#include <generalised_newtonian_constitutive_models.h>

Inheritance diagram for oomph::HerschelBulkleyBerEngRegConstitutiveEquation< DIM >:

Public Member Functions
	HerschelBulkleyBerEngRegConstitutiveEquation (double yield_stress_pt, double flow_index_pt, double *regularisation_parameter_pt)

double	viscosity (const double &second_invariant_of_rate_of_strain_tensor)

double	dviscosity_dinvariant (const double &second_invariant_of_rate_of_strain_tensor)

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 tau_y More...

double *	Flow_index_pt
	power law index n More...

double *	Regularisation_parameter_pt
	regularisation parameter e << 1 More...

Detailed Description

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

A GeneralisedNewtonianConstitutiveEquation class defining a Herschel-Bulkley fluid using Bercovier and Engelman's (1980) regularisation

Constructor & Destructor Documentation

◆ HerschelBulkleyBerEngRegConstitutiveEquation()

template<unsigned DIM>

oomph::HerschelBulkleyBerEngRegConstitutiveEquation< DIM >::HerschelBulkleyBerEngRegConstitutiveEquation	(	double *	yield_stress_pt,
		double *	flow_index_pt,
		double *	regularisation_parameter_pt
	)

inline

       : GeneralisedNewtonianConstitutiveEquation<DIM>(),
         Yield_stress_pt(yield_stress_pt),
         Flow_index_pt(flow_index_pt),
         Regularisation_parameter_pt(regularisation_parameter_pt)
     {
     }

Member Function Documentation

◆ dviscosity_dinvariant()

template<unsigned DIM>

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

inlinevirtual

Function returning the derivative of the viscosity w.r.t. the second invariant of the rate of strain tensor For Newtonian behaviour this returns 0.0

Implements oomph::GeneralisedNewtonianConstitutiveEquation< DIM >.

     {
       // 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;
       }
  
       // std::ostringstream error_stream;
       // error_stream << "This has not been implemented yet!";
       // throw OomphLibError(
       //  error_stream.str(),
       //  OOMPH_CURRENT_FUNCTION,
       //  OOMPH_EXCEPTION_LOCATION);
  
       return sign * pow(2.0, (*Flow_index_pt) - 2.0) *
                ((*Flow_index_pt) - 1.0) *
                pow(sign * second_invariant_of_rate_of_strain_tensor +
                      (*Regularisation_parameter_pt),
                    ((*Flow_index_pt) - 1.0) / 2.0 - 1.0) -
              sign * (*Yield_stress_pt) /
                (4.0 * pow(sign * second_invariant_of_rate_of_strain_tensor +
                             (*Regularisation_parameter_pt),
                           3.0 / 2.0));
     }

References oomph::HerschelBulkleyBerEngRegConstitutiveEquation< DIM >::Flow_index_pt, Eigen::bfloat16_impl::pow(), oomph::HerschelBulkleyBerEngRegConstitutiveEquation< DIM >::Regularisation_parameter_pt, and SYCL::sign().

◆ viscosity()

template<unsigned DIM>

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

inlinevirtual

Function implementing the constitutive model Input: second invariant of the rate of strain Output: the viscosity For Newtonian behaviour this returns 1

Implements oomph::GeneralisedNewtonianConstitutiveEquation< DIM >.

     {
       // 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;
       }
  
       // 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 +
              (*Regularisation_parameter_pt));
  
       return (*Yield_stress_pt) / (2.0 * measure_of_rate_of_strain) +
              pow(2.0 * measure_of_rate_of_strain, *Flow_index_pt - 1.0);
     }