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    This study introduces a new method for visualizing fluid flow vortices using interactive local reference frames. It accurately extracts Lagrangian vortex core lines with controllable numerical error.

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    Area of Science:

    • Fluid Dynamics
    • Computational Science
    • Scientific Visualization

    Background:

    • Detecting and visualizing vortex structures in unsteady 2D fluid flows is crucial for understanding complex fluid phenomena.
    • Existing methods may lack accuracy or interactivity in identifying and tracking vortex core lines.

    Purpose of the Study:

    • To develop and present a novel, interactive method for detecting and visualizing vortex structures in unsteady 2D fluid flows.
    • To enable accurate extraction of Lagrangian vortex core lines with user-steered control and controllable numerical error.

    Main Methods:

    • Employs interactive local reference frame estimation to minimize the time derivative of the flow field.
    • Utilizes a user-steered 'vortex lens' for focused visualization via Observed Line Integral Convolution (LIC).
    • Seeds vortex core lines from critical points (where flow field equals reference frame) and solves an ODE with strict error bounds.

    Main Results:

    • The method successfully identifies and visualizes vortex structures in unsteady 2D flows.
    • Lagrangian vortex core lines are extracted as simultaneous solutions to two ODEs, with error controllable by integration step size.
    • Experimental verification confirms the relationship between step size and extraction error.

    Conclusions:

    • The proposed interactive method provides an effective and user-friendly approach for vortex structure detection and visualization.
    • It offers accurate extraction of Lagrangian vortex core lines with controllable numerical precision, outperforming state-of-the-art methods.
    • The system's usability is demonstrated through an interactive lens metaphor.