Analysis of the Turkel-Zwas scheme for the shallow-water equations. (English) Zbl 0669.76037

A transfer function analysis is used to analyze the Turkel-Zwas explicit large time step scheme applied to the shallow-water equations [E. Turkel and G. Zwas in: Advances in computer methods for partial differential equations. Proc. third IMACS Internat. Sympos. Comput. Meth. Partial Diff. Equ., Lehigh Univ., Bethlehem, Pennsylv., USA (1979; Zbl 0477.65067); ed. by R. Vichnevetsky and R. S. Stepleman]. The transfer function concept leads to insight into the behavior of this discretization scheme in terms of comparison between continuous and discrete amplitude, phase, and group velocity coefficients. The dependence of the distortion increases with the increase in the time-step size taken for the Turkel-Zwas scheme, which depends on the ratio between a coarse and a fine mesh. A comparison with earlier results of A. L. Schoenstadt [Naval Post-Graduate School Report NPS-53-79-001, 1978 (unpublished)] shows the Turkel-Zwas scheme to give reasonable results up to time steps three times larger than the CFL limit.


76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
65Z05 Applications to the sciences


Zbl 0477.65067
Full Text: DOI


[1] Arakawa, A.; Lamb, V. R., Computational design of the basic dynamical processes of the U.C.L.A. general circulation model, (Methods in Computational Physics, Vol 17 (1977), Academic Press: Academic Press New York), 174
[2] Gadd, A., Q.J. Roy Meteorol. Soc., 104, 569 (1978)
[3] Gadd, A., Q.J. Roy. Meteorol. Soc., 104, 583 (1978)
[4] Haltiner, G. J.; Williams, R. T., Numerical Prediction and Dynamic Meteorology, ((1980), Wiley: Wiley New York), 49
[5] Jespersen, D. C., (Proceedings, AIAA 7th Computational Fluid Dynamics Conference. Proceedings, AIAA 7th Computational Fluid Dynamics Conference, Cincinnati, OH (July 15-17 1985)), 85-1493-CP
[6] Navon, I. M.; De Villiers, R., Mon. Weather Rev., 115, No. 5, 1036 (1987)
[7] Schoenstadt, A. L., J. Comput. Phys., 23, 364 (1977)
[9] Schoenstadt, A. L., Mont. Weather Rev., 108, 1248 (1980)
[10] Turkel, E.; Zwas, G., (Vichnevetsky, R.; Stepleman, R. S., Proceedings, Third IMACS Symposium on Advances in Computer Methods for Partial Differential Equations (1979), Publications IMACS, Lehigh University)
[11] Blumen, W., Rev. Geophys. Space Phys., 10, No. 2, 458 (1972)
[12] Gill, A. E., Atmosphere-Ocean Dynamics, (International Geophysics Series, Vol. 30 (1982), Academic Press: Academic Press New York)
[13] Pedlovsky, J., Geophysical Fluid Dynamics (1982), Springer-Verlag: Springer-Verlag New York
[14] Obukhov, A. M., IZCV Akad. Nauk. SSR. Ser. Geograph-Geofiz., 13, No. 4, 281 (1949)
[15] Rossby, C. G., J. Mar. Res., 1, 239 (1938)
[16] Cahn, A., J. Meteorol., 2, 113 (1945)
[17] Rossby, C. G., J. Mar. Res., 2, 38 (1939)
[18] Phillips, N. A., Rev. Geophysics J., 1, 123 (1963)
[19] Mesinger, F.; Arakawa, a., (GARP Publishing Series, Vol. 14 (1976), WMO/ICSU Joint Organizing Committee: WMO/ICSU Joint Organizing Committee Geneva)
[20] Winninghoff, F. J., (Ph.D. thesis (1968), Department of Meteorology, University of California: Department of Meteorology, University of California Los Angeles), (unpublished)
[21] Navon, I. M., J. Comput. Phys., 52, 313 (1983)
[22] Navon, I. M.; Riphagen, H., Comput. Geosci., 12, 129 (1986)
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