Abstract
The results of this study have shown that: (i) direct matrix inversions are competitive with FFT's for calculating pseudo-spectral representations; (ii) all real space Poisson solvers are possible with the use of a predictor-corrector procedure; (iii) the iterative time integration scheme is very attractive for use in incompressible flows; (iv) energy conservation in stratified flow using finite difference techniques can be accomplished using a combination of conservative and Piacsek-Williams differencing; and (v) computation times for pseudo-spectral calculations are faster than finite difference calculations of equivalent accuracy.
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References
Abarbanel, S., and Zwas, G.: An iterative finite difference method for hyperbolic systems, Math. Comp., 23, 549–565, 1969.
Gary, J.: On certain finite difference schemes for hyperbolic systems, Math. Comp., 18, 1–18, 1964.
Taylor, T. D., Hirsh, R. S., Nadworny, M. M., and Kerr, J. L.: FFT vs conjugate gradient method for solution of flow equations by pseudo-spectral methods, in Proceedings of the Fourth GAMM Conference on Numerical Methods in Fluid Mechanics, H. Viviand, ed., pp 311–325, F. Vieweg, Braunschweig, 1982.
Peyret, R. and Taylor, T. D.: Computational Methods for Fluid Flow, Springer, New York, 1982.
Orszag, S.: Spectral methods for problems in complex geometries, in Numerical Methods for PDE's, pp 273–305, Academic Press, New York, 1979.
Morchoisne, Y.: Pseudo-spectral space-time calculations of incompressible viscous flows, presented at AIAA 19th Aerospace Sciences Meeting, St. Louis, January 1981.
Piacsek, S. A. and Williams, G. P., Conservation properties of Convection Difference Schemes, J.' Comp. Phys., 6, 392–405, 1970.
Myers, R. B., Taylor, T. D., and Murdock, J. W.: Pseudo-spectral simulation of a two-dimensional vortex flow in a stratified incompressible fluid, J. Comp. Phys., 43, 180–188, 1981.
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© 1982 Springer-Verlag
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Hirsh, R.S., Taylor, T.D., Nadworny, M.M., Kerr, J.L. (1982). Techniques for efficient implementation of pseudo-spectral methods and comparisons with finite difference solutions of the Navier-Stokes equations. In: Krause, E. (eds) Eighth International Conference on Numerical Methods in Fluid Dynamics. Lecture Notes in Physics, vol 170. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-11948-5_27
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DOI: https://doi.org/10.1007/3-540-11948-5_27
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