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

.. py:module:: FELiCS.Equation.Equations.MassEquation


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

Classes
~~~~~~~

.. autoapisummary::

   FELiCS.Equation.Equations.MassEquation.MassEquation




Attributes
~~~~~~~~~~

.. autoapisummary::

   FELiCS.Equation.Equations.MassEquation.logger


.. py:data:: logger

   

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


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

   Class representing the mass conservation equation.

   This class implements the weak form expressions for the mass conservation
   equation, both linear and nonlinear, in the tensorial framework. It
   handles the addition of relevant terms such as advection and boundary
   contributions, and accounts for specific analysis modes like
   Input-Output.

   **Initialize the MassEquation object**

   :param eqColl: The equation collection object.
   :type eqColl: :py:class:`EquationCollection`
   :param fluc: The fluctuations object.
   :type fluc: :py:class:`Fluctuations`
   :param X: The solution function.
   :type X: :py:class:`Function`
   :param param: The parameters object.
   :type param: :py:class:`Parameters`

   :ivar fluc: Fluctuating quantities used in the formulation.
   :vartype fluc: :py:class:`Fluctuations`
   :ivar X: Trial/test function in the variational formulation.
   :vartype X: :py:class:`Function`
   :ivar param: Configuration and problem parameters.
   :vartype param: :py:class:`Parameters`
   :ivar J_hat: Jacobian determinant for integration.
   :vartype J_hat: :py:class:`Expression`
   :ivar all_ds: Boundary integration measure.
   :vartype all_ds: :py:class:`Measure`
   :ivar n: Unit normal vector on boundaries.

   :vartype n: :py:class:`FacetNormal`

   .. admonition:: Notes

      This class inherits from EquationTemplate and raises an exception if
      a Discontinuous Galerkin scheme is selected, which 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 to which the expression is added.
      :type weakForm: :py:class:`Form`
      :param mean: The mean function providing averaged quantities.
      :type mean: :py:class:`Function`

      .. admonition:: Notes

         Adds the time-derivative term to the weak form if density is among the
         transported quantities.


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

      Add the linear expression to the weak form.

      :param weakForm: The weak form object to which the expression is added.
      :type weakForm: :py:class:`Form`
      :param mean: The mean function providing averaged quantities.
      :type mean: :py:class:`Function`

      .. admonition:: Notes

         Constructs the weak form of the linearized mass conservation equation,
         including volume and boundary terms via integration by parts. Special
         handling is added for boundary forcing in Input-Output analysis mode.


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

      Add the nonlinear expression to the weak form.

      :param weakForm: The weak form object to which the expression is added.
      :type weakForm: :py:class:`Form`
      :param mean: The mean function providing averaged quantities.
      :type mean: :py:class:`Function`

      .. admonition:: Notes

         Constructs the weak form of the full nonlinear mass conservation
         equation using integration by parts for advection terms.