This class is derived from the abstract class DifferentiableFuncClass and should provide functionality to evaluate the viscosity function specified by PowerLaw model (see [1]) More...

#include <PowerLaw_decl.hpp>

Inheritance diagram for FEDD::PowerLaw< SC, LO, GO, NO >:

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Public Types
typedef MultiVector< SC, LO, GO, NO >	MultiVector_Type

typedef Teuchos::RCP< MultiVector_Type >	MultiVectorPtr_Type

typedef Teuchos::RCP< const MultiVector_Type >	MultiVectorConstPtr_Type

typedef DifferentiableFuncClass< SC, LO, GO, NO >	DifferentiableFuncClass_Type

Public Types inherited from FEDD::DifferentiableFuncClass< default_sc, default_lo, default_go, default_no >
typedef MultiVector< default_sc, default_lo, default_go, default_no >	MultiVector_Type

typedef Teuchos::RCP< MultiVector_Type >	MultiVectorPtr_Type

typedef Teuchos::RCP< const MultiVector_Type >	MultiVectorConstPtr_Type

Public Types inherited from FEDD::InputToOutputMappingClass< default_sc, default_lo, default_go, default_no >
typedef MultiVector< default_sc, default_lo, default_go, default_no >	MultiVector_Type

typedef Teuchos::RCP< MultiVector_Type >	MultiVectorPtr_Type

typedef Teuchos::RCP< const MultiVector_Type >	MultiVectorConstPtr_Type

Public Member Functions
void	setParams (ParameterListPtr_Type params) override
	Each constitutive model includes different material parameters which will be specified in parametersProblem.xml This function should set the specififc needed parameters for each model to the defined values.

void	evaluateMapping (ParameterListPtr_Type params, double shearRate, double &viscosity) override
	Update the viscosity according to a chosen shear thinning generalized newtonian constitutive equation. Viscosity depends on spatial coordinates due to its dependency on velocity gradients.

void	evaluateDerivative (ParameterListPtr_Type params, double shearRate, double &res) override
	For Newton method and NOX we need additional term in Jacobian considering directional derivative of our functional formulation. IMPORTANT: Here we implement the contribution of this: d(eta)/ d(gamma_Dot) * d(gamma_Dot)*d(Pi_\|\|). For each constitutive model the function looks different and will be defined inside this function.

void	echoInformationMapping () override
	Print parameter values used in model at runtime.

double	getViscosity ()

	PowerLaw (ParameterListPtr_Type parameters)
	Constructor for CarreauYasuda.

Public Member Functions inherited from FEDD::DifferentiableFuncClass< default_sc, default_lo, default_go, default_no >
virtual void	evaluateMapping (ParameterListPtr_Type params, MultiVectorConstPtr_Type input, MultiVectorPtr_Type &output) override
	Implement a mapping for evaluating output in dependence of given input and specified parameters for MultiVectorPtr_Type inputs/ outputs.

virtual void	evaluateDerivative (ParameterListPtr_Type params, MultiVectorConstPtr_Type x, MultiVectorPtr_Type &res) override
	Computes value of derivative of defined function in evaluateMapping.

Public Member Functions inherited from FEDD::InputToOutputMappingClass< default_sc, default_lo, default_go, default_no >
virtual void	updateParams (ParameterListPtr_Type params)
	Set or update the parameters read from the ParameterList.

Additional Inherited Members
Protected Member Functions inherited from FEDD::DifferentiableFuncClass< default_sc, default_lo, default_go, default_no >
	DifferentiableFuncClass (ParameterListPtr_Type parameters)
	Constructor.

Protected Member Functions inherited from FEDD::InputToOutputMappingClass< default_sc, default_lo, default_go, default_no >
	InputToOutputMappingClass (ParameterListPtr_Type parameters)
	Constructor.

Protected Attributes inherited from FEDD::DifferentiableFuncClass< default_sc, default_lo, default_go, default_no >
ParameterListPtr_Type	params_

Protected Attributes inherited from FEDD::InputToOutputMappingClass< default_sc, default_lo, default_go, default_no >
ParameterListPtr_Type	params_

Detailed Description

template<class SC = default_sc, class LO = default_lo, class GO = default_go, class NO = default_no>
class FEDD::PowerLaw< SC, LO, GO, NO >

This class is derived from the abstract class DifferentiableFuncClass and should provide functionality to evaluate the viscosity function specified by PowerLaw model (see [1])

Template Parameters

SC	The scalar type. So far, this is always double, but having it as a template parameter would allow flexibily, e.g., for using complex instead
LO	The local ordinal type. The is the index type for local indices
GO	The global ordinal type. The is the index type for global indices
NO	The Kokkos Node type. This would allow for performance portibility when using Kokkos. Currently, this is not used.

In general, there are several equations used to describe the material behavior of blood. Here (in this folder), we implement generalized Newtonian constitutive equations that capture the shear-thinning behavior of blood. The chosen shear-thinning model, such as the Power-Law or Carreau-Yasuda model, provides a function to update viscosity, which is no longer constant but depends on the shear rate (and other fixed constant parameters).

In our FEM code, we need an update function for viscosity, depending on the chosen model. If we apply Newton's method or NOX, we also require the directional derivative of the viscosity function, which also depends on the chosen model. Additionally, we need functions to set the required parameters of the chosen model and a function to print the parameter values.

The material parameters can be provided through a Teuchos::ParameterList object, which contains all the parameters specified in the input file 'parametersProblem.xml'. The structure of the input file and, consequently, the resulting parameter list can be chosen freely. The FEDDLib will handle reading the parameters from the file and making them available.

IMPORTANT: Regard e.g. following paper for computation of derivative @article{article_he, author = {He, Xin and Neytcheva, Maya and Vuik, C.}, year = {2015}, month = {06}, pages = {33-58}, title = {On Preconditioning of Incompressible Non-Newtonian Flow Problems}, volume = {33}, journal = {Journal of Computational Mathematics}, doi = {10.4208/jcm.1407-m4486} }

In our Finite Element Method (FEM) assembly, we require the directional derivative of the shear stress term with respect to the velocity vector for Newton's method. Since our viscosity function depends nonlinearly on the shear rate, which in turn depends on velocity, we must account for this contribution. Thus, when assembling the directional derivative term (in AssembleFEGeneralizedNewtonian), we call the function "this->viscosityModel->computeDerivative." It's crucial to note that through the chain rule, we obtain different contributions when computing the directional derivative of eta(gamma_dot) with respect to velocity. The individual terms are, for instance, detailed in the literature paper above. In general one obtain:

d (eta( gamma_Dot(v + eps*delta_v) ) )/ d(eps) |eps=0 = d(eta)/ d(gamma_Dot) * d(gamma_Dot)*d(Pi_||) * d(Pi_||)/ d(D) : d (D(v+eps*delta_v))/d(eps) |eps=0 Here Pi_|| is the second invariant of the strain-rate tensor D(v). In total we get four contributions: IMPORTANT: Consider that the contraction operator : is used in the formula above

d(eta)/ d(gamma_Dot) - Compute the derivative of eta with respect to gamma_Dot – For e.g. Carreau-Yasuda model just compute it analytically
d(gamma_Dot)*d(Pi_||) - The shear rate can be defined in terms of the second invariant of D by means of gamma_Dot = 2 \sqrt( - Pi_||) – So the derivative is just d(gamma_Dot)*d(Pi_||) = - 1/ sqrt( - Pi_||) = -2/ gamma_Dot
d(Pi_||)/ d(D) - Derivative of second invariant of D with respect to D – For incompressible fluids, the first invariant is zero, and the result can be found in the literature. However, as it depends on velocity, this contribution will be implemented in the assemblyFESpecific
d (D(v+eps*delta_v))/d(eps) |eps=0 - Directional derivative of D with respect to v - also implemented in assemblyFESpecific

For our viscosity models we define our derivative function "computeDerivative" to return the result of d(eta)/ d(gamma_Dot) * d(gamma_Dot)*d(Pi_||), which encompasses the first two contributions dependent on the chosen viscosity model.

Constructor & Destructor Documentation

◆ PowerLaw()

template<class SC, class LO, class GO, class NO>

FEDD::PowerLaw< SC, LO, GO, NO >::PowerLaw ( ParameterListPtr_Type parameters )

Constructor for CarreauYasuda.

Parameters

[in] parameters Parameterlist for current problem

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Member Function Documentation

◆ echoInformationMapping()

template<class SC, class LO, class GO, class NO>

void FEDD::PowerLaw< SC, LO, GO, NO >::echoInformationMapping ( )

overridevirtual

Print parameter values used in model at runtime.

Implements FEDD::DifferentiableFuncClass< default_sc, default_lo, default_go, default_no >.

◆ evaluateDerivative()

template<class SC, class LO, class GO, class NO>

void FEDD::PowerLaw< SC, LO, GO, NO >::evaluateDerivative	(	ParameterListPtr_Type	params,
		double	shearRate,
		double &	res )

overridevirtual

For Newton method and NOX we need additional term in Jacobian considering directional derivative of our functional formulation. IMPORTANT: Here we implement the contribution of this: d(eta)/ d(gamma_Dot) * d(gamma_Dot)*d(Pi_||). For each constitutive model the function looks different and will be defined inside this function.

Parameters

[in]	params	as read from the xml file (maybe redundant)
[in]	shearRate	scalar value of computed shear rate
[in,out]	res	scalar value of d(eta)/ d(gamma_Dot) * d(gamma_Dot)*d(Pi_\|\|)

Implements FEDD::DifferentiableFuncClass< default_sc, default_lo, default_go, default_no >.

◆ evaluateMapping()

template<class SC, class LO, class GO, class NO>

void FEDD::PowerLaw< SC, LO, GO, NO >::evaluateMapping	(	ParameterListPtr_Type	params,
		double	shearRate,
		double &	viscosity )

overridevirtual

Update the viscosity according to a chosen shear thinning generalized newtonian constitutive equation. Viscosity depends on spatial coordinates due to its dependency on velocity gradients.

Parameters

[in]	params	as read from the xml file (maybe redundant)
[in]	shearRate	scalar value of computed shear rate
[in,out]	viscosity	value of viscosity

Implements FEDD::DifferentiableFuncClass< default_sc, default_lo, default_go, default_no >.

◆ setParams()

template<class SC, class LO, class GO, class NO>

void FEDD::PowerLaw< SC, LO, GO, NO >::setParams ( ParameterListPtr_Type params )

overridevirtual

Each constitutive model includes different material parameters which will be specified in parametersProblem.xml This function should set the specififc needed parameters for each model to the defined values.

Parameters

[in] ParameterList as read from the xml file (maybe redundant)

Implements FEDD::DifferentiableFuncClass< default_sc, default_lo, default_go, default_no >.

The documentation for this class was generated from the following files:

feddlib/core/AceFemAssembly/specific/GeneralizedNewtonianModels/PowerLaw_decl.hpp
feddlib/core/AceFemAssembly/specific/GeneralizedNewtonianModels/PowerLaw_def.hpp

Public Types

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ PowerLaw()

Member Function Documentation

◆ echoInformationMapping()

◆ evaluateDerivative()

◆ evaluateMapping()

◆ setParams()