×

Resolution of the 2D Navier-Stokes equations in velocity-vorticity form by means of an influence matrix technique. (English) Zbl 0763.76046

Summary: An influence matrix technique is proposed to enforce both the continuity equation and the definition of the vorticity in the treatment of the two- dimensional incompressible Navier-Stokes equations. It is shown and supported by numerical experiments that at each time step the divergence is actually equal to zero within machine accuracy. The same result is obtained for the definition of the vorticity.

MSC:

76M20 Finite difference methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Speziale, C. G., J. Comput. Phys., 73, 476 (1987)
[2] Guevremont, G.; Habashi, W. G.; Hafez, M. M., Int. J. Num. Methods Fluids, 10, 461 (1990)
[3] Fasel, H., J. Fluid Mech., 78, 355 (1976)
[4] Dennis, S. C.R.; Ingham, D. B.; Cook, R. N., J. Comput. Phys., 33, 325 (1979)
[5] Osswald, G. A.; Ghia, K. N.; Ghia, U., (Dwoyer, D. L.; etal., Proceedings, 11th International Conference on Numerical Methods in Fluid Dynamics. Proceedings, 11th International Conference on Numerical Methods in Fluid Dynamics, Williamsburg, VA, 1988 (1989), Springer-Verlag: Springer-Verlag Berlin), 454
[6] Gatski, T. B.; Grosch, C. E.; Rose, M. E., J. Comput. Phys., 48, 1 (1982)
[7] Gatski, T. B.; Grosch, C. E.; Rose, M. E., J. Comput. Phys., 82, 298 (1989)
[8] Orlandi, P., Comput. Fluids, 15, 137 (1987)
[9] Toumi, A.; Phuoc Loc, T., (Taylor, C.; etal., Proceedings, 5th International Conference on Numerical Methods in Laminar and Turbulent Flows. Proceedings, 5th International Conference on Numerical Methods in Laminar and Turbulent Flows, Montreal, Canada, 1987 (1987), Pineridge Press: Pineridge Press Swansea, UK), 595
[10] Cottet, G. H., (Catlish, R. E., Mathematical Aspects of Vortex Methods (1988), SIAM: SIAM Providence, RI), 129
[11] Labidi, W.; Phuoc Loc, T., (Dwoyer, D. L.; etal., Proceedings, 11th International Conference on Numerical Methods in Fluids Dynamics. Proceedings, 11th International Conference on Numerical Methods in Fluids Dynamics, Williamsburg, VA (1989), Springer-Verlag: Springer-Verlag Berlin), 354
[12] Farouk, B.; Fugesi, T., Int. J. Num. Methods Fluids, 5, 1017 (1985)
[13] Stella, F.; Guj, G., Int. J. Num. Methods Fluids, 9, 1285 (1989)
[14] Daube, O.; Guermond, J. L.; Sellier, A., C. R. Acad. Sci. Paris Sir. II, 313, 377 (1991)
[15] Hockney, R., Methods Comput. Phys., 9, 135 (1970)
[16] Proskurowski, W.; Widlund, O., Math. Comput., 30, 433 (1976)
[17] Proskurowski, W., ACM Trans. Math. Software, 5, 36 (1979)
[18] Pares-Sierra, A.; Vallis, G. K., J. Comput. Phys., 82, 398 (1989)
[19] Kleiser, L.; Schumann, U., (Hirschel, E. H., Proceedings, 3rd GAMM-Conference on Numerical Methods in Fluid Mechanics. Proceedings, 3rd GAMM-Conference on Numerical Methods in Fluid Mechanics, Köln, Germany, 1979. Proceedings, 3rd GAMM-Conference on Numerical Methods in Fluid Mechanics. Proceedings, 3rd GAMM-Conference on Numerical Methods in Fluid Mechanics, Köln, Germany, 1979, Notes on Num. Fluid Mech. (1980), Vieweg: Vieweg Wiesbaden), 165
[20] Le Quérée, P.; Alziary de Roquefort, T., C.R. Acad. Sci. Paris, Sér. II, 294, 941 (1982)
[21] Le Quéré, P.; Alziary de Roquefort, T., J. Comput. Phys., 57, 210 (1985)
[22] Tuckermann, L., J. Comput. Phys., 80, 403 (1989)
[23] Dennis, S. C.R.; Quartapelle, L., J. Comput. Phys., 52, 448 (1983)
[24] Tuckermann, L., (Ph.D. thesis (1983), MIT: MIT Cambridge, MA), (unpublished)
[25] Vanel, J. M.; Peyret, R.; Bontoux, P., (Morton, K. W.; Baines, M. J., Proceedings, International Conference on Numerical Methods for Fluids Dynamics. Proceedings, International Conference on Numerical Methods for Fluids Dynamics, Reading, UK, 1985 (1986), Clarendon Press: Clarendon Press New York), 463
[26] Quartapelle, L.; Napolitano, M., J. Comput. Phys., 62, 340 (1986)
[27] Quartapelle, L.; Muzzio, A., (De Vahl Davis, G.; Fletcher, C., Proceedings, International Symposium on Computational Fluid Dynamics. Proceedings, International Symposium on Computational Fluid Dynamics, Sydney, Australia, 1987 (1988), North-Holland: North-Holland Amsterdam), 609
[28] Quartapelle, L., (Proceedings, International Conference for Computational Methods in Flow Analysis. Proceedings, International Conference for Computational Methods in Flow Analysis, Okayama, Japan (1988)), 337
[29] Glowinski, R.; Pironneau, O., SIAM Rev., 21, 167 (1979)
[30] Peyret, R.; Taylor, T. D., Computational Methods for Fluid Flows, ((1983), Springer-Verlag: Springer-Verlag New York), 151
[31] Hockney, R. W., J. Assoc. Comput. Mach., 12, 95 (1965)
[32] Fischer, D.; Golub, G.; Hald, O.; Leiva, C.; Widlund, O., Math. Comput., 28, 349 (1974)
[33] Daube, O.; Phuoc Loc, T., J. Méc., 17, 651 (1978)
[34] Escudier, M. P., Exp. Fluids, 2, 189 (1984)
[35] Lugt, H. J.; Abboud, M., J. Fluid Mech., 179, 179 (1987)
[36] Lopez, J. M., J. Fluid Mech., 221, 533 (1990)
[37] Daube, O.; Sørensen, J. N., C.R. Acad. Sci. Paris Sir. II, 308, 463 (1989)
[38] Rhie, C. M.; Chow, W. L., AIAA J., 21, 1525 (1983)
[39] Strikwerda, J. C., SIAM J. Sci. Stat. Comput., 5, 56 (1984)
[40] Schneider, G.; Raw, M., Numer. Heat Transf., 11, 363 (1987)
[41] Armfield, S. W., Comput. & Fluids, 20, 1 (1991)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.