A GeneralisedNewtonianConstitutiveEquation class defining a Casson model fluid using Tanner and Milthorpe's (1983) regularisation with a smooth transition using a cubic. More...

#include <generalised_newtonian_constitutive_models.h>

Inheritance diagram for oomph::CassonTanMilRegWithBlendingConstitutiveEquation< DIM >:

Public Member Functions
	CassonTanMilRegWithBlendingConstitutiveEquation (double yield_stress_pt, double critical_second_invariant_pt)
	"Cutoff regularised" Casson constitutive equation

double	calculate_cutoff_viscosity ()
	Function that calculates the viscosity at the cutoff invariant Note: this is NOT the viscosity at zero I2.

double	calculate_viscosity_offset_at_zero_shear (double &cut_off_viscosity)
	Offset by how much the zero shear rate viscosity lies above the viscosity at I2_cutoff Hard-coded to a value that ensures a smooth transition.

double	calculate_zero_shear_viscosity ()
	Function that calculates the viscosity at zero I2.

void	report_cut_off_values (double &cut_off_invariant, double &cut_off_viscosity, double &zero_shear_viscosity)
	Report cutoff values.

void	calculate_fitting_parameters_of_cubic (double &a, double &b)

double	viscosity (const double &second_invariant_of_rate_of_strain_tensor)
	Viscosity ratio as a fct of strain rate invariant.

double	dviscosity_dinvariant (const double &second_invariant_of_rate_of_strain_tensor)
	Deriv of viscosity w.r.t. strain rate invariant.

Public Member Functions inherited from oomph::GeneralisedNewtonianConstitutiveEquation< DIM >
	GeneralisedNewtonianConstitutiveEquation ()
	Empty constructor.

virtual	~GeneralisedNewtonianConstitutiveEquation ()
	Empty virtual destructor.

Private Attributes
double *	Yield_stress_pt
	Yield stress.

double *	Critical_second_invariant_pt
	value of the second invariant below which we have constant (Newtonian) viscosity – assumed to be always positive

Detailed Description

template<unsigned DIM>
class oomph::CassonTanMilRegWithBlendingConstitutiveEquation< DIM >

A GeneralisedNewtonianConstitutiveEquation class defining a Casson model fluid using Tanner and Milthorpe's (1983) regularisation with a smooth transition using a cubic.

Definition at line 889 of file generalised_newtonian_constitutive_models.h.

Constructor & Destructor Documentation

◆ CassonTanMilRegWithBlendingConstitutiveEquation()

template<unsigned DIM>

oomph::CassonTanMilRegWithBlendingConstitutiveEquation< DIM >::CassonTanMilRegWithBlendingConstitutiveEquation	(	double *	yield_stress_pt,
		double *	critical_second_invariant_pt
	)

inline

"Cutoff regularised" Casson constitutive equation

get the cutoff viscosity

get the zero shear viscosity

Definition at line 903 of file generalised_newtonian_constitutive_models.h.

References oomph::CassonTanMilRegWithBlendingConstitutiveEquation< DIM >::calculate_cutoff_viscosity(), oomph::CassonTanMilRegWithBlendingConstitutiveEquation< DIM >::calculate_zero_shear_viscosity(), oomph::CassonTanMilRegWithBlendingConstitutiveEquation< DIM >::Critical_second_invariant_pt, and oomph::oomph_info.

Member Function Documentation

◆ calculate_cutoff_viscosity()

template<unsigned DIM>

double oomph::CassonTanMilRegWithBlendingConstitutiveEquation< DIM >::calculate_cutoff_viscosity ( )

inline

Function that calculates the viscosity at the cutoff invariant Note: this is NOT the viscosity at zero I2.

Definition at line 929 of file generalised_newtonian_constitutive_models.h.

References oomph::CassonTanMilRegWithBlendingConstitutiveEquation< DIM >::Critical_second_invariant_pt, and oomph::CassonTanMilRegWithBlendingConstitutiveEquation< DIM >::Yield_stress_pt.

Referenced by oomph::CassonTanMilRegWithBlendingConstitutiveEquation< DIM >::calculate_fitting_parameters_of_cubic(), oomph::CassonTanMilRegWithBlendingConstitutiveEquation< DIM >::calculate_zero_shear_viscosity(), oomph::CassonTanMilRegWithBlendingConstitutiveEquation< DIM >::CassonTanMilRegWithBlendingConstitutiveEquation(), and oomph::CassonTanMilRegWithBlendingConstitutiveEquation< DIM >::report_cut_off_values().

◆ calculate_fitting_parameters_of_cubic()

template<unsigned DIM>

void oomph::CassonTanMilRegWithBlendingConstitutiveEquation< DIM >::calculate_fitting_parameters_of_cubic	(	double &	a,
		double &	b
	)

inline

Definition at line 972 of file generalised_newtonian_constitutive_models.h.

References oomph::CassonTanMilRegWithBlendingConstitutiveEquation< DIM >::calculate_cutoff_viscosity(), oomph::CassonTanMilRegWithBlendingConstitutiveEquation< DIM >::calculate_viscosity_offset_at_zero_shear(), oomph::CassonTanMilRegWithBlendingConstitutiveEquation< DIM >::Critical_second_invariant_pt, and oomph::CassonTanMilRegWithBlendingConstitutiveEquation< DIM >::Yield_stress_pt.

Referenced by oomph::CassonTanMilRegWithBlendingConstitutiveEquation< DIM >::dviscosity_dinvariant(), and oomph::CassonTanMilRegWithBlendingConstitutiveEquation< DIM >::viscosity().

◆ calculate_viscosity_offset_at_zero_shear()

template<unsigned DIM>

double oomph::CassonTanMilRegWithBlendingConstitutiveEquation< DIM >::calculate_viscosity_offset_at_zero_shear ( double & cut_off_viscosity )

inline

Offset by how much the zero shear rate viscosity lies above the viscosity at I2_cutoff Hard-coded to a value that ensures a smooth transition.

Definition at line 942 of file generalised_newtonian_constitutive_models.h.

Referenced by oomph::CassonTanMilRegWithBlendingConstitutiveEquation< DIM >::calculate_fitting_parameters_of_cubic(), and oomph::CassonTanMilRegWithBlendingConstitutiveEquation< DIM >::calculate_zero_shear_viscosity().

◆ calculate_zero_shear_viscosity()

template<unsigned DIM>

double oomph::CassonTanMilRegWithBlendingConstitutiveEquation< DIM >::calculate_zero_shear_viscosity ( )

inline

Function that calculates the viscosity at zero I2.

Offset by how much the zero shear rate viscosity lies above the viscosity at I2_cutoff

Definition at line 948 of file generalised_newtonian_constitutive_models.h.

References oomph::CassonTanMilRegWithBlendingConstitutiveEquation< DIM >::calculate_cutoff_viscosity(), and oomph::CassonTanMilRegWithBlendingConstitutiveEquation< DIM >::calculate_viscosity_offset_at_zero_shear().

Referenced by oomph::CassonTanMilRegWithBlendingConstitutiveEquation< DIM >::CassonTanMilRegWithBlendingConstitutiveEquation(), oomph::CassonTanMilRegWithBlendingConstitutiveEquation< DIM >::report_cut_off_values(), and oomph::CassonTanMilRegWithBlendingConstitutiveEquation< DIM >::viscosity().

◆ dviscosity_dinvariant()

template<unsigned DIM>

double oomph::CassonTanMilRegWithBlendingConstitutiveEquation< DIM >::dviscosity_dinvariant ( const double & second_invariant_of_rate_of_strain_tensor )

inlinevirtual

Deriv of viscosity w.r.t. strain rate invariant.

Implements oomph::GeneralisedNewtonianConstitutiveEquation< DIM >.

Definition at line 1048 of file generalised_newtonian_constitutive_models.h.

References oomph::CassonTanMilRegWithBlendingConstitutiveEquation< DIM >::calculate_fitting_parameters_of_cubic(), oomph::CassonTanMilRegWithBlendingConstitutiveEquation< DIM >::Critical_second_invariant_pt, and oomph::CassonTanMilRegWithBlendingConstitutiveEquation< DIM >::Yield_stress_pt.

◆ report_cut_off_values()

template<unsigned DIM>

void oomph::CassonTanMilRegWithBlendingConstitutiveEquation< DIM >::report_cut_off_values	(	double &	cut_off_invariant,
		double &	cut_off_viscosity,
		double &	zero_shear_viscosity
	)