Abstract
This paper presents a modified Goda scheme in the simulation of unsteady incompressible Navier–Stokes flows in cylindrical geometries. The study is restricted to the case of axisymmetric flows. For the justification of the robustness of our scheme some computational test cases are investigated. It turns out that by adopting the new approach, a significant accuracy improvement on both pressure and velocity can be obtained relative to the classical Goda scheme.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
Azaiez, M., Ben Belgacem, F., Grundmann, M., and Khallouf, H. (1998). Staggered grids hybrid-dual spectral element method for second order elliptic problems. Application to high-order time splitting for Navier–Stokes equations. Comp. Meth. Appl. Mech. and Engrg. 166(3/4), 183–199.
Bernardi, C., and Maday, Y. (1992). Approximations Spectrales de Problèmes aux Limites Elliptiques, Springer-Verlag.
Bernardi, C., Dauge, M., and Maday, Y. (1998). Spectral Methods for Axisymmetric Domains, Series in Applied Mathematics, Gauthier-Villars.
Canuto, C., Hussaini, M. Y., Quarteroni, A., and Zang, T. A. (1987). Spectral Methods in Fluid Dynamics, Springer-Verlag.
Chorin, A. (1968). Numerical Simulation of the Navier–Stokes Equations. Math. Comput. 22, 745–762.
Goda, K. (1979). A multistep technique with implicit difference schemes for calculating two and three dimensional cavity flows. J. Comput. Physics. 30, 76–95.
Guermond, J.-L. (1998). Un résultat de convergence d'ordre deux en temps pour l'approximation des équations de Navier–Stokes par une technique de projection incrémentale. Modél. Math. Anal. Numér. 30, 169–189.
Lynch, R. E., Rice, J. R., and Thomas, D. H. (1964). Direct solution of partial difference equations by tensor product methods. Numer. Math. 6, 185–199.
Quarteroni, A., Saleri, F. and Veneziani, A. (2000). Factorization methods for the numerical approximation of Navier–Stokes equations. Comp. Methods. Appl. Mech. Engrg. 188, 505–526.
Temam, R. (1964). Une méthode d'approximation de la solution des équations de Navier–Stokes. Bull. Soc. Math. France 98, 115–152.
Timmermans, L. J. P., Minev, P. D., and Van de Vosse, F. N. (1996). An approximate projection scheme for incompressible flow using spectral elements. Int. J. Numer. Meth. Fluids. 22, 673–688.
Vandeven (1989). Compatibilité des espaces discrets pour l'approxiamtion spectrale du problème de Stokes périodiques/non périodique. Modél. Math. et Anal. Numér. 23, 649–688.
Van de Vosse, F. N., Minev, P. D., and Timmermans, L. J. P. (1996). A spectral element projection scheme for incompressible flow with application to shear-layer stability studies. In Ilin, A. V., and Scott, R. (eds.), Houston J. Mathematics, Proceedings 3rd ICOSAHOM, pp. 295–303.
Van Kan (1986). A second-order accurate pressure-correction scheme for viscous incompressible flow. SIAM J. Sci. Stat. Comput. 7, 870–891.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Azaiez, M. A Spectral Element Projection Scheme for Incompressible Flow with Application to the Unsteady Axisymmetric Stokes Problem. Journal of Scientific Computing 17, 573–584 (2002). https://doi.org/10.1023/A:1015170629969
Issue Date:
DOI: https://doi.org/10.1023/A:1015170629969