polar_stress_integral_elements.h

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// LIC// ====================================================================
// LIC// This file forms part of oomph-lib, the object-oriented,
// LIC// multi-physics finite-element library, available
// LIC// at http://www.oomph-lib.org.
// LIC//
// LIC// Copyright (C) 2006-2023 Matthias Heil and Andrew Hazel
// LIC//
// LIC// This library is free software; you can redistribute it and/or
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// LIC// License as published by the Free Software Foundation; either
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// LIC// Lesser General Public License for more details.
// LIC//
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// LIC// The authors may be contacted at oomph-lib@maths.man.ac.uk.
// LIC//
// LIC//====================================================================
// Header file for elements that are used to integrate the shear stress
// along either side wall
 
#ifndef OOMPH_POLAR_STRESS_INTEGRAL_ELEMENTS_HEADER
#define OOMPH_POLAR_STRESS_INTEGRAL_ELEMENTS_HEADER
 
// Config header generated by autoconfig
#ifdef HAVE_CONFIG_H
#include <config.h>
#endif
 
 
// OOMPH-LIB headers
#include "../generic/Qelements.h"
 
namespace oomph
{
  //======================================================================
  /// A class for elements that allow the imposition of an applied traction
  /// to the Navier--Stokes equations
  /// The geometrical information can be read from the FaceGeometery<ELEMENT>
  /// class and and thus, we can be generic enough without the need to have
  /// a separate equations class
  //======================================================================
  template<class ELEMENT>
  class PolarStressIntegralElement : public virtual FaceGeometry<ELEMENT>,
                                     public virtual FaceElement
  {
  private:
    /// Pointer to an imposed traction function
    void (*Traction_fct_pt)(const double& time,
                            const Vector<double>& x,
                            Vector<double>& result);
 
    /// The highest dimension of the problem
    unsigned Dim;
 
  protected:
    /// Access function that returns the local equation numbers
    /// for velocity components.
    /// u_local_eqn(n,i) = local equation number or < 0 if pinned.
    /// The default is to asssume that n is the local node number
    /// and the i-th velocity component is the i-th unknown stored at the node.
    virtual inline int u_local_eqn(const unsigned& n, const unsigned& i)
    {
      return nodal_local_eqn(n, i);
    }
 
    /// Function to compute the shape and test functions and to return
    /// the Jacobian of mapping
    inline double shape_and_test_at_knot(const unsigned& ipt,
                                         Shape& psi,
                                         Shape& test) const
    {
      // Find number of nodes
      unsigned n_node = nnode();
      // Calculate the shape functions
      shape_at_knot(ipt, psi);
      // Set the test functions to be the same as the shape functions
      for (unsigned i = 0; i < n_node; i++)
      {
        test[i] = psi[i];
      }
      // Return the value of the jacobian
      return J_eulerian_at_knot(ipt);
    }
 
    /// Pointer to the angle alpha
    double* Alpha_pt;
 
    // Traction elements need to know whether they're at the inlet or outlet
    // as the unit outward normal has a differing sign dependent on
    // the boundary
    // phi=-1, phi=1
    int Boundary;
 
  public:
    /// Alpha
    const double& alpha() const
    {
      return *Alpha_pt;
    }
 
    /// Pointer to Alpha
    double*& alpha_pt()
    {
      return Alpha_pt;
    }
 
    /// Boundary
    const int boundary() const
    {
      return Boundary;
    }
 
    /// Function to set boundary
    void set_boundary(int bound)
    {
      Boundary = bound;
    }
 
    /// Function to calculate the shear stress along boundary
    double get_shear_stress();
 
    /// Constructor, which takes a "bulk" element and the value of the index
    /// and its limit
    PolarStressIntegralElement(FiniteElement* const& element_pt,
                               const int& face_index)
      : FaceGeometry<ELEMENT>(), FaceElement()
    {
      // Attach the geometrical information to the element. N.B. This function
      // also assigns nbulk_value from the required_nvalue of the bulk element
      element_pt->build_face_element(face_index, this);
 
#ifdef PARANOID
      {
        // Check that the element is not a refineable 3d element
        ELEMENT* elem_pt = dynamic_cast<ELEMENT*>(element_pt);
 
        // If it's three-d
        if (elem_pt->dim() == 3)
        {
          // Is it refineable
          RefineableElement* ref_el_pt =
            dynamic_cast<RefineableElement*>(elem_pt);
          if (ref_el_pt != 0)
          {
            if (this->has_hanging_nodes())
            {
              throw OomphLibError("This flux element will not work correctly "
                                  "if nodes are hanging\n",
                                  OOMPH_CURRENT_FUNCTION,
                                  OOMPH_EXCEPTION_LOCATION);
            }
          }
        }
      }
#endif
 
      // Set the dimension from the dimension of the first node
      Dim = this->node_pt(0)->ndim();
    }
 
    /// Destructor should not delete anything
    ~PolarStressIntegralElement() {}
 
    /// This function returns just the residuals
    inline void fill_in_contribution_to_residuals(Vector<double>& residuals)
    {
      // Do nothing
    }
 
    /// This function returns the residuals and the jacobian
    inline void fill_in_contribution_to_jacobian(Vector<double>& residuals,
                                                 DenseMatrix<double>& jacobian)
    {
      // Do nothing
    }
 
    /// Compute the element's residual Vector and the jacobian matrix
    /// Plus the mass matrix especially for eigenvalue problems
    void fill_in_contribution_to_jacobian_and_mass_matrix(
      Vector<double>& residuals,
      DenseMatrix<double>& jacobian,
      DenseMatrix<double>& mass_matrix)
    {
      // Do nothing
    }
 
    /// Overload the output function
    void output(std::ostream& outfile)
    {
      FiniteElement::output(outfile);
    }
 
    /// Output function: x,y,[z],u,v,[w],p in tecplot format
    void output(std::ostream& outfile, const unsigned& nplot)
    {
      FiniteElement::output(outfile, nplot);
    }
 
    /// local velocities
    double u(const unsigned& l, const unsigned& i)
    {
      return nodal_value(l, i);
    }
 
    /// local position
    double x(const unsigned& l, const unsigned& i)
    {
      return nodal_position(l, i);
    }
  };
 
  //============================================================================
  /// Function that returns the shear stress
  //============================================================================
  template<class ELEMENT>
  double PolarStressIntegralElement<ELEMENT>::get_shear_stress()
  {
    // Storage for shear stress
    double dudphi, shear_contribution = 0.0;
 
    // Set the value of n_intpt
    unsigned n_intpt = integral_pt()->nweight();
 
    // Storage for local coordinate
    Vector<double> s_local(1);
    // Storage for local coordinate in bulk
    Vector<double> s_bulk(2);
 
    // Find out how many nodes there are
    unsigned n_node = nnode();
 
    // Set up memory for the shape and test functions
    Shape psif(n_node), testf(n_node);
 
    // Loop over the integration points
    for (unsigned ipt = 0; ipt < n_intpt; ipt++)
    {
      // Get the integral weight
      double w = integral_pt()->weight(ipt);
 
      // Find the shape and test functions and return the Jacobian
      // of the mapping
      double J = shape_and_test_at_knot(ipt, psif, testf);
 
      // Premultiply the weights and the Jacobian
      double W = w * J;
 
      // Need to find position to feed into Traction function
      Vector<double> interpolated_x(Dim);
 
      // Initialise to zero
      for (unsigned i = 0; i < Dim; i++)
      {
        interpolated_x[i] = 0.0;
      }
 
      // Calculate velocities and derivatives
      for (unsigned l = 0; l < n_node; l++)
      {
        // Loop over velocity components
        for (unsigned i = 0; i < Dim; i++)
        {
          interpolated_x[i] += nodal_position(l, i) * psif[l];
        }
      }
 
      // Get the local coordinate
      s_local[0] = integral_pt()->knot(ipt, 0);
 
      // Get bulk coordinate
      s_bulk = this->local_coordinate_in_bulk(s_local);
 
      // Upcast from GeneralisedElement to the present element
      ELEMENT* el_pt = dynamic_cast<ELEMENT*>(this->Bulk_element_pt);
 
      // Get du_dphi from bulk element
      dudphi = el_pt->interpolated_dudx_pnst(s_bulk, 0, 1);
 
      // The contribution to the unweighted shear stress
      shear_contribution += dudphi * W;
      // dudphi*interpolated_x[0]*W;
 
    } // End of loop over integration points
 
    return shear_contribution;
 
  } // End of get_shear_stress
 
} // End of namespace oomph
 
#endif