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Analysis of the Turkel-Zwas scheme for the two-dimensional shallow water equations in spherical coordinates. (English) Zbl 0883.76060

A linear analysis of the shallow water equations in spherical coordinates for the Turkel-Zwas (T-Z) explicit large time-step scheme is presented. This coordinate system is more realistic in meteorology and more complicated to analyze, since the coefficients are no longer constant. The analysis suggests that the T-Z scheme must be staggered in a certain way in order to get eigenvalues and eigenfunctions approaching those of the continuous case. Numerical experiments comparing the original (unstaggered) and staggered versions of the T-Z scheme are presented.

MSC:

76M20 Finite difference methods applied to problems in fluid mechanics
76U05 General theory of rotating fluids
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
86A05 Hydrology, hydrography, oceanography

Software:

Exshall
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Full Text: DOI

References:

[1] Turkel, E.; Zwas, G., Explicit large time-step schemes for the shallow water equations, Advances in Computer Methods for Partial Differential Equations (1979), Lehigh UniversityIMACS, p. 65-
[2] Schoenstadt, A. L., A transfer function analysis of numerical schemes used to simulate geostrophic adjustment, Mon. Weather Rev., 108, 1248 (1980)
[3] Neta, B.; Navon, I. M., Analysis for the Turkel-Zwas scheme for the shallow water equations, J. Comput. Phys., 81, 277 (1989) · Zbl 0669.76037
[4] Neta, B.; DeVito, C. L., The transfer function analysis of various schemes for the two dimensional shallow water equations, Comput. Math. App., 16, 111 (1988) · Zbl 0647.76011
[5] Navon, I. M.; deVilliers, R., The application of the T-Z explicit large time step scheme to a hemispheric barotropic model with constraint restoration, Mon. Weather Rev., 115, 1036 (1987)
[6] Navon, I. M.; Yu, J., EXSHALL—A Turkel-Zwas large-time step explicit Fortran program for solving the shallow-water equations on the sphere, Comput. Geosci., 17, 1311 (1991)
[7] Stremler, F. G., Introduction to Communication Systems (1977), Addison-Wesley: Addison-Wesley Reading
[8] Steppeler, J., Analysis of group velocities of various finite element schemes, Contrib. Atmos. Phys., 62, 151 (1989)
[9] Steppeler, J.; Navon, I. M.; Lu, H.-I., Finite element schemes for extended integration of atmospheric models, J. Comput. Phys., 89, 95 (1990) · Zbl 0696.76031
[10] Neta, B., Analysis of the Turkel-Zwas scheme for the 2-D shallow water equations, (Ames, W. F.; Brezinski, C., Transactions on Scientific Computing 1988, Vols. 1.1 and 1.2: Numerical and Applied Mathematics (1989), IMACS) · Zbl 0669.76037
[11] Pedlosky, J., Geophysical Fluid Dynamics (1979), Springer-Verlag: Springer-Verlag New York · Zbl 0429.76001
[12] Longuet-Higgins, M. S., The eigenfunctions of Laplace’s tidal equations over a sphere, Phil. Trans. R. Soc. London A, 262, 511 (1968) · Zbl 0207.27501
[13] Song, Y.; Tang, T., On staggered Turkel-Zwas schemes for two-dimensional shallow water equations, Mon. Weather Rev., 122, 223 (1994)
[14] McDonald, A.; Bates, J. R., Semi-Lagrangian integration of a gridpoint shallow water model on the sphere, Mon. Weather Rev., 117, 130 (1989)
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