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‎source/2_theory.rst‎

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Theory of FTLE and LCS
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======================
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This page introduces the theory of Finite-Time Lyapunov Exponents (FTLE) and Lagrangian Coherent Structures (LCS). It covers the mathematical foundations and applications of these concepts in fluid dynamics and other fields.
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This page introduces the theory of Finite-Time Lyapunov Exponents (FTLE) and Lagrangian Coherent Structures (LCS). It covers the mathematical foundations and applications of these concepts in fluid dynamics and other fields.
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.. _steady:
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Steady LCS
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--------------
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.. _unsteady:
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Unsteady LCS
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--------------

‎source/6_inputdeck.rst‎

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Input and Range Control
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---------------------------------
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+-------------------+------------------------------------------------------+-------------------------+-----------------------------------------+
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| Key | Description | Value(s) | Explaination and Notes |
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+===================+======================================================+=========================+=========================================+
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| ``vtk_folder`` | Path to folder containing VTK input data | ``<string>`` | NA |
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+-------------------+------------------------------------------------------+-------------------------+-----------------------------------------+
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| ``output_dir`` | Path to directory for saving results | ``<string>`` | NA |
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+-------------------+------------------------------------------------------+-------------------------+-----------------------------------------+
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| ``auto_wall`` | Flag for automatic wall detection | ``0`` | Manually indicate computation bounds |
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+-------------------+------------------------------------------------------+-------------------------+-----------------------------------------+
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| | | (``1``) | Auto detect bounds from input mesh |
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+-------------------+------------------------------------------------------+-------------------------+-----------------------------------------+
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| ``wall_xrange`` | X-direction wall bounds [xmin, xmax] | ``[<float>, <float>]`` | |
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+-------------------+------------------------------------------------------+-------------------------+-----------------------------------------+
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| ``wall_yrange`` | Y-direction wall bounds [ymin, ymax] | ``[<float>, <float>]`` | |
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+-------------------+------------------------------------------------------+-------------------------+-----------------------------------------+
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| ``wall_zrange`` | Z-direction wall bounds [zmin, zmax] | ``[<float>, <float>]`` | |
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+-------------------+------------------------------------------------------+-------------------------+-----------------------------------------+
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| ``x`` | Number of seed points in X direction | ``<int>`` | |
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+-------------------+------------------------------------------------------+-------------------------+-----------------------------------------+
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| ``y`` | Number of seed points in Y direction | ``<int>`` | |
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+-------------------+------------------------------------------------------+-------------------------+-----------------------------------------+
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| ``z`` | Number of seed points in Z direction | ``<int>`` | |
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+-------------------+------------------------------------------------------+-------------------------+-----------------------------------------+
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| ``T_range`` | Time range [``T_start``, ``T_end``] in frames | ``[<float>, <float>]`` | ``T_end`` no larger than ``N_frames`` |
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+-------------------+------------------------------------------------------+-------------------------+-----------------------------------------+
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| ``dt`` | Time step for particle advection in frames | ``<float>`` | NA |
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+-------------------+------------------------------------------------------+-------------------------+-----------------------------------------+
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+-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------+
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| Key | Description | Value(s) | Explaination and Notes |
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+===================+======================================================+=========================+=========================================================+
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| ``vtk_folder`` | Path to folder containing VTK input data | ``<string>`` | NA |
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+-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------+
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| ``output_dir`` | Path to directory for saving results | ``<string>`` | NA |
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+-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------+
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| ``auto_wall`` | Flag for automatic wall detection | ``0`` | Manually indicate computation bounds |
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+-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------+
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| | | (``1``) | Auto detect bounds from input mesh |
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+-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------+
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| ``wall_xrange`` | X-direction wall bounds [xmin, xmax] | ``[<float>, <float>]`` | |
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+-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------+
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| ``wall_yrange`` | Y-direction wall bounds [ymin, ymax] | ``[<float>, <float>]`` | |
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+-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------+
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| ``wall_zrange`` | Z-direction wall bounds [zmin, zmax] | ``[<float>, <float>]`` | |
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+-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------+
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| ``x`` | Number of seed points in X direction | ``<int>`` | |
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+-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------+
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| ``y`` | Number of seed points in Y direction | ``<int>`` | |
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+-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------+
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| ``z`` | Number of seed points in Z direction | ``<int>`` | |
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+-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------+
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| ``T_range`` | Time range [``T_start``, ``T_end``] in frames | ``[<float>, <float>]`` | ``T_end`` no larger than ``N_frames`` |
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+-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------+
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| ``dt`` | Time step for particle advection in frames | ``<float>`` | NA |
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+-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------+
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Numerical Methods
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---------------------------------
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+-------------------+------------------------------------------------------+-------------------------+-----------------------------------------+
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| Key | Description | Value(s) | Explaination and Notes |
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+===================+======================================================+=========================+=========================================+
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| ``if_backward`` | Backward integration flag | ``0`` | Only compute forward advection |
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+-------------------+------------------------------------------------------+-------------------------+-----------------------------------------+
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| | | (``1``) | Compute in both side |
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+-------------------+------------------------------------------------------+-------------------------+-----------------------------------------+
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| ``advc_method`` | Advection scheme | ``<string>`` | NA |
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+-------------------+------------------------------------------------------+-------------------------+-----------------------------------------+
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| ``interp_method`` | Interpolation method | ``<string>`` | NA |
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+-------------------+------------------------------------------------------+-------------------------+-----------------------------------------+
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| ``wall_treatment``| Wall-treatment strategy | ``clamp`` | NA |
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+-------------------+------------------------------------------------------+-------------------------+-----------------------------------------+
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| ``grad_order`` | Gradient approximation scheme | ``<int>`` | NA |
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+-------------------+------------------------------------------------------+-------------------------+-----------------------------------------+
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| ``Eigen_method`` | Eigenvalue computation method | ``<string>`` | NA |
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+-------------------+------------------------------------------------------+-------------------------+-----------------------------------------+
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| ``if_visual`` | Glace visualization enabler | ``0`` or ``1`` | NA |
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+-------------------+------------------------------------------------------+-------------------------+-----------------------------------------+
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+-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------+
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| Key | Description | Value(s) | Explaination and Notes |
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+===================+======================================================+=========================+=========================================================+
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| ``if_backward`` | Backward integration flag | ``0`` | Only compute forward advection |
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+-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------+
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| | | (``1``) | Compute in both side |
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+-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------+
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| ``advc_method`` | Advection scheme | ``<string>`` | NA |
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+-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------+
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| ``interp_method`` | Interpolation method | ``<string>`` | NA |
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+-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------+
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| ``wall_treatment``| Wall-treatment strategy | ``clamp`` | NA |
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+-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------+
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| ``grad_order`` | Gradient approximation scheme | ``<int>`` | NA |
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+-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------+
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| ``Eigen_method`` | Eigenvalue computation method | ``<string>`` | NA |
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+-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------+
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| ``if_visual`` | Glace visualization enabler | ``0`` or ``1`` | NA |
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+-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------+
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Dynamic LCS Window
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+-------------------+------------------------------------------------------+-------------------------+-----------------------------------------+
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| Key | Description | Value(s) | Explaination and Notes |
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+===================+======================================================+=========================+=========================================+
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| ``dyn_mode`` | Dynamic LCS mode selector | ``0`` or ``1`` | NA |
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+-------------------+------------------------------------------------------+-------------------------+-----------------------------------------+
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| ``win_size`` | Window size for dynamic LCS | ``<float>`` | NA |
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+-------------------+------------------------------------------------------+-------------------------+-----------------------------------------+
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| ``win_step`` | Window step for dynamic LCS | ``<float>`` | NA |
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+-------------------+------------------------------------------------------+-------------------------+-----------------------------------------+
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+-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------+
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| Key | Description | Value(s) | Explaination and Notes |
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+===================+======================================================+=========================+=========================================================+
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| ``dyn_mode`` | Dynamic LCS mode selector | (``0``) | Treat this input as a steady whole :ref:``steady``. |
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+-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------+
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| | | ``1`` | |
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+-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------+
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| ``win_size`` | Window size for dynamic LCS | ``<float>`` | NA |
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+-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------+
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| ``win_step`` | Window step for dynamic LCS | ``<float>`` | NA |
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+-------------------+------------------------------------------------------+-------------------------+---------------------------------------------------------+
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.. _flow_vars:

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