From chaos of lines to Lagrangian structures in flux conservative fields

From chaos of lines to Lagrangian structures in flux conservative fields
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从混沌线到通量保守场中的拉格朗日结构

DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
C. Chandre
C. Chandre
中科院分区：
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文献类型：
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作者：
X. Leoncini;O. Agullo;M. Muraglia;C. Chandre

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摘要。提出了一种数值跟踪的方法
Abstract.A numerical method is proposed in order to track field lines of three-dimensional divergence free fields. Field lines are computed by a locally valid Hamiltonian mapping, which is computed using a symplectic scheme. The method is theoretically valid everywhere but at points where the field is null or infinite. For any three dimensional flux conservative field for which problematic points are sufficiently sparse, a systematic procedure is proposed and implemented. Construction of field lines is achieved by means of tracers and the introduction of various Hamiltonians adapted to the “geometrical state” each line or tracer is. The states are artificially defined by an a priori given frame of reference and Cartesian coordinates, and refer to a Hamiltonian which is locally valid at the time step to be computed. This procedure ensures the preservation of the volume (flux condition) during the iteration. This method is first tested with an ABC-type flow. Its benefits when compared to typical Runge-Kutta scheme are demonstrated. Potential use of the method to exhibit “coherent” Lagrangian structures in a chaotic setting is shown. An illustration to the computation of magnetic field lines resulting from a three-dimensional MHD simulation is also provided.