FELiCS.Equation.Equations.MomentumEquation

FELiCS.Equation.Equations.MomentumEquation#

Module Contents#

Classes#

MomentumEquation

Class representing the momentum conservation equation.

Attributes#

logger

FELiCS.Equation.Equations.MomentumEquation.logger#
class FELiCS.Equation.Equations.MomentumEquation.MomentumEquation(index, eqColl, fluc, X, param)#

Bases: 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

Parameters:

  • index (int) – Index of the equation in the system.

  • eqColl (EquationCollection) – The equation collection object.

  • fluc (Fluctuations) – The fluctuations object.

  • X (Function) – The function representing the mesh coordinates.

  • param (Parameters) – The parameters object.

Notes

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

addWeightMatrixExpression(weakForm, mean)#

Add the weight matrix expression to the weak form.

Parameters:

  • weakForm (Form) – The weak form object.

  • mean (MeanFields) – The mean fields object.

Notes

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

addLinearExpression(weakForm, mean)#

Construct the weak form of the linearized momentum conservation equation.

Parameters:

  • weakForm (Form) – The weak form object.

  • mean (MeanFields) – The mean fields object.

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.

addNonlinearExpression(weakForm, mean)#

Add the nonlinear expression to the weak form.

Parameters:

  • weakForm (Form) – The weak form object to be updated.

  • mean (MeanFields) – The mean fields object containing time-averaged variables.

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.

addBilinearExpression(weakForm, mean)#

Add the bilinear convection term for incompressible flows.

Parameters:

  • weakForm (Form) – The weak form object to be updated.

  • mean (MeanFields) – The mean fields object containing time-averaged variables.

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.

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