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Incompressible Viscous Flow

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Book cover Computational Techniques for Fluid Dynamics

Part of the book series: Springer Series in Computational Physics ((SSCP))

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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.

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References

  • Amsden, A.A., Harlow, F.H. (1970): J. Comput. Phys. 6, 322–325

    MATH  ADS  Google Scholar 

  • Aregbesola, Y.A.S., Burley, D.M. (1977): J. Comput. Phys. 24, 398

    MATH  ADS  Google Scholar 

  • Aziz, K., Heliums, J.D. (1967): Phys. Fluids 10, 314–324

    MATH  ADS  Google Scholar 

  • Baker, A.J. (1983): Finite Element Computational Fluid Mechanics (McGraw-Hill, New York)

    MATH  Google Scholar 

  • Baker, A.J., Kim, J.W., Freels, J.D., Orzechowski, J.A. (1987): Int. J. Numer. Methods Fluids 7, 1235–1260

    MATH  ADS  Google Scholar 

  • Brachet, M.E., Meiron, D.I., Orszag, S.A., Nickel, B.G., Morf, R.H., Frisch, U. (1983): J. Fluid Mech. 130, 411–452

    MATH  ADS  Google Scholar 

  • Briley, W.R. (1974): J. Comput. Phys. 14, 8–28

    MATH  ADS  Google Scholar 

  • Briley, W.R., McDonald, H. (1984): J. Fluid Mech. 144, 47–77

    MATH  ADS  Google Scholar 

  • Brooks, A.N., Hughes, T.J.R. (1982): Comput. Methods Appl. Mech. Eng. 30, 199–259

    ADS  MathSciNet  Google Scholar 

  • Campion-Renson, A., Crochet, M.J. (1978): Int. J. Numer. Methods Eng., 12, 1809–1818

    MATH  Google Scholar 

  • Castro, I.P., Cliffe, K.A., Norgett, M.J. (1982): Int. J. Numer. Methods Fluids 2, 61–88

    ADS  Google Scholar 

  • Cazalbou, J.B., Braza, M., HaMinh, H. (1983): In Proc. 3rd Int. Conf. Numer. Methods Laminar and Turbulent Flow, Seattle (Pineridge Press, Swansea) pp. 786–797

    Google Scholar 

  • Chorin, A.J. (1967): J. Comput. Phys. 2, 12–26

    MATH  ADS  Google Scholar 

  • Chorin, A.J. (1968): Math. Comput. 22, 745–762

    MATH  MathSciNet  Google Scholar 

  • Connell, S.D., Stow, P. (1986): Comput. Fluids 14, 1–10

    MATH  ADS  Google Scholar 

  • Davis, R.W., Moore, E.F. (1982): J. Fluid Mech. 116, 475–506

    MATH  ADS  Google Scholar 

  • Davis, R.W., Moore, E.F., Purtell, L.P. (1984): Phys. Fluids 27, 46–57

    ADS  Google Scholar 

  • 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. 23–36

    Google Scholar 

  • Dennis, S.C.R., Ingham, D.B., Cook, R.N. (1979): J. Comput. Phys. 33, 325–339

    MATH  ADS  Google Scholar 

  • de Vahl Davis, G., Mallinson, G.D. (1976): Comput. Fluids 4, 29–43

    MATH  ADS  Google Scholar 

  • de Vahl Davis, G., Jones, I. (1983): Int. J. Numer. Methods Fluids 3, 227–248

    MATH  Google Scholar 

  • Deville, M.O. (1974): J. Comput. Phys. 15, 362–374

    MATH  ADS  Google Scholar 

  • Dodge, P.R. (1977): AIAA J. 15, 961–965

    MATH  ADS  Google Scholar 

  • Easton, C.R. (1972): J. Comput. Phys. 9, 375–379

    MATH  ADS  Google Scholar 

  • Engelman, M.S. (1982): Adv. Eng. Software 4, 163–175; also FIDAP Theoretical and User’s Manuals, Fluid Dynamics International, Evanston, Illinois

    Google Scholar 

  • Engelman, M.S., Sani, R.L., Gresho, P.M., Bercovier, M. (1982): Int. J. Numer. Methods Fluids 2, 25–42

    MATH  ADS  MathSciNet  Google Scholar 

  • Fasel, H. (1976): J. Fluid Mech. 78, 353–383

    ADS  Google Scholar 

  • Fasel, H. (1978): Von Karman Institute Lecture Series 78–4, 1–90

    Google Scholar 

  • Fletcher, C.A.J. (1982): Comput. Methods Appl. Mech. Eng. 30, 307–322

    MATH  ADS  Google Scholar 

  • Fletcher, C.A.J. (1984): Computational Galerkin Methods, Springer Ser. Comput. Phys. (Springer, Berlin, Heidelberg)

    MATH  Google Scholar 

  • Fletcher, C.A.J., Srinivas, K. (1983): Comput. Methods Appl. Mech. Eng. 41, 299–322

    ADS  Google Scholar 

  • Fletcher, C.A.J., Srinivas, K. (1984): Comput. Methods Appl. Mech. Eng. 46, 313–327

    MATH  ADS  Google Scholar 

  • Fletcher, C.A.J., Barbuto, J. (1986a): Appl. Math. Model. 10, 176–184

    MATH  Google Scholar 

  • 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. 245–251

    Google Scholar 

  • Freitas, C.J., Street, R.L., Findikakis, A.N., Koseff, J.R. (1985): Int. J. Numer. Methods Fluids 5, 561–575

    MATH  ADS  Google Scholar 

  • Gatski, T.B., Grosch, C.E., Rose, M.E. (1982): J. Comput. Phys. 48, 1–22

    MATH  ADS  Google Scholar 

  • 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. 235–239

    Google Scholar 

  • Ghia, K.N., Sokhey, J.S. (1977): J. Fluids Eng. 99, 640–648

    Google Scholar 

  • Ghia, K.N., Hankey, W.L., Hodge, J.K. (1979): AIAA J. 17, 298–301

    MATH  ADS  Google Scholar 

  • Ghia, U., Ghia, K.N., Shin, C.T. (1982): J. Comput. Phys. 48, 387–411

    MATH  ADS  Google Scholar 

  • Goda, K. (1979): J. Comput. Phys. 30, 76–95

    MATH  ADS  Google Scholar 

  • Goldstein, R.J., Ericksen, V.L., Olson, R.M., Eckert, E.R.G. (1970): J. Basic Eng. 92, 732–741

    Google Scholar 

  • Gottlieb, D., Orszag, S.A. (1977): Numerical Analysis of Spectral Methods (SIAM, Philadelphia)

    MATH  Google Scholar 

  • 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. 1–54

    Google Scholar 

  • Gresho, P.M., Lee, R. (1981): Comput. Fluids 9, 223–253

    MathSciNet  Google Scholar 

  • Gupta, M.M., Manohar, R.P. (1979): J. Comput. Phys. 31, 265–288

    MATH  ADS  MathSciNet  Google Scholar 

  • Haltiner, G.J., Williams, R.T. (1980): Numerical Prediction and Dynamic Meteorology, 2nd ed. (Wiley, New York)

    Google Scholar 

  • Harlow, F.H., Welch, J.E. (1965): Phys. Fluids 8, 2182–2189

    MATH  ADS  Google Scholar 

  • Harlow, F.H., Shannon, J.P. (1967): Science 157, 547–550

    ADS  Google Scholar 

  • Hirasaki, G.J., Heliums, J.D. (1968): Q. Appl. Math. 26, 331

    MATH  Google Scholar 

  • Hirasaki, G.J., Heliums, J.D. (1970): Q. Appl. Math. 28, 293

    MATH  Google Scholar 

  • Hirt, C.W., Cook, J.L. (1972): J. Comput. Phys. 10, 324–340

    MATH  ADS  Google Scholar 

  • 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-5852

    Google Scholar 

  • Hood, P. (1976): Int. J. Numer. Methods Eng. 10, 379–399

    MATH  Google Scholar 

  • Hood, P., Taylor, C. (1974): “Navier-Stokes Equations Using Mixed Interpolation”, in Finite Element Methods in Flow Problems (University of Alabama Press, Huntsville) pp. 121–132

    Google Scholar 

  • Hughes, T.J.R., Liu, W.K., Brooks, A. (1979): J. Comput. Phys. 30, 1–75

    MATH  ADS  MathSciNet  Google Scholar 

  • Hussaini, M.Y., Zang, T.A. (1987): Annu. Rev. Fluid Mech. 19, 339–367

    ADS  Google Scholar 

  • Israeli, M. (1972): Stud. Appl. Math. 51, 67–71

    MATH  Google Scholar 

  • Jensen, V.G. (1959): Proc. R. Soc. London, Ser. A 249, 346–366

    ADS  Google Scholar 

  • 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. 217–228

    Google Scholar 

  • Khosla, P.K., Rubin, S.G. (1974): Comput. Fluids 2, 207–209

    MATH  Google Scholar 

  • Khosla, P.K., Rubin, S.G. (1983): AIAA J. 21, 1546–1551

    MATH  ADS  Google Scholar 

  • Kim, J., Moin, P. (1985): J. Comput. Phys. 59, 308–323

    MATH  ADS  MathSciNet  Google Scholar 

  • Korczak, K.Z., Patera, A.T. (1986): J. Comput. Phys. 62, 361–382

    MATH  ADS  MathSciNet  Google Scholar 

  • Ku, H.C., Hatziavramidis, D. (1985): Comput. Fluids 13, 99–113

    MATH  ADS  Google Scholar 

  • Ku, H.C., Taylor, T.D., Hirsh, R.S. (1987a): Comput. Fluids, 15, 195–214

    MATH  ADS  Google Scholar 

  • Ku, H.C., Hirsh, R.S., Taylor, T.D. (1987b): J. Comput. Phys., 70, 439–462

    MATH  ADS  Google Scholar 

  • Kwak, D., Chang, J.L.C., Shanks, S.P., Chakravarthy, S.R. (1986a): AIAA J. 24, 390–396

    MATH  ADS  Google Scholar 

  • Kwak, D., Rogers, S.E., Kaul, U.K., Chang, J.C.L. (1986b): “A Numerical Study of Incompressible Juncture Flows”, NASA Tech. Memo 88319

    Google Scholar 

  • Leonard, A. (1980): J. Comput. Phys. 37, 289–335

    MATH  ADS  MathSciNet  Google Scholar 

  • Leonard, A. (1985): Annu. Rev. Fluid Mech. 17, 17–24

    Google Scholar 

  • Leonard, B.P. (1979): Comput. Methods Appl. Mech. Eng. 19, 59–98

    MATH  ADS  Google Scholar 

  • Lugt, H.J., Schwiderski, E.W. (1965): Proc. R. Soc. London, Ser. A 285, 382–399

    ADS  MathSciNet  Google Scholar 

  • Macaraeg, M., Streett, C.L. (1986): Appl. Numer. Methods, 2, 95–108

    MATH  MathSciNet  Google Scholar 

  • Mallinson, G.D., de Vahl Davis, G. (1973): J. Comput. Phys. 12, 435–461

    MATH  ADS  Google Scholar 

  • Mallinson, G.D., de Vahl Davis, G. (1977): J. Fluid Mech. 83, 1–31

    ADS  Google Scholar 

  • Moin, P., Kim, J. (1980): J. Comput. Phys. 35, 381–392

    MATH  ADS  MathSciNet  Google Scholar 

  • Orlandi, P. (1987): Comput. Fluids, 15, 137–149

    MATH  ADS  Google Scholar 

  • Orszag, S.A. (1980): J. Comput. Phys. 37, 70–92

    MATH  ADS  MathSciNet  Google Scholar 

  • Orszag, S.A., Kells, L.C. (1980): J. Fluid Mech. 96, 159–205

    MATH  ADS  Google Scholar 

  • Orszag, S.A., Patera, A.T. (1981): Phys. Rev. Lett. 47, 832–835

    ADS  Google Scholar 

  • Orszag, S.A., Patera, A.T. (1983): J. Fluid Mech. 128, 347–385

    MATH  ADS  Google Scholar 

  • Ortega, J.M., Voigt, R.G. (1985): SIAM Rev. 27, 149–240

    MATH  MathSciNet  Google Scholar 

  • 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. 511–515

    Google Scholar 

  • Patankar, S.V. (1980): Numerical Heat Transfer and Fluid Flow (Hemisphere, Washington, D.C.)

    MATH  Google Scholar 

  • Patankar, S.V., Spalding, D.B. (1972): Int J. Heat Mass Transfer 15, 1787–1806

    MATH  Google Scholar 

  • Patel, N.R., Briggs, D.G. (1983): Numer. Heat Transfer 6, 383–394

    MATH  ADS  Google Scholar 

  • Patel, M.K., Markatos, N.C. (1986): Int. J. Numer. Methods Fluids 6, 129–154

    MATH  ADS  MathSciNet  Google Scholar 

  • Patera, A.T. (1984): J. Comput. Phys. 54, 468–488

    MATH  ADS  Google Scholar 

  • Pearson, C.E. (1965): J. Fluid Mech. 21, 611–622

    MATH  ADS  Google Scholar 

  • Peyret, R., Taylor, T.D. (1983): Computational Methods for Fluid Flow, Springer Ser. Comput. Phys. (Springer, Berlin, Heidelberg)

    MATH  Google Scholar 

  • Phillips, R.E., Schmidt, F.W. (1985): Numer. Heat Transfer 8, 573–594

    MATH  ADS  Google Scholar 

  • Pollard, A., Siu, A.L. (1982): Comput. Methods Appl. Mech. Eng. 35, 293–313

    MATH  ADS  Google Scholar 

  • Quartapelle, L., Valz-Gris, F. (1981): Int. J. Numer. Meth. Fluids, 1, 129–144

    MATH  MathSciNet  Google Scholar 

  • Raithby, G.D., Schneider, G.E. (1979): Numer. Heat Transfer 2, 417–440

    ADS  Google Scholar 

  • Raithby, G.D., Galpin, P.F., Van Doormal, J.P. (1986): Numer. Heat Transfer 9, 125–142

    ADS  Google Scholar 

  • Roache, P.J. (1972): Computational Fluid Dynamics (Hermosa, Albuquerque, N.M.)

    MATH  Google Scholar 

  • Rubin, S.G., Khosla, P.K. (1981): Comput. Fluids 9, 163–180

    MATH  MathSciNet  Google Scholar 

  • Sakamoto, Y., Matuo, Y. (1980): Appl. Math. Model. 4, 67–72

    MATH  Google Scholar 

  • Samarskii, A.A., Andreev, V.B. (1963): USSR Comput. Math. Math. Phys. (Engl. Transl.) 3, 1373–1378

    MathSciNet  Google Scholar 

  • Sani, R.L., Gresho, P.M., Lee, R.L., Griffiths, D.F. (1981): Int. J. Numer. Methods Fluids 1, 17–43, 171–204

    MATH  ADS  MathSciNet  Google Scholar 

  • Schneider, G.E., Raithby, G.D., Yovanovich, M.M. (1978): Numer. Heat Transfer 1, 433–451

    ADS  Google Scholar 

  • Shyy, W., Tong, S.S., Correa, S.M. (1985): Numer. Heat Transfer 8, 99–113

    MATH  ADS  Google Scholar 

  • Sinha, S.N., Gupta, A.K., Oberai, M.M. (1981): AIAA J. 19, 1527–1530

    ADS  Google Scholar 

  • Srinivas, K., Fletcher, C.A.J. (1984): Int. J. Numer. Methods Fluids 4, 421–439

    MATH  ADS  Google Scholar 

  • Steger, J.L., Kutler, P. (1977): AIAA J. 15, 581–590

    MATH  ADS  MathSciNet  Google Scholar 

  • Swartztrauber, P.N. (1974): SIAM J. Numer. Anal. 11, 1136–1150

    ADS  MathSciNet  Google Scholar 

  • Takemoto, Y., Yamabe, H., Abe, Y., Minami, I. (1985): Trans. Jpn. Soc. Irrig. Drain. Reclam. Eng. 118, 23–31

    Google Scholar 

  • Takemoto, Y., Nakamura, Y., Yamabe, H., Abe, Y., Minami, I. (1986): Trans. Jpn. Soc. Irrig. Drain. Reclam. Eng. 121, 57–65

    Google Scholar 

  • 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. 594–599

    Google Scholar 

  • Temam, R. (1968): Bull. Soc. Math. Fr. 96, 115–152

    MATH  MathSciNet  Google Scholar 

  • Temam, R. (1969): Arch. Ration. Mech. Anal. 32, 377–385

    Google Scholar 

  • Thom, A. (1933): Proc. R. Soc. London, Ser. A 141, 651–666

    MATH  ADS  Google Scholar 

  • Van Doormaal, J.R., Raithby, G.D. (1984): Numer. Heat Transfer 7, 147–163

    MATH  ADS  Google Scholar 

  • Viecelli, J.A. (1971): J. Comput. Phys. 8, 119–143

    MATH  ADS  Google Scholar 

  • Wong, A.K., Reizes, J.A. (1984): J. Comput. Phys. 55, 98–114

    MATH  ADS  MathSciNet  Google Scholar 

  • 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. 533–552

    Google Scholar 

  • Zienkiewicz, O.C. (1977): The Finite Element Method in Engineering Science, 2nd ed. (McGraw-Hill, New York)

    Google Scholar 

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  1. Department of Mechanical Engineering, The University of Sydney, New South Wales, 2006, Australia

    Dr. Clive A. J. Fletcher

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    Clive A. J. Fletcher

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Fletcher, C.A.J. (1988). Incompressible Viscous Flow. In: Fletcher, C.A.J. (eds) Computational Techniques for Fluid Dynamics. Springer Series in Computational Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-97071-9_7

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  • DOI: https://doi.org/10.1007/978-3-642-97071-9_7

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