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

.. py:module:: FELiCS.Equation.Equations.EnergyPressureEquation


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

Classes
~~~~~~~

.. autoapisummary::

   FELiCS.Equation.Equations.EnergyPressureEquation.EnergyPressureEquation




Attributes
~~~~~~~~~~

.. autoapisummary::

   FELiCS.Equation.Equations.EnergyPressureEquation.logger


.. py:data:: logger

   

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


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

   Class representing the energy-pressure equation in FELiCS.

   This class constructs and manages the weak formulation of the energy
   conservation equation in a compressible fluid system. The formulation
   is based on total energy conservation and is expressed in terms of
   pressure, using the Perfect Gas Law and continuity equations.

   :param eqColl: The equation collection object that stores various equations.
   :type eqColl: :py:class:`EquationCollection`
   :param fluc: The fluctuations object representing perturbations in the system.
   :type fluc: :py:class:`Fluctuations`
   :param X: The solution function representing the unknowns of the equation.
   :type X: :py:class:`Function`
   :param param: The parameters object containing simulation and physical parameters.
   :type param: :py:class:`Parameters`

   :raises RuntimeError: If an unsupported numerical scheme like Discontinuous Galerkin is used.

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

      Add the weight matrix expression to the weak form.

      This function contributes the time derivative terms
      to the weak formulation.

      :param weakForm: The weak form object to which the expression is added.
      :type weakForm: :py:class:`Form`
      :param mean: The mean function representing the average state.
      :type mean: :py:class:`Function`


   .. py:method:: addNonlinearExpression()

      Add the nonlinear expression to the weak form.

      This method is currently not implemented.


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

      Add the linear expression to the weak form.

      This function builds the weak form of the linearized energy
      conservation equation in the tensorial framework. The formulation
      is based on total energy conservation for a compressible fluid,
      expressed in terms of pressure by substituting the Perfect Gas Law
      and the continuity equation. The equation is implemented in
      primitive variables.

      :param weakForm: The weak form object to which the expression is added.
      :type weakForm: :py:class:`Form`
      :param mean: The mean function representing the average state.
      :type mean: :py:class:`Function`


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

      Add the bilinear convection term. CAUTION: not tested yet, treat with care!
      Only for linearization around p, not T.

      :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`