Adaptive geometric numerical integration for point vortex dynamics.
In this paper we describe a variable stepsize integration method for the Hamiltonian dynamics of point vortices based on the explicit symplectic Zhang and Qin scheme. The adapted method is also explicit and preserves the reversible structure of the flow. In order to check the behavior of this adaptive method a numerical study of the exchange-scattering phenomenon in the three-vortex problem is made. The symmetry of the orbit and the energy evolution are discussed for the exchange-scattering model. A long-term integration of this and other models composed also of three vortices indicates that the adaptive Zhang-Qin method has good properties of efficiency and preservation of the first integrals associated with point vortex systems.
San Miguel
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Departamento de Matemática Aplicada, Universidad de Valladolid Facultad de Ciencias, Prado de la Magdalena s/n, 47005 Valladolid, Spain. asmiguel@maf.uva.es