Abstract
In recent years, vortex methods have been used for numerical simulations of various flows. Vortex methods can directly simulate the time evolutions of vorticity field through Lagrangian calculation of the behavior of vortex elements discretizing vorticity fields. In order to extend the applicability of vortex methods, we propose a higher-order time integration method known as Hermite integration method in the field of non-colliding many-body systems called the gravitational N-body problem in Astrophysics. The key ideas of this method are based on derivation of the time derivatives of the Biot-Savart law and base on expanding the solution in the Taylor series. The proposed integration method is applied to simulate three and five vortex systems. Simulation results demonstrate that the proposed integration method has substantially forth-order accuracy and is able to capture the motion of an eye of the Hurricane Isabel.
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