Abstract
Explicit symplectic integration schemes for the Arnold-Beltrami-Childress flows are presented and compared to a fourth order Runge-Kutta method. For moderate accuracy the symplectic schemes are more efficient for the calculation of stable orbits. The structure of the Hamiltonian prevents the implementation of symplectic methods with constant time steps.
Zusammenfassung
Es werden explizite symplektische Integrationsverfahren für Arnold-Beltrami-Childress Strömungen beschrieben und mit einer Runge-Kutta Methode vierte Ordnung verglichen. Für moderate Genauigkeit sind die symplektischen Verfahren leistungfähiger für die Berechnung stabiler Bahnen. Die Struktur der Hamilton-Funktion verhindert die Implementierung symplektischer Methoden mit konstanten Zeitschritten.
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Tippett, M.K. Symplectic integration schemes for the ABC flow. Computing 57, 63–75 (1996). https://doi.org/10.1007/BF02238358
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DOI: https://doi.org/10.1007/BF02238358