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

[legend]

Public Types
typedef Matrix< SC, LO, GO, NO >	Matrix_Type

typedef Teuchos::RCP< Matrix_Type >	MatrixPtr_Type

typedef SmallMatrix< SC >	SmallMatrix_Type

typedef Teuchos::RCP< SmallMatrix_Type >	SmallMatrixPtr_Type

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

typedef Teuchos::RCP< MultiVector_Type >	MultiVectorPtr_Type

typedef AssembleFE< SC, LO, GO, NO >	AssembleFE_Type

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

typedef Teuchos::RCP< DifferentiableFuncClass_Type >	DifferentiableFuncClassPtr_Type

typedef InputToOutputMappingClass< SC, LO, GO, NO >	InputToOutputMappingClass_Type

typedef Teuchos::RCP< InputToOutputMappingClass_Type >	InputToOutputMappingClassPtr_Type

Public Types inherited from FEDD::AssembleFENavierStokes< default_sc, default_lo, default_go, default_no >
typedef Matrix< default_sc, default_lo, default_go, default_no >	Matrix_Type

typedef Teuchos::RCP< Matrix_Type >	MatrixPtr_Type

typedef SmallMatrix< default_sc >	SmallMatrix_Type

typedef Teuchos::RCP< SmallMatrix_Type >	SmallMatrixPtr_Type

typedef MultiVector< default_sc, default_lo, default_go, default_no >	MultiVector_Type

typedef Teuchos::RCP< MultiVector_Type >	MultiVectorPtr_Type

typedef AssembleFE< default_sc, default_lo, default_go, default_no >	AssembleFE_Type

Public Types inherited from FEDD::AssembleFE< default_sc, default_lo, default_go, default_no >
typedef SmallMatrix< default_sc >	SmallMatrix_Type

typedef Teuchos::RCP< SmallMatrix_Type >	SmallMatrixPtr_Type

typedef AssembleFE< default_sc, default_lo, default_go, default_no >	AssembleFE_Type

Public Member Functions
void	assembleJacobian () override
	Assemble the element Jacobian matrix.

void	assembleRHS () override
	Assemble the element right hand side vector.

void	assembleJacobianBlock (LO i)
	Assemble the element Jacobian matrix.

void	computeLocalconstOutputField () override
	Compute the viscosity for an element depending on the knwon velocity solution.

void	assembleFixedPoint ()

SmallMatrixPtr_Type	getFixedPointMatrix ()

Public Member Functions inherited from FEDD::AssembleFENavierStokes< default_sc, default_lo, default_go, default_no >
void	assembleJacobian () override
	Assemble the element Jacobian matrix.

void	assembleRHS () override
	Assemble the element right hand side vector.

void	assembleJacobianBlock (default_lo i) override
	Assemble the element Jacobian matrix.

void	setCoeff (SmallMatrix_Type coeff)

void	assembleFixedPoint ()
	Assembly of FixedPoint- Matrix (System Matrix K with current u)

SmallMatrixPtr_Type	getFixedPointMatrix ()

Public Member Functions inherited from FEDD::AssembleFE< default_sc, default_lo, default_go, default_no >
SmallMatrixPtr_Type	getJacobian ()
	Get the currently assembled element Jacobian matrix.

SmallMatrixPtr_Type	getJacobianBlock (default_lo i)
	Get the currently assembled element Jacobian matrix.

vec_dbl_ptr_Type	getRHS ()
	Get the currently assembled right hand side vector.

virtual void	checkParameters ()
	Check the input parameters from the constructor and the ParameterList for completeness and consistency.

virtual void	updateParams (ParameterListPtr_Type params)
	Set or update the parameters read from the ParameterList.

virtual void	updateParameter (std::string type, double value)
	Update the parameter read from the ParameterList.

virtual void	advanceInTime (double dt)
	This function is called every time the FEDDLib proceeds from one to the next time step. The size of the time step will always be provided as input.

double	getTimeStep ()
	Get the time state of the object.

void	advanceNewtonStep ()
	This function is called every time the FEDDLib proceeds from one to the next newton step. The size of the time step will always be provided as input.

int	getNewtonStep ()
	Get the time state of the object.

void	updateSolution (vec_dbl_Type solution)
	Update the solution vector.

vec_dbl_ptr_Type	getSolution ()
	Get the current local solution vector.

void	preProcessing ()
	This function is called in the beginning of each Newton step before actually assmblying anything.

void	postProcessing ()
	This function is called at the end of each Newton step after updating the solution vector.

int	getDim ()
	Get the spatial dimension. (Typically 2 or 3)

vec2D_dbl_Type	getNodesRefConfig ()
	Return the coordnates of the finite element nodes.

void	addRHSFunc (RhsFunc_Type rhsFunc)

tuple_sd_vec_ptr_Type	getTupleElement ()
	Return vector of tupled with element based values. First column per tuple string with description, second column with corresponding value.

double	getTimeIncrement ()
	Returns the time increment. Required by AceGen implementation.

void	setGlobalElementID (default_go goID)

default_go	getGlobalElementID ()

vec_dbl_Type	getLocalconstOutputField ()
	Obtain value of resulting postprocessing field at nodes/ inside an element.

Protected Member Functions
	AssembleFEGeneralizedNewtonian (int flag, vec2D_dbl_Type nodesRefConfig, ParameterListPtr_Type parameters, tuple_disk_vec_ptr_Type tuple)
	Constructor for AssembleFEAceNavierStokes.

void	assemblyStress (SmallMatrixPtr_Type &elementMatrix)
	Assembly function for shear stress tensor which includes viscosity function $\int_T \nabla v : (2\eta(\Dot{\gamma}(u))) D(u) ~dx$ , which is a highly nonlinear Term.

void	assemblyStressDev (SmallMatrixPtr_Type &elementMatrix)
	Assembly function for directional derivative contribution of shear stress tensor term (see function for detailed formula)

void	assemblyOutflowNeumannBoundaryTerm (SmallMatrixPtr_Type &elementMatrix)
	Assembly function for neumann boundary term - If we want to have same outflow boundary condition as for the Newtonian case (Laplace operator) we have to subtract boundary integral term see @article{Pacheco2021, abstract = {The matter of appropriate boundary conditions for open or truncated outflow regions in internal flow is still focus of discussion and research. In most practical applications, one can at best estimate mean pressure values or flow rates at such outlets. In the context of finite element methods, it is known that enforcing mean pressures through the pseudo-tractions arising from the Laplacian Navier-Stokes formulation yields accurate, physically consistent solutions. Nevertheless, when generalised Newtonian fluid models are considered, the resulting non-uniform viscosity fields render the classical Laplacian formulation inadequate. Thus, it is common practice to use the socalled stress-divergence formulation with natural boundary conditions known for causing nonphysical outflow behaviour. In order to overcome such a limitation, this work presents a novel mixed variational formulation that can be seen as a generalisation of the Laplacian Navier-Stokes form to fluids with shear-rate-dependent viscosity, as appearing in hemodynamic and polymeric flows. By appropriately manipulating the viscous terms in the variational formulation and employing a simple projection of the constitutive law, it is possible to devise a formulation with the desired natural boundary conditions and low computational complexity. Several numerical examples are presented to showcase the potential of our method, revealing improved accuracy and robustness in comparison with the state of the art.}, author = {Pacheco, Douglas R Q and Steinbach, Olaf}, doi = {10.51375/ijcvse.2021.1.6}, file = {:home/user/.local/share/data/Mendeley Ltd./Mendeley Desktop/Downloaded/Pacheco, Steinbach - 2021 - On outflow boundary conditions in finite element simulations of non-Newtonian internal flows.pdf:pdf}, journal = {International Journal of Computing and Visualization in Science and Engineering}, mendeley-groups = {DoctoralThesis/Numerical Fluid Dynamics/NonNewtonian/Boundary_Conditions}, number = {April}, title = {{On outflow boundary conditions in finite element simulations of non-Newtonian internal flows}}, year = {2021} }.

void	assemblyOutflowNeumannBoundaryTermDev (SmallMatrixPtr_Type &elementMatrix)
	Assembly function for directional derivative contribution neumann boundary term.

void	computeShearRate (vec3D_dbl_Type dPhiTrans, vec_dbl_ptr_Type &gammaDot, int dim)
	Computation of shear rate using the current velocity solution at the nodes and the derivative of the shape function.

Protected Member Functions inherited from FEDD::AssembleFENavierStokes< default_sc, default_lo, default_go, default_no >
	AssembleFENavierStokes (int flag, vec2D_dbl_Type nodesRefConfig, ParameterListPtr_Type parameters, tuple_disk_vec_ptr_Type tuple)
	Constructor for AssembleFEAceNavierStokes.

void	assemblyLaplacian (SmallMatrixPtr_Type &elementMatrix)
	Assembly function for vector values laplacian $\int_T \nabla v \cdot \nabla u ~dx$ .

void	assemblyAdvection (SmallMatrixPtr_Type &elementMatrix)
	Assembly advection vector field $\int_T \nabla v \cdot u(\nabla u) ~dx$ .

void	assemblyAdvectionInU (SmallMatrixPtr_Type &elementMatrix)
	Assembly advection vector field in u TODO: [JK] What is this? Is this the portion that needs to be added for Newton's method? Basically: A+N+W, A:Laplace, N is assemblyAdvection and W is assemblyAdvectionInU?

void	assemblyDivAndDivT (SmallMatrixPtr_Type &elementMatrix)
	Assembly $\int_T div(v) p ~dx$ / $\int_T div(u) q ~dx$ .

void	buildTransformation (SmallMatrix< default_sc > &B)
	Building Transformation.

void	applyBTinv (vec3D_dbl_ptr_Type &dPhiIn, vec3D_dbl_Type &dPhiOut, SmallMatrix< default_sc > &Binv)

Protected Member Functions inherited from FEDD::AssembleFE< default_sc, default_lo, default_go, default_no >
	AssembleFE (int flag, vec2D_dbl_Type nodesRefConfig, ParameterListPtr_Type parameters, tuple_disk_vec_ptr_Type tuple)
	Constructor.

Protected Attributes
std::string	shearThinningModel

int	dofsElementViscosity_

InputToOutputMappingClassPtr_Type	viscosityModel

Protected Attributes inherited from FEDD::AssembleFENavierStokes< default_sc, default_lo, default_go, default_no >
int	dofsVelocity_

int	dofsPressure_

std::string	FETypeVelocity_

std::string	FETypePressure_

int	numNodesVelocity_

int	numNodesPressure_

int	dofsElementVelocity_

int	dofsElementPressure_

int	dofsElement_

vec_dbl_Type	solutionVelocity_

vec_dbl_Type	solutionPressure_

SmallMatrixPtr_Type	constantMatrix_

SmallMatrixPtr_Type	ANB_

SmallMatrix_Type	coeff_

double	viscosity_

double	density_

std::string	linearization_

Protected Attributes inherited from FEDD::AssembleFE< default_sc, default_lo, default_go, default_no >
SmallMatrixPtr_Type	jacobian_

SmallMatrixPtr_Type	jacobianBlock_

vec_dbl_ptr_Type	rhsVec_

RhsFunc_Type	rhsFunc_

int	dim_

tuple_disk_vec_ptr_Type	diskTuple_

tuple_sd_vec_ptr_Type	elementIntormation_

vec2D_dbl_Type	nodesRefConfig_

bool	timeProblem_

int	flag_

double	timeStep_

int	newtonStep_

ParameterListPtr_Type	paramsMaterial_

ParameterListPtr_Type	params_

vec_dbl_ptr_Type	solution_

double	timeIncrement_

default_go	globalElementID_

vec_dbl_Type	constOutputField_

Friends
class	AssembleFEFactory< SC, LO, GO, NO >

Constructor & Destructor Documentation

◆ AssembleFEGeneralizedNewtonian()

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

FEDD::AssembleFEGeneralizedNewtonian< SC, LO, GO, NO >::AssembleFEGeneralizedNewtonian	(	int	flag,
		vec2D_dbl_Type	nodesRefConfig,
		ParameterListPtr_Type	parameters,
		tuple_disk_vec_ptr_Type	tuple )

protected

Constructor for AssembleFEAceNavierStokes.

Parameters

[in]	flag	Flag of element
[in]	nodesRefConfig	Nodes of element in reference configuration
[in]	params	Parameterlist for current problem
[in]	tuple	vector of element information tuples.

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Member Function Documentation

◆ assembleJacobian()

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

void FEDD::AssembleFEGeneralizedNewtonian< SC, LO, GO, NO >::assembleJacobian ( )

overridevirtual

Assemble the element Jacobian matrix.

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

◆ assembleJacobianBlock()

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

void FEDD::AssembleFEGeneralizedNewtonian< SC, LO, GO, NO >::assembleJacobianBlock ( LO i )

inlinevirtual

Assemble the element Jacobian matrix.

Parameters

[in] block ID i

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

◆ assembleRHS()

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

void FEDD::AssembleFEGeneralizedNewtonian< SC, LO, GO, NO >::assembleRHS ( )

overridevirtual

Assemble the element right hand side vector.

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

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◆ assemblyOutflowNeumannBoundaryTerm()

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

void FEDD::AssembleFEGeneralizedNewtonian< SC, LO, GO, NO >::assemblyOutflowNeumannBoundaryTerm ( SmallMatrixPtr_Type & elementMatrix )

inlineprotected

Assembly function for neumann boundary term - If we want to have same outflow boundary condition as for the Newtonian case (Laplace operator) we have to subtract boundary integral term see @article{Pacheco2021, abstract = {The matter of appropriate boundary conditions for open or truncated outflow regions in internal flow is still focus of discussion and research. In most practical applications, one can at best estimate mean pressure values or flow rates at such outlets. In the context of finite element methods, it is known that enforcing mean pressures through the pseudo-tractions arising from the Laplacian Navier-Stokes formulation yields accurate, physically consistent solutions. Nevertheless, when generalised Newtonian fluid models are considered, the resulting non-uniform viscosity fields render the classical Laplacian formulation inadequate. Thus, it is common practice to use the socalled stress-divergence formulation with natural boundary conditions known for causing nonphysical outflow behaviour. In order to overcome such a limitation, this work presents a novel mixed variational formulation that can be seen as a generalisation of the Laplacian Navier-Stokes form to fluids with shear-rate-dependent viscosity, as appearing in hemodynamic and polymeric flows. By appropriately manipulating the viscous terms in the variational formulation and employing a simple projection of the constitutive law, it is possible to devise a formulation with the desired natural boundary conditions and low computational complexity. Several numerical examples are presented to showcase the potential of our method, revealing improved accuracy and robustness in comparison with the state of the art.}, author = {Pacheco, Douglas R Q and Steinbach, Olaf}, doi = {10.51375/ijcvse.2021.1.6}, file = {:home/user/.local/share/data/Mendeley Ltd./Mendeley Desktop/Downloaded/Pacheco, Steinbach - 2021 - On outflow boundary conditions in finite element simulations of non-Newtonian internal flows.pdf:pdf}, journal = {International Journal of Computing and Visualization in Science and Engineering}, mendeley-groups = {DoctoralThesis/Numerical Fluid Dynamics/NonNewtonian/Boundary_Conditions}, number = {April}, title = {{On outflow boundary conditions in finite element simulations of non-Newtonian internal flows}}, year = {2021} }.

/*!

Parameters

[in] &elementMatrix

◆ assemblyOutflowNeumannBoundaryTermDev()

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

void FEDD::AssembleFEGeneralizedNewtonian< SC, LO, GO, NO >::assemblyOutflowNeumannBoundaryTermDev ( SmallMatrixPtr_Type & elementMatrix )

inlineprotected

Assembly function for directional derivative contribution neumann boundary term.

/*!

Parameters

[in] &elementMatrix

◆ assemblyStress()

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

void FEDD::AssembleFEGeneralizedNewtonian< SC, LO, GO, NO >::assemblyStress ( SmallMatrixPtr_Type & elementMatrix )

protected

Assembly function for shear stress tensor which includes viscosity function $\int_T \nabla v : (2\eta(\Dot{\gamma}(u))) D(u) ~dx$ , which is a highly nonlinear Term.

Parameters

[in] &elementMatrix

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◆ assemblyStressDev()

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

void FEDD::AssembleFEGeneralizedNewtonian< SC, LO, GO, NO >::assemblyStressDev ( SmallMatrixPtr_Type & elementMatrix )

protected

Assembly function for directional derivative contribution of shear stress tensor term (see function for detailed formula)

Parameters

[in] &elementMatrix

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◆ computeLocalconstOutputField()

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

void FEDD::AssembleFEGeneralizedNewtonian< SC, LO, GO, NO >::computeLocalconstOutputField ( )

overridevirtual

Compute the viscosity for an element depending on the knwon velocity solution.

Reimplemented from FEDD::AssembleFE< default_sc, default_lo, default_go, default_no >.

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◆ computeShearRate()

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

void FEDD::AssembleFEGeneralizedNewtonian< SC, LO, GO, NO >::computeShearRate	(	vec3D_dbl_Type	dPhiTrans,
		vec_dbl_ptr_Type &	gammaDot,
		int	dim )

protected

Computation of shear rate using the current velocity solution at the nodes and the derivative of the shape function.

Parameters

[in]	dPhiTrans	- Derivative of shape function
[in]	dim	- dimension of the problem
[in,out]	gammaDot	- shear rate value depending on inputs

Building Transformation

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

feddlib/core/AceFemAssembly/specific/AssembleFEGeneralizedNewtonian_decl.hpp
feddlib/core/AceFemAssembly/specific/AssembleFEGeneralizedNewtonian_def.hpp

Public Types

Public Member Functions

Protected Member Functions

Protected Attributes

Friends

Constructor & Destructor Documentation

◆ AssembleFEGeneralizedNewtonian()

Member Function Documentation

◆ assembleJacobian()

◆ assembleJacobianBlock()

◆ assembleRHS()

◆ assemblyOutflowNeumannBoundaryTerm()

◆ assemblyOutflowNeumannBoundaryTermDev()

◆ assemblyStress()

◆ assemblyStressDev()

◆ computeLocalconstOutputField()

◆ computeShearRate()