): J. Fluid Mech. 116, 475–506MATHADSGoogle Scholar
  17. Davis, R.W., Moore, E.F., Purtell, L.P. (1984): Phys. Fluids 27, 46–57ADSGoogle Scholar
  18. Dennis, S.C.R. (1985): In 9th Int. Conf. Numer. Methods in Fluid Dynamics, ed. by Soubbaramayey, J.B. Boujot, Lecture Notes in Physics, Vol. 218 (Springer, Berlin, Heidelberg) pp. 23–36Google Scholar
  19. Dennis, S.C.R., Ingham, D.B., Cook, R.N. (1979): J. Comput. Phys. 33, 325–339MATHADSGoogle Scholar
  20. de Vahl Davis, G., Mallinson, G.D. (1976): Comput. Fluids 4, 29–43MATHADSGoogle Scholar
  21. de Vahl Davis, G., Jones, I. (1983): Int. J. Numer. Methods Fluids 3, 227–248MATHGoogle Scholar
  22. Deville, M.O. (1974): J. Comput. Phys. 15, 362–374MATHADSGoogle Scholar
  23. Dodge, P.R. (1977): AIAA J. 15, 961–965MATHADSGoogle Scholar
  24. Easton, C.R. (1972): J. Comput. Phys. 9, 375–379MATHADSGoogle Scholar
  25. Engelman, M.S. (1982): Adv. Eng. Software 4, 163–175; also FIDAP Theoretical and User’s Manuals, Fluid Dynamics International, Evanston, IllinoisGoogle Scholar
  26. Engelman, M.S., Sani, R.L., Gresho, P.M., Bercovier, M. (1982): Int. J. Numer. Methods Fluids 2, 25–42MATHADSMathSciNetGoogle Scholar
  27. Fasel, H. (1976): J. Fluid Mech. 78, 353–383ADSGoogle Scholar
  28. Fasel, H. (1978): Von Karman Institute Lecture Series 78–4, 1–90Google Scholar
  29. Fletcher, C.A.J. (1982): Comput. Methods Appl. Mech. Eng. 30, 307–322MATHADSGoogle Scholar
  30. Fletcher, C.A.J. (1984): Computational Galerkin Methods, Springer Ser. Comput. Phys. (Springer, Berlin, Heidelberg)MATHGoogle Scholar
  31. Fletcher, C.A.J., Srinivas, K. (1983): Comput. Methods Appl. Mech. Eng. 41, 299–322ADSGoogle Scholar
  32. Fletcher, C.A.J., Srinivas, K. (1984): Comput. Methods Appl. Mech. Eng. 46, 313–327MATHADSGoogle Scholar
  33. Fletcher, C.A.J., Barbuto, J. (1986a): Appl. Math. Model. 10, 176–184MATHGoogle Scholar
  34. Fletcher, C.A.J., Barbuto, J. (1986b): “Backward-Facing Cavity Flow with Suction and Blowing”, in Proc. Int. Symp. Comp. Fluid Dynamics, ed. by K. Oshima (Japan Soc. of Comp. Fluid Dynamics, Tokyo) Vol. 1, pp. 245–251Google Scholar
  35. Freitas, C.J., Street, R.L., Findikakis, A.N., Koseff, J.R. (1985): Int. J. Numer. Methods Fluids 5, 561–575MATHADSGoogle Scholar
  36. Gatski, T.B., Grosch, C.E., Rose, M.E. (1982): J. Comput. Phys. 48, 1–22MATHADSGoogle Scholar
  37. Gatski, J.B., Grosch, C.E. (1985): In 9th Int. Conf. Numer. Methods in Fluid Dynamics, ed. by Soubbaramayer, J.P. Boujot, Lecture Notes in Physics, Vol. 218 (Springer, Berlin, Heidelberg) pp. 235–239Google Scholar
  38. Ghia, K.N., Sokhey, J.S. (1977): J. Fluids Eng. 99, 640–648Google Scholar
  39. Ghia, K.N., Hankey, W.L., Hodge, J.K. (1979): AIAA J. 17, 298–301MATHADSGoogle Scholar
  40. Ghia, U., Ghia, K.N., Shin, C.T. (1982): J. Comput. Phys. 48, 387–411MATHADSGoogle Scholar
  41. Goda, K. (1979): J. Comput. Phys. 30, 76–95MATHADSGoogle Scholar
  42. Goldstein, R.J., Ericksen, V.L., Olson, R.M., Eckert, E.R.G. (1970): J. Basic Eng. 92, 732–741Google Scholar
  43. Gottlieb, D., Orszag, S.A. (1977): Numerical Analysis of Spectral Methods (SIAM, Philadelphia)MATHGoogle Scholar
  44. Gottlieb, D., Hussaini, M.V., Orszag, S.A. (1984): In Spectral Methods for Partial Differential Equations, ed. by R.G. Voigt, D. Gottlieb, M.Y. Hussaini (SIAM, Philadelphia) pp. 1–54Google Scholar
  45. Gresho, P.M., Lee, R. (1981): Comput. Fluids 9, 223–253MathSciNetGoogle Scholar
  46. Gupta, M.M., Manohar, R.P. (1979): J. Comput. Phys. 31, 265–288MATHADSMathSciNetGoogle Scholar
  47. Haltiner, G.J., Williams, R.T. (1980): Numerical Prediction and Dynamic Meteorology, 2nd ed. (Wiley, New York)Google Scholar
  48. Harlow, F.H., Welch, J.E. (1965): Phys. Fluids 8, 2182–2189MATHADSGoogle Scholar
  49. Harlow, F.H., Shannon, J.P. (1967): Science 157, 547–550ADSGoogle Scholar
  50. Hirasaki, G.J., Heliums, J.D. (1968): Q. Appl. Math. 26, 331MATHGoogle Scholar
  51. Hirasaki, G.J., Heliums, J.D. (1970): Q. Appl. Math. 28, 293MATHGoogle Scholar
  52. Hirt, C.W., Cook, J.L. (1972): J. Comput. Phys. 10, 324–340MATHADSGoogle Scholar
  53. Hirt, C.W., Nichols, B.D., Romero, N.C. (1975): “SOLA-A Numerical Solution Algorithm for Transient Fluid Flows”, Los Alamos Scientific Lab. Rep. LA-5852Google Scholar
  54. Hood, P. (1976): Int. J. Numer. Methods Eng. 10, 379–399MATHGoogle Scholar
  55. Hood, P., Taylor, C. (1974): “Navier-Stokes Equations Using Mixed Interpolation”, in Finite Element Methods in Flow Problems (University of Alabama Press, Huntsville) pp. 121–132Google Scholar
  56. Hughes, T.J.R., Liu, W.K., Brooks, A. (1979): J. Comput. Phys. 30, 1–75MATHADSMathSciNetGoogle Scholar
  57. Hussaini, M.Y., Zang, T.A. (1987): Annu. Rev. Fluid Mech. 19, 339–367ADSGoogle Scholar
  58. Israeli, M. (1972): Stud. Appl. Math. 51, 67–71MATHGoogle Scholar
  59. Jensen, V.G. (1959): Proc. R. Soc. London, Ser. A 249, 346–366ADSGoogle Scholar
  60. Kato, S., Murakami, S. (1986): “Three-Dimensional Numerical Simulation of Turbulent Air Flow in a Ventilated Room, by means of Two-Equation Model”, in Proc. Int. Symp. Comp. Fluids Dynamics, ed. by K. Oshima (Japan Soc. of Comp. Fluid Dynamics, Tokyo) Vol. 2, pp. 217–228Google Scholar
  61. Khosla, P.K., Rubin, S.G. (1974): Comput. Fluids 2, 207–209MATHGoogle Scholar
  62. Khosla, P.K., Rubin, S.G. (1983): AIAA J. 21, 1546–1551MATHADSGoogle Scholar
  63. Kim, J., Moin, P. (1985): J. Comput. Phys. 59, 308–323MATHADSMathSciNetGoogle Scholar
  64. Korczak, K.Z., Patera, A.T. (1986): J. Comput. Phys. 62, 361–382MATHADSMathSciNetGoogle Scholar
  65. Ku, H.C., Hatziavramidis, D. (1985): Comput. Fluids 13, 99–113MATHADSGoogle Scholar
  66. Ku, H.C., Taylor, T.D., Hirsh, R.S. (1987a): Comput. Fluids, 15, 195–214MATHADSGoogle Scholar
  67. Ku, H.C., Hirsh, R.S., Taylor, T.D. (1987b): J. Comput. Phys., 70, 439–462MATHADSGoogle Scholar
  68. Kwak, D., Chang, J.L.C., Shanks, S.P., Chakravarthy, S.R. (1986a): AIAA J. 24, 390–396MATHADSGoogle Scholar
  69. Kwak, D., Rogers, S.E., Kaul, U.K., Chang, J.C.L. (1986b): “A Numerical Study of Incompressible Juncture Flows”, NASA Tech. Memo 88319Google Scholar
  70. Leonard, A. (1980): J. Comput. Phys. 37, 289–335MATHADSMathSciNetGoogle Scholar
  71. Leonard, A. (1985): Annu. Rev. Fluid Mech. 17, 17–24Google Scholar
  72. Leonard, B.P. (1979): Comput. Methods Appl. Mech. Eng. 19, 59–98MATHADSGoogle Scholar
  73. Lugt, H.J., Schwiderski, E.W. (1965): Proc. R. Soc. London, Ser. A 285, 382–399ADSMathSciNetGoogle Scholar
  74. Macaraeg, M., Streett, C.L. (1986): Appl. Numer. Methods, 2, 95–108MATHMathSciNetGoogle Scholar
  75. Mallinson, G.D., de Vahl Davis, G. (1973): J. Comput. Phys. 12, 435–461MATHADSGoogle Scholar
  76. Mallinson, G.D., de Vahl Davis, G. (1977): J. Fluid Mech. 83, 1–31ADSGoogle Scholar
  77. Moin, P., Kim, J. (1980): J. Comput. Phys. 35, 381–392MATHADSMathSciNetGoogle Scholar
  78. Orlandi, P. (1987): Comput. Fluids, 15, 137–149MATHADSGoogle Scholar
  79. Orszag, S.A. (1980): J. Comput. Phys. 37, 70–92MATHADSMathSciNetGoogle Scholar
  80. Orszag, S.A., Kells, L.C. (1980): J. Fluid Mech. 96, 159–205MATHADSGoogle Scholar
  81. Orszag, S.A., Patera, A.T. (1981): Phys. Rev. Lett. 47, 832–835ADSGoogle Scholar
  82. Orszag, S.A., Patera, A.T. (1983): J. Fluid Mech. 128, 347–385MATHADSGoogle Scholar
  83. Ortega, J.M., Voigt, R.G. (1985): SIAM Rev. 27, 149–240MATHMathSciNetGoogle Scholar
  84. Oshima, K., Oshima, Y., Izutsu, N., Ishii, Y., Noguchi, T. (1986): In 10th Int. Conf. Numer. Methods in Fluid Dynamics, ed. by F.G. Zhuang, Y.L. Zhu, Lecture Notes in Physics, Vol. 264 (Springer, Berlin, Heidelberg) pp. 511–515Google Scholar
  85. Patankar, S.V. (1980): Numerical Heat Transfer and Fluid Flow (Hemisphere, Washington, D.C.)MATHGoogle Scholar
  86. Patankar, S.V., Spalding, D.B. (1972): Int J. Heat Mass Transfer 15, 1787–1806MATHGoogle Scholar
  87. Patel, N.R., Briggs, D.G. (1983): Numer. Heat Transfer 6, 383–394MATHADSGoogle Scholar
  88. Patel, M.K., Markatos, N.C. (1986): Int. J. Numer. Methods Fluids 6, 129–154MATHADSMathSciNetGoogle Scholar
  89. Patera, A.T. (1984): J. Comput. Phys. 54, 468–488MATHADSGoogle Scholar
  90. Pearson, C.E. (1965): J. Fluid Mech. 21, 611–622MATHADSGoogle Scholar
  91. Peyret, R., Taylor, T.D. (1983): Computational Methods for Fluid Flow, Springer Ser. Comput. Phys. (Springer, Berlin, Heidelberg)MATHGoogle Scholar
  92. Phillips, R.E., Schmidt, F.W. (1985): Numer. Heat Transfer 8, 573–594MATHADSGoogle Scholar
  93. Pollard, A., Siu, A.L. (1982): Comput. Methods Appl. Mech. Eng. 35, 293–313MATHADSGoogle Scholar
  94. Quartapelle, L., Valz-Gris, F. (1981): Int. J. Numer. Meth. Fluids, 1, 129–144MATHMathSciNetGoogle Scholar
  95. Raithby, G.D., Schneider, G.E. (1979): Numer. Heat Transfer 2, 417–440ADSGoogle Scholar
  96. Raithby, G.D., Galpin, P.F., Van Doormal, J.P. (1986): Numer. Heat Transfer 9, 125–142ADSGoogle Scholar
  97. Roache, P.J. (1972): Computational Fluid Dynamics (Hermosa, Albuquerque, N.M.)MATHGoogle Scholar
  98. Rubin, S.G., Khosla, P.K. (1981): Comput. Fluids 9, 163–180MATHMathSciNetGoogle Scholar
  99. Sakamoto, Y., Matuo, Y. (1980): Appl. Math. Model. 4, 67–72MATHGoogle Scholar
  100. Samarskii, A.A., Andreev, V.B. (1963): USSR Comput. Math. Math. Phys. (Engl. Transl.) 3, 1373–1378MathSciNetGoogle Scholar
  101. Sani, R.L., Gresho, P.M., Lee, R.L., Griffiths, D.F. (1981): Int. J. Numer. Methods Fluids 1, 17–43, 171–204MATHADSMathSciNetGoogle Scholar
  102. Schneider, G.E., Raithby, G.D., Yovanovich, M.M. (1978): Numer. Heat Transfer 1, 433–451ADSGoogle Scholar
  103. Shyy, W., Tong, S.S., Correa, S.M. (1985): Numer. Heat Transfer 8, 99–113MATHADSGoogle Scholar
  104. Sinha, S.N., Gupta, A.K., Oberai, M.M. (1981): AIAA J. 19, 1527–1530ADSGoogle Scholar
  105. Srinivas, K., Fletcher, C.A.J. (1984): Int. J. Numer. Methods Fluids 4, 421–439MATHADSGoogle Scholar
  106. Steger, J.L., Kutler, P. (1977): AIAA J. 15, 581–590MATHADSMathSciNetGoogle Scholar
  107. Swartztrauber, P.N. (1974): SIAM J. Numer. Anal. 11, 1136–1150ADSMathSciNetGoogle Scholar
  108. Takemoto, Y., Yamabe, H., Abe, Y., Minami, I. (1985): Trans. Jpn. Soc. Irrig. Drain. Reclam. Eng. 118, 23–31Google Scholar
  109. Takemoto, Y., Nakamura, Y., Yamabe, H., Abe, Y., Minami, I. (1986): Trans. Jpn. Soc. Irrig. Drain. Reclam. Eng. 121, 57–65Google Scholar
  110. Takemoto, Y., Nakamura, Y. (1986): “A Three-Dimensional Incompressible Flow Solver”, in 10th Int. Conf. Numer. Methods in Fluid Dynamics, ed. by F.G. Zhuang, Y.L. Zhu, Lecture Notes in Physics, Vol. 264 (Springer, Berlin, Heidelberg) pp. 594–599Google Scholar
  111. Temam, R. (1968): Bull. Soc. Math. Fr. 96, 115–152MATHMathSciNetGoogle Scholar
  112. Temam, R. (1969): Arch. Ration. Mech. Anal. 32, 377–385Google Scholar
  113. Thom, A. (1933): Proc. R. Soc. London, Ser. A 141, 651–666MATHADSGoogle Scholar
  114. Van Doormaal, J.R., Raithby, G.D. (1984): Numer. Heat Transfer 7, 147–163MATHADSGoogle Scholar
  115. Viecelli, J.A. (1971): J. Comput. Phys. 8, 119–143MATHADSGoogle Scholar
  116. Wong, A.K., Reizes, J.A. (1984): J. Comput. Phys. 55, 98–114MATHADSMathSciNetGoogle Scholar
  117. Yashchin, D., Israeli, M., Wolfshtein, M. (1984): In Proc. of Computational Techniques and Applications Conference, CTAC-83, ed. by B.J. Noye, C.A.J. Fletcher (North-Holland, Amsterdam) pp. 533–552Google Scholar
  118. Zienkiewicz, O.C. (1977): The Finite Element Method in Engineering Science, 2nd ed. (McGraw-Hill, New York)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Clive A. J. Fletcher
    • 1
  1. 1.Department of Mechanical EngineeringThe University of SydneyNew South WalesAustralia

Personalised recommendations