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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Amsden, A.A., Harlow, F.H. (1970): J. Comput. Phys. 6, 322–325
Aregbesola, Y.A.S., Burley, D.M. (1977): J. Comput. Phys. 24, 398
Aziz, K., Heliums, J.D. (1967): Phys. Fluids 10, 314–324
Baker, A.J. (1983): Finite Element Computational Fluid Mechanics (McGraw-Hill, New York)
Baker, A.J., Kim, J.W., Freels, J.D., Orzechowski, J.A. (1987): Int. J. Numer. Methods Fluids 7, 1235–1260
Brachet, M.E., Meiron, D.I., Orszag, S.A., Nickel, B.G., Morf, R.H., Frisch, U. (1983): J. Fluid Mech. 130, 411–452
Briley, W.R. (1974): J. Comput. Phys. 14, 8–28
Briley, W.R., McDonald, H. (1984): J. Fluid Mech. 144, 47–77
Brooks, A.N., Hughes, T.J.R. (1982): Comput. Methods Appl. Mech. Eng. 30, 199–259
Campion-Renson, A., Crochet, M.J. (1978): Int. J. Numer. Methods Eng., 12, 1809–1818
Castro, I.P., Cliffe, K.A., Norgett, M.J. (1982): Int. J. Numer. Methods Fluids 2, 61–88
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
Chorin, A.J. (1967): J. Comput. Phys. 2, 12–26
Chorin, A.J. (1968): Math. Comput. 22, 745–762
Connell, S.D., Stow, P. (1986): Comput. Fluids 14, 1–10
Davis, R.W., Moore, E.F. (1982): J. Fluid Mech. 116, 475–506
Davis, R.W., Moore, E.F., Purtell, L.P. (1984): Phys. Fluids 27, 46–57
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
Dennis, S.C.R., Ingham, D.B., Cook, R.N. (1979): J. Comput. Phys. 33, 325–339
de Vahl Davis, G., Mallinson, G.D. (1976): Comput. Fluids 4, 29–43
de Vahl Davis, G., Jones, I. (1983): Int. J. Numer. Methods Fluids 3, 227–248
Deville, M.O. (1974): J. Comput. Phys. 15, 362–374
Dodge, P.R. (1977): AIAA J. 15, 961–965
Easton, C.R. (1972): J. Comput. Phys. 9, 375–379
Engelman, M.S. (1982): Adv. Eng. Software 4, 163–175; also FIDAP Theoretical and User’s Manuals, Fluid Dynamics International, Evanston, Illinois
Engelman, M.S., Sani, R.L., Gresho, P.M., Bercovier, M. (1982): Int. J. Numer. Methods Fluids 2, 25–42
Fasel, H. (1976): J. Fluid Mech. 78, 353–383
Fasel, H. (1978): Von Karman Institute Lecture Series 78–4, 1–90
Fletcher, C.A.J. (1982): Comput. Methods Appl. Mech. Eng. 30, 307–322
Fletcher, C.A.J. (1984): Computational Galerkin Methods, Springer Ser. Comput. Phys. (Springer, Berlin, Heidelberg)
Fletcher, C.A.J., Srinivas, K. (1983): Comput. Methods Appl. Mech. Eng. 41, 299–322
Fletcher, C.A.J., Srinivas, K. (1984): Comput. Methods Appl. Mech. Eng. 46, 313–327
Fletcher, C.A.J., Barbuto, J. (1986a): Appl. Math. Model. 10, 176–184
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
Freitas, C.J., Street, R.L., Findikakis, A.N., Koseff, J.R. (1985): Int. J. Numer. Methods Fluids 5, 561–575
Gatski, T.B., Grosch, C.E., Rose, M.E. (1982): J. Comput. Phys. 48, 1–22
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
Ghia, K.N., Sokhey, J.S. (1977): J. Fluids Eng. 99, 640–648
Ghia, K.N., Hankey, W.L., Hodge, J.K. (1979): AIAA J. 17, 298–301
Ghia, U., Ghia, K.N., Shin, C.T. (1982): J. Comput. Phys. 48, 387–411
Goda, K. (1979): J. Comput. Phys. 30, 76–95
Goldstein, R.J., Ericksen, V.L., Olson, R.M., Eckert, E.R.G. (1970): J. Basic Eng. 92, 732–741
Gottlieb, D., Orszag, S.A. (1977): Numerical Analysis of Spectral Methods (SIAM, Philadelphia)
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
Gresho, P.M., Lee, R. (1981): Comput. Fluids 9, 223–253
Gupta, M.M., Manohar, R.P. (1979): J. Comput. Phys. 31, 265–288
Haltiner, G.J., Williams, R.T. (1980): Numerical Prediction and Dynamic Meteorology, 2nd ed. (Wiley, New York)
Harlow, F.H., Welch, J.E. (1965): Phys. Fluids 8, 2182–2189
Harlow, F.H., Shannon, J.P. (1967): Science 157, 547–550
Hirasaki, G.J., Heliums, J.D. (1968): Q. Appl. Math. 26, 331
Hirasaki, G.J., Heliums, J.D. (1970): Q. Appl. Math. 28, 293
Hirt, C.W., Cook, J.L. (1972): J. Comput. Phys. 10, 324–340
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
Hood, P. (1976): Int. J. Numer. Methods Eng. 10, 379–399
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
Hughes, T.J.R., Liu, W.K., Brooks, A. (1979): J. Comput. Phys. 30, 1–75
Hussaini, M.Y., Zang, T.A. (1987): Annu. Rev. Fluid Mech. 19, 339–367
Israeli, M. (1972): Stud. Appl. Math. 51, 67–71
Jensen, V.G. (1959): Proc. R. Soc. London, Ser. A 249, 346–366
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
Khosla, P.K., Rubin, S.G. (1974): Comput. Fluids 2, 207–209
Khosla, P.K., Rubin, S.G. (1983): AIAA J. 21, 1546–1551
Kim, J., Moin, P. (1985): J. Comput. Phys. 59, 308–323
Korczak, K.Z., Patera, A.T. (1986): J. Comput. Phys. 62, 361–382
Ku, H.C., Hatziavramidis, D. (1985): Comput. Fluids 13, 99–113
Ku, H.C., Taylor, T.D., Hirsh, R.S. (1987a): Comput. Fluids, 15, 195–214
Ku, H.C., Hirsh, R.S., Taylor, T.D. (1987b): J. Comput. Phys., 70, 439–462
Kwak, D., Chang, J.L.C., Shanks, S.P., Chakravarthy, S.R. (1986a): AIAA J. 24, 390–396
Kwak, D., Rogers, S.E., Kaul, U.K., Chang, J.C.L. (1986b): “A Numerical Study of Incompressible Juncture Flows”, NASA Tech. Memo 88319
Leonard, A. (1980): J. Comput. Phys. 37, 289–335
Leonard, A. (1985): Annu. Rev. Fluid Mech. 17, 17–24
Leonard, B.P. (1979): Comput. Methods Appl. Mech. Eng. 19, 59–98
Lugt, H.J., Schwiderski, E.W. (1965): Proc. R. Soc. London, Ser. A 285, 382–399
Macaraeg, M., Streett, C.L. (1986): Appl. Numer. Methods, 2, 95–108
Mallinson, G.D., de Vahl Davis, G. (1973): J. Comput. Phys. 12, 435–461
Mallinson, G.D., de Vahl Davis, G. (1977): J. Fluid Mech. 83, 1–31
Moin, P., Kim, J. (1980): J. Comput. Phys. 35, 381–392
Orlandi, P. (1987): Comput. Fluids, 15, 137–149
Orszag, S.A. (1980): J. Comput. Phys. 37, 70–92
Orszag, S.A., Kells, L.C. (1980): J. Fluid Mech. 96, 159–205
Orszag, S.A., Patera, A.T. (1981): Phys. Rev. Lett. 47, 832–835
Orszag, S.A., Patera, A.T. (1983): J. Fluid Mech. 128, 347–385
Ortega, J.M., Voigt, R.G. (1985): SIAM Rev. 27, 149–240
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
Patankar, S.V. (1980): Numerical Heat Transfer and Fluid Flow (Hemisphere, Washington, D.C.)
Patankar, S.V., Spalding, D.B. (1972): Int J. Heat Mass Transfer 15, 1787–1806
Patel, N.R., Briggs, D.G. (1983): Numer. Heat Transfer 6, 383–394
Patel, M.K., Markatos, N.C. (1986): Int. J. Numer. Methods Fluids 6, 129–154
Patera, A.T. (1984): J. Comput. Phys. 54, 468–488
Pearson, C.E. (1965): J. Fluid Mech. 21, 611–622
Peyret, R., Taylor, T.D. (1983): Computational Methods for Fluid Flow, Springer Ser. Comput. Phys. (Springer, Berlin, Heidelberg)
Phillips, R.E., Schmidt, F.W. (1985): Numer. Heat Transfer 8, 573–594
Pollard, A., Siu, A.L. (1982): Comput. Methods Appl. Mech. Eng. 35, 293–313
Quartapelle, L., Valz-Gris, F. (1981): Int. J. Numer. Meth. Fluids, 1, 129–144
Raithby, G.D., Schneider, G.E. (1979): Numer. Heat Transfer 2, 417–440
Raithby, G.D., Galpin, P.F., Van Doormal, J.P. (1986): Numer. Heat Transfer 9, 125–142
Roache, P.J. (1972): Computational Fluid Dynamics (Hermosa, Albuquerque, N.M.)
Rubin, S.G., Khosla, P.K. (1981): Comput. Fluids 9, 163–180
Sakamoto, Y., Matuo, Y. (1980): Appl. Math. Model. 4, 67–72
Samarskii, A.A., Andreev, V.B. (1963): USSR Comput. Math. Math. Phys. (Engl. Transl.) 3, 1373–1378
Sani, R.L., Gresho, P.M., Lee, R.L., Griffiths, D.F. (1981): Int. J. Numer. Methods Fluids 1, 17–43, 171–204
Schneider, G.E., Raithby, G.D., Yovanovich, M.M. (1978): Numer. Heat Transfer 1, 433–451
Shyy, W., Tong, S.S., Correa, S.M. (1985): Numer. Heat Transfer 8, 99–113
Sinha, S.N., Gupta, A.K., Oberai, M.M. (1981): AIAA J. 19, 1527–1530
Srinivas, K., Fletcher, C.A.J. (1984): Int. J. Numer. Methods Fluids 4, 421–439
Steger, J.L., Kutler, P. (1977): AIAA J. 15, 581–590
Swartztrauber, P.N. (1974): SIAM J. Numer. Anal. 11, 1136–1150
Takemoto, Y., Yamabe, H., Abe, Y., Minami, I. (1985): Trans. Jpn. Soc. Irrig. Drain. Reclam. Eng. 118, 23–31
Takemoto, Y., Nakamura, Y., Yamabe, H., Abe, Y., Minami, I. (1986): Trans. Jpn. Soc. Irrig. Drain. Reclam. Eng. 121, 57–65
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
Temam, R. (1968): Bull. Soc. Math. Fr. 96, 115–152
Temam, R. (1969): Arch. Ration. Mech. Anal. 32, 377–385
Thom, A. (1933): Proc. R. Soc. London, Ser. A 141, 651–666
Van Doormaal, J.R., Raithby, G.D. (1984): Numer. Heat Transfer 7, 147–163
Viecelli, J.A. (1971): J. Comput. Phys. 8, 119–143
Wong, A.K., Reizes, J.A. (1984): J. Comput. Phys. 55, 98–114
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
Zienkiewicz, O.C. (1977): The Finite Element Method in Engineering Science, 2nd ed. (McGraw-Hill, New York)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1988 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/978-3-642-97071-9_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-97073-3
Online ISBN: 978-3-642-97071-9
eBook Packages: Springer Book Archive