.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/Analytic_Solutions_Front/plot_as_frt_time.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_auto_examples_Analytic_Solutions_Front_plot_as_frt_time.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_Analytic_Solutions_Front_plot_as_frt_time.py:


Plot front position over time.
===========================
This section shows how to use *show_fronts_over_time* function to plot front position depending on time.

For each case, we will use an initial water depth :math:`h_0 = 20m`. For Mangeney's method, we use a slope of :math:`\theta = 30°`
and a friction angle of :math:`\delta = 25°`. For Stoker's method, we use a domain depth of :math:`h_r = 1m`:

Implementation
-----------------

.. GENERATED FROM PYTHON SOURCE LINES 12-19

.. code-block:: Python


    from tilupy.analytic_sol import Front_result

    import numpy as np

    A = Front_result(h0=20)








.. GENERATED FROM PYTHON SOURCE LINES 20-21

---------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 24-25

**Case 1**: computing only for :math:`t = 5s`.

.. GENERATED FROM PYTHON SOURCE LINES 25-35

.. code-block:: Python

    t = 5

    A.xf_mangeney(t, delta=25, theta=30)
    A.xf_dressler(t)
    A.xf_ritter(t)
    A.xf_stoker(t, hr=1)
    A.xf_chanson(t, f=0.05)

    A.show_fronts_over_time()




.. image-sg:: /auto_examples/Analytic_Solutions_Front/images/sphx_glr_plot_as_frt_time_001.png
   :alt: plot as frt time
   :srcset: /auto_examples/Analytic_Solutions_Front/images/sphx_glr_plot_as_frt_time_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 36-37

---------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 40-41

**Case 2**: computing for :math:`t = {1, 5, 10, 15, 20}s`.

.. GENERATED FROM PYTHON SOURCE LINES 41-52

.. code-block:: Python

    T = [1, 10, 15, 20]  # t = 5 already compute

    for t in T:
        A.xf_mangeney(t, delta=25, theta=30)
        A.xf_dressler(t)
        A.xf_ritter(t)
        A.xf_stoker(t, hr=1)
        A.xf_chanson(t, f=0.05)

    A.show_fronts_over_time()




.. image-sg:: /auto_examples/Analytic_Solutions_Front/images/sphx_glr_plot_as_frt_time_002.png
   :alt: plot as frt time
   :srcset: /auto_examples/Analytic_Solutions_Front/images/sphx_glr_plot_as_frt_time_002.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 53-54

Ritter and Dressler's solutions are the same.

.. GENERATED FROM PYTHON SOURCE LINES 56-57

---------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 60-61

**Case 3**: computing for :math:`t \in [0, 20]`.

.. GENERATED FROM PYTHON SOURCE LINES 61-74

.. code-block:: Python

    T = np.linspace(0, 20, 100)  # t = 5 already compute

    A = Front_result(h0=20)  # Reset values

    for t in T:
        A.xf_mangeney(t, delta=25, theta=30)
        A.xf_dressler(t)
        A.xf_ritter(t)
        A.xf_stoker(t, hr=1)
        A.xf_chanson(t, f=0.05)

    A.show_fronts_over_time()




.. image-sg:: /auto_examples/Analytic_Solutions_Front/images/sphx_glr_plot_as_frt_time_003.png
   :alt: plot as frt time
   :srcset: /auto_examples/Analytic_Solutions_Front/images/sphx_glr_plot_as_frt_time_003.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 75-76

Ritter and Dressler's solutions are the same.


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.175 seconds)


.. _sphx_glr_download_auto_examples_Analytic_Solutions_Front_plot_as_frt_time.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_as_frt_time.ipynb <plot_as_frt_time.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_as_frt_time.py <plot_as_frt_time.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_as_frt_time.zip <plot_as_frt_time.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_