#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 More...

double	calculate_cutoff_viscosity ()

double	calculate_viscosity_offset_at_zero_shear (double &cut_off_viscosity)

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

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

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. More...

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

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

virtual	~GeneralisedNewtonianConstitutiveEquation ()
	Empty virtual destructor. More...

Private Attributes
double *	Yield_stress_pt
	Yield stress. More...

double *	Critical_second_invariant_pt

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

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

       : GeneralisedNewtonianConstitutiveEquation<DIM>(),
         Yield_stress_pt(yield_stress_pt),
         Critical_second_invariant_pt(critical_second_invariant_pt)
     {
       double cut_off_viscosity = calculate_cutoff_viscosity();
  
       double zero_shear_viscosity = calculate_zero_shear_viscosity();
  
       oomph_info << "CassonTanMilRegWithBlendingConstitutiveEquation: "
                  << " zero shear viscosity = " << zero_shear_viscosity
                  << std::endl;
  
       oomph_info << "CassonTanMilRegWithBlendingConstitutiveEquation: "
                  << " cut off viscosity = " << cut_off_viscosity << std::endl;
  
       oomph_info << "                                              "
                  << " cutoff invariant = " << *Critical_second_invariant_pt
                  << std::endl;
     }

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

     {
       // Calculate the Newtonian cutoff viscosity from the constitutive
       // equation and the cutoff value of the second invariant
       return (*Yield_stress_pt) / (2.0 * sqrt(*Critical_second_invariant_pt)) +
              2.0 * sqrt(*Yield_stress_pt /
                         (2.0 * sqrt(*Critical_second_invariant_pt))) +
              1.0;
     }

References oomph::CassonTanMilRegWithBlendingConstitutiveEquation< DIM >::Critical_second_invariant_pt, sqrt(), 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

     {
       // get the viscosity at the cutoff invariant
       double Cut_off_viscosity = calculate_cutoff_viscosity();
  
       // calculate the offset at zero shear
       double epsilon =
         calculate_viscosity_offset_at_zero_shear(Cut_off_viscosity);
  
       a = 1.0 / pow(*Critical_second_invariant_pt, 39.0 / 4.0) *
           (pow(*Critical_second_invariant_pt, 27.0 / 4.0) *
              (2.0 * (Cut_off_viscosity + epsilon) -
               2.0 * sqrt(2.0) *
                 sqrt(*Yield_stress_pt / sqrt(*Critical_second_invariant_pt)) -
               2.0) -
            5.0 / 4.0 * (*Yield_stress_pt) *
              pow(*Critical_second_invariant_pt, 25.0 / 4.0) -
            1.0 / (2.0 * sqrt(2.0)) * sqrt(*Yield_stress_pt) *
              pow(*Critical_second_invariant_pt, 13.0 / 2.0));
  
       b = 1.0 / pow(*Critical_second_invariant_pt, 27.0 / 4.0) *
           (pow(*Critical_second_invariant_pt, 19.0 / 4.0) *
              (-3.0 * (Cut_off_viscosity + epsilon) +
               3.0 * sqrt(2.0) *
                 sqrt(*Yield_stress_pt / sqrt(*Critical_second_invariant_pt)) +
               3.0) +
            7.0 / 4.0 * (*Yield_stress_pt) *
              pow(*Critical_second_invariant_pt, 17.0 / 4.0) +
            1.0 / (2.0 * sqrt(2.0)) * sqrt(*Yield_stress_pt) *
              pow(*Critical_second_invariant_pt, 9.0 / 2.0));
     }

References a, b, oomph::CassonTanMilRegWithBlendingConstitutiveEquation< DIM >::calculate_cutoff_viscosity(), oomph::CassonTanMilRegWithBlendingConstitutiveEquation< DIM >::calculate_viscosity_offset_at_zero_shear(), oomph::CassonTanMilRegWithBlendingConstitutiveEquation< DIM >::Critical_second_invariant_pt, oomph::SarahBL::epsilon, Eigen::bfloat16_impl::pow(), sqrt(), 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

     {
       return cut_off_viscosity / 5.0;
     }

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

     {
       // get the viscosity at the cutoff point
       double cut_off_viscosity = calculate_cutoff_viscosity();
  
       double epsilon =
         calculate_viscosity_offset_at_zero_shear(cut_off_viscosity);
  
       return cut_off_viscosity + epsilon;
     }

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

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 >.

     {
       // Get the parameters of the cubic
       double a;
       double b;
  
       calculate_fitting_parameters_of_cubic(a, b);
  
       // Pre-multiply the second invariant with +/-1 depending on whether it's
       // positive or not
       double sign = -1.0;
       if (second_invariant_of_rate_of_strain_tensor >= 0.0)
       {
         sign = 1.0;
       }
  
       if (sign * second_invariant_of_rate_of_strain_tensor <
           (*Critical_second_invariant_pt))
       {
         return sign * 3.0 * a *
                  pow(sign * second_invariant_of_rate_of_strain_tensor, 2.0) +
                2.0 * b * second_invariant_of_rate_of_strain_tensor;
       }
       else
       {
         return -sqrt(*Yield_stress_pt) *
                  second_invariant_of_rate_of_strain_tensor /
                  (2.0 * sqrt(2.0) *
                   pow(sign * second_invariant_of_rate_of_strain_tensor,
                       9.0 / 4.0)) -
                (*Yield_stress_pt) * second_invariant_of_rate_of_strain_tensor /
                  (4.0 * pow(sign * second_invariant_of_rate_of_strain_tensor,
                             5.0 / 2.0));
       }
     }

References a, b, oomph::CassonTanMilRegWithBlendingConstitutiveEquation< DIM >::calculate_fitting_parameters_of_cubic(), oomph::CassonTanMilRegWithBlendingConstitutiveEquation< DIM >::Critical_second_invariant_pt, Eigen::bfloat16_impl::pow(), SYCL::sign(), sqrt(), 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
	)

inline

Report cutoff values.

     {
       cut_off_invariant = *Critical_second_invariant_pt;
       cut_off_viscosity = calculate_cutoff_viscosity();
       zero_shear_viscosity = calculate_zero_shear_viscosity();
     }

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

◆ viscosity()

template<unsigned DIM>

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

inlinevirtual

Viscosity ratio as a fct of strain rate invariant.

Implements oomph::GeneralisedNewtonianConstitutiveEquation< DIM >.

     {
       // Get the parameters of the cubic
       double a;
       double b;
  
       calculate_fitting_parameters_of_cubic(a, b);
  
       double zero_shear_viscosity = calculate_zero_shear_viscosity();
  
       // Pre-multiply the second invariant with +/-1 depending on whether it's
       // positive or not
       double sign = -1.0;
       if (second_invariant_of_rate_of_strain_tensor >= 0.0)
       {
         sign = 1.0;
       }
  
       // if the second invariant is below the cutoff we have a constant,
       // Newtonian viscosity
       if (sign * second_invariant_of_rate_of_strain_tensor <
           (*Critical_second_invariant_pt))
       {
         return a * pow(sign * second_invariant_of_rate_of_strain_tensor, 3.0) +
                b * pow(sign * second_invariant_of_rate_of_strain_tensor, 2.0) +
                zero_shear_viscosity;
       }
       else
       {
         // Calculate the square root of the absolute value of the
         // second invariant of the rate of strain tensor
         double measure_of_rate_of_strain =
           sqrt(sign * second_invariant_of_rate_of_strain_tensor);
  
         return *Yield_stress_pt / (2.0 * measure_of_rate_of_strain) +
                2.0 *
                  sqrt(*Yield_stress_pt / (2.0 * measure_of_rate_of_strain)) +
                1.0;
       }
     }