:py:mod:`FELiCS.Equation.Equations.MomentumEquation`
====================================================

.. py:module:: FELiCS.Equation.Equations.MomentumEquation


Module Contents
---------------

Classes
~~~~~~~

.. autoapisummary::

   FELiCS.Equation.Equations.MomentumEquation.MomentumEquation




Attributes
~~~~~~~~~~

.. autoapisummary::

   FELiCS.Equation.Equations.MomentumEquation.logger


.. py:data:: logger

   

.. py:class:: MomentumEquation(index, eqColl, fluc, X, param)


   Bases: :py:obj:`FELiCS.Equation.Equations.EquationTemplate.EquationTemplate`

   Class representing the momentum conservation equation.

   This class formulates the momentum conservation equation in a tensorial framework.
   It includes convective, pressure gradient, and diffusion terms while supporting
   both weak and strong formulations. The class integrates with the overall equation
   collection and handles interactions with mean fields and fluctuations.

   **Initialize the MomentumEquation object**

   :param index: Index of the equation in the system.
   :type index: :py:class:`int`
   :param eqColl: The equation collection object.
   :type eqColl: :py:class:`EquationCollection`
   :param fluc: The fluctuations object.
   :type fluc: :py:class:`Fluctuations`
   :param X: The function representing the mesh coordinates.
   :type X: :py:class:`Function`
   :param param: The parameters object.
   :type param: :py:class:`Parameters`

   .. admonition:: Notes

      If the numerical scheme is 'Discontinuous Galerkin', an error will be raised
      since it is not implemented in the tensorial framework.

   .. py:method:: addWeightMatrixExpression(weakForm, mean)

      Add the weight matrix expression to the weak form.

      :param weakForm: The weak form object.
      :type weakForm: :py:class:`Form`
      :param mean: The mean fields object.
      :type mean: :py:class:`MeanFields`

      .. admonition:: Notes

         This method incorporates time derivative terms into the weak form for the momentum equation.


   .. py:method:: addLinearExpression(weakForm, mean)

      Construct the weak form of the linearized momentum conservation equation.

      :param weakForm: The weak form object.
      :type weakForm: :py:class:`Form`
      :param mean: The mean fields object.
      :type mean: :py:class:`MeanFields`

      .. admonition:: Notes

         - This function builds the weak form of the momentum conservation equation
           in a tensorial framework.
         - Convective, pressure gradient, and diffusion terms are considered.
         - Integration by parts is optionally applied depending on the coordinate system.
         - Certain terms may require adjustments in future implementations.


   .. py:method:: addNonlinearExpression(weakForm, mean)

      Add the nonlinear expression to the weak form.

      :param weakForm: The weak form object to be updated.
      :type weakForm: :py:class:`Form`
      :param mean: The mean fields object containing time-averaged variables.
      :type mean: :py:class:`MeanFields`

      .. admonition:: Notes

         - This method assembles the full nonlinear form of the momentum conservation equation.
         - It supports integration by parts for convective and pressure terms and includes the diffusion term using the mean stress tensor.


   .. py:method:: addBilinearExpression(weakForm, mean)

      Add the bilinear convection term for incompressible flows.

      :param weakForm: The weak form object to be updated.
      :type weakForm: :py:class:`Form`
      :param mean: The mean fields object containing time-averaged variables.
      :type mean: :py:class:`MeanFields`

      .. admonition:: Notes

         - This method implements a simplified bilinear form for incompressible flow cases in the BOA project.
         - Only the convective term is considered, using a strong formulation.