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

.. only:: html

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

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

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

.. _sphx_glr_examples_gallery_pde_collection.py:


Multiple coupled PDEs
=====================

Demonstrates how multiple PDEs can be coupled.

.. GENERATED FROM PYTHON SOURCE LINES 8-39



.. image-sg:: /examples_gallery/images/sphx_glr_pde_collection_001.png
   :alt: pde collection
   :srcset: /examples_gallery/images/sphx_glr_pde_collection_001.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none


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.. code-block:: Python


    from pde import PDE, FieldCollection, ScalarField, UnitGrid

    import emulsim

    # parameters
    a, b = 1, 3
    d0, d1 = 1, 0.1

    # set up state
    grid = UnitGrid([64, 64])
    u = ScalarField(grid, a, label="Field $u$")
    v = b / a + 0.1 * ScalarField.random_normal(grid, label="Field $v$")
    field = FieldCollection([u, v])
    element = emulsim.FieldCollectionElement.from_fields(field)
    state = emulsim.State({"field": element})

    # set up simulation
    simulation = emulsim.Simulation(state)
    eq = PDE(  # Brusselator equations
        {
            "u": f"{d0} * laplace(u) + {a} - ({b} + 1) * u + u**2 * v",
            "v": f"{d1} * laplace(v) + {b} * u - u**2 * v",
        }
    )
    simulation.add_actor("field", emulsim.CollectionPDEActor(eq))

    # run simulation
    result = simulation.run(t_range=20, dt=1e-3)

    result.plot()


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

   **Total running time of the script:** (0 minutes 15.935 seconds)


.. _sphx_glr_download_examples_gallery_pde_collection.py:

.. only:: html

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

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

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

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

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

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

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