FELiCS.Equation.Equations.SpeciesEquation

FELiCS.Equation.Equations.SpeciesEquation#

Module Contents#

Classes#

SpeciesEquation

Class representing the species transport equation.

Attributes#

logger

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

Bases: FELiCS.Equation.Equations.EquationTemplate.EquationTemplate

Class representing the species transport equation.

This class formulates the species transport equation in a tensorial framework, capturing the effects of advection, diffusion, and chemical reactions. It supports boundary forcing and input-output analysis, while enforcing integration by parts to enable more robust numerical handling of fluxes and boundary conditions.

Initialize the SpeciesEquation object

Parameters:

  • eqColl (EquationCollection) – The equation collection object.

  • fluc (Fluctuations) – The fluctuations object.

  • X (Function) – The trial/test function in the weak formulation.

  • species (str) – The species name being transported.

  • param (Parameters) – The configuration and simulation parameters.

Variables:

  • species (str) – Name of the species for which the equation is formulated.

  • fluc (Fluctuations) – Fluctuating quantities used in the formulation.

  • X (Function) – Trial/test function in the variational formulation.

  • param (Parameters) – Configuration and problem parameters.

  • J_hat (Expression) – Jacobian determinant for integration.

  • all_ds (Measure) – Boundary integration measure.

  • n (FacetNormal) – Unit normal vector on boundaries.

Notes

Discontinuous Galerkin schemes are not supported in this tensorial framework.

addWeightMatrixExpression(weakForm, mean)#

Add the weight matrix expression to the weak form.

Parameters:

  • weakForm (Form) – The weak form object.

  • mean (MeanFlow) – The mean flow object.

Notes

Adds the time derivative term to the weak form for the species equation. This term incorporates fluctuations weighted by the mean density.

addNonlinearExpression()#

Add the nonlinear expression to the weak form.

Warning

This method is currently a placeholder and not implemented.

addLinearExpression(weakForm, mean)#

Construct the weak form of the linearized species transport equation.

Parameters:

  • weakForm (Form) – The weak form object.

  • mean (MeanFlow) – The mean flow object.

Notes

Constructs the weak form using a tensorial formulation. The method includes: - Integration by parts for advection terms to capture boundary contributions. - Volume-only integration of diffusion terms, effectively imposing Neumann boundary conditions. - Reaction terms based on a KaiserCnF2023 mechanism if specified. - Forcing terms for input-output analysis, including both body and boundary forcing. A warning is issued if the case parameter m > 0, as it has not been validated.

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