fish_domain.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
// LIC// version 2.1 of the License, or (at your option) any later version.
// LIC//
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// LIC// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
// LIC// Lesser General Public License for more details.
// LIC//
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// LIC//
// LIC// The authors may be contacted at oomph-lib@maths.man.ac.uk.
// LIC//
// LIC//====================================================================
// Include guards
#ifndef OOMPH_FISH_DOMAIN_HEADER
#define OOMPH_FISH_DOMAIN_HEADER
 
// Generic oomph-lib includes
#include "../generic/quadtree.h"
#include "../generic/domain.h"
#include "../generic/geom_objects.h"
 
namespace oomph
{
  //===========start_of_fish_domain=======================================
  /// Fish shaped domain, represented by four
  /// MacroElements. Shape is parametrised by GeomObject
  /// that represents the fish's back.
  //=======================================================================
  class FishDomain : public Domain
  {
  public:
    /// Constructor: Pass pointer to GeomObject that represents the
    /// (upper) curved boundary of the fish's body, and the start and end values
    /// of the Lagrangian coordinates along the GeomObject.
    FishDomain(GeomObject* back_pt,
               const double& xi_nose,
               const double& xi_tail)
      : Xi_nose(xi_nose), Xi_tail(xi_tail), Back_pt(back_pt)
    {
      // Set values for private data members that are describe
      // geometric features of the fish: x-coordinate of the fin,
      // (half-)height of the fin, and x-position of the mouth.
      X_fin = 1.7;
      Y_fin = 0.9;
      X_mouth = 0.0;
 
      // There are four macro elements
      unsigned nmacro = 4;
      Macro_element_pt.resize(nmacro);
 
      // Build them
      for (unsigned i = 0; i < nmacro; i++)
      {
        Macro_element_pt[i] = new QMacroElement<2>(this, i);
      }
    } // end of constructor
 
 
    /// Broken copy constructor
    FishDomain(const FishDomain&) = delete;
 
    /// Broken assignment operator
    void operator=(const FishDomain&) = delete;
 
    /// Destructor for FishDomain: Empty; cleanup done in base class
    virtual ~FishDomain() {}
 
 
    /// x-position of fin tip
    double& x_fin()
    {
      return X_fin;
    }
 
    /// y-position of fin tip
    double& y_fin()
    {
      return Y_fin;
    }
 
    /// x-position of mouth
    double& x_mouth()
    {
      return X_mouth;
    }
 
    /// Start coordinate on wall (near nose)
    double& xi_nose()
    {
      return Xi_nose;
    }
 
    /// End coordinate on wall (near tail)
    double& xi_tail()
    {
      return Xi_tail;
    }
 
    /// Vector representation of the  i_macro-th macro element
    /// boundary i_direct (N/S/W/E) at the discrete time level t
    /// (t=0: present; t>0: previous): \f$ {\bf r}({\bf zeta}) \f$
    /// Note that the local coordinate \b zeta is a 1D
    /// Vector rather than a scalar -- this is unavoidable because
    /// this function implements the pure virtual function in the
    /// Domain base class.
    void macro_element_boundary(const unsigned& t,
                                const unsigned& i_macro,
                                const unsigned& i_direct,
                                const Vector<double>& zeta,
                                Vector<double>& r);
 
  private:
    /// "Nose" limit for the (1D) coordinates along the wall
    double Xi_nose;
 
    /// "Tail" limit for the (1D) coordinates along the wall
    double Xi_tail;
 
    /// X coordinate of fin tip
    double X_fin;
 
    /// Y coordinate of fin tip
    double Y_fin;
 
    /// X coordinate of corner of mouth
    double X_mouth;
 
    /// Pointer to the fish's back
    GeomObject* Back_pt;
 
    /// Boundary of upper body macro element zeta \f$ \in [-1,1] \f$
    void r_upper_body_N(const unsigned& t,
                        const Vector<double>& zeta,
                        Vector<double>& f);
 
    /// Boundary of upper body macro element zeta \f$ \in [-1,1] \f$
    void r_upper_body_W(const unsigned& t,
                        const Vector<double>& zeta,
                        Vector<double>& f);
 
    /// Boundary of upper body macro element zeta \f$ \in [-1,1] \f$
    void r_upper_body_S(const unsigned& t,
                        const Vector<double>& zeta,
                        Vector<double>& f);
 
    /// Boundary of upper body macro element zeta \f$ \in [-1,1] \f$
    void r_upper_body_E(const unsigned& t,
                        const Vector<double>& zeta,
                        Vector<double>& f);
 
    /// Boundary of upper fin macro element zeta \f$ \in [-1,1] \f$
    void r_upper_fin_N(const unsigned& t,
                       const Vector<double>& zeta,
                       Vector<double>& f);
 
    /// Boundary of upper fin macro element zeta \f$ \in [-1,1] \f$
    void r_upper_fin_W(const unsigned& t,
                       const Vector<double>& zeta,
                       Vector<double>& f);
 
    /// Boundary of upper fin macro element zeta \f$ \in [-1,1] \f$
    void r_upper_fin_S(const unsigned& t,
                       const Vector<double>& zeta,
                       Vector<double>& f);
 
    /// Boundary of upper fin macro element zeta \f$ \in [-1,1] \f$
    void r_upper_fin_E(const unsigned& t,
                       const Vector<double>& zeta,
                       Vector<double>& f);
 
 
    /// Boundary of lower body macro element zeta \f$ \in [-1,1] \f$
    void r_lower_body_N(const unsigned& t,
                        const Vector<double>& zeta,
                        Vector<double>& f)
    {
      // North of lower body is element is south of upper one.
      // Direction of the coordinate stays the same.
      r_upper_body_S(t, zeta, f);
      // Reflect vertical position
      f[1] = -f[1];
    }
 
 
    /// Boundary of lower body macro element zeta \f$ \in [-1,1] \f$
    void r_lower_body_W(const unsigned& t,
                        const Vector<double>& zeta,
                        Vector<double>& f)
    {
      // West of lower body is element is west of upper one.
      // Direction of the coordinate is inverted
      Vector<double> zeta_new(1);
      zeta_new[0] = -zeta[0];
      r_upper_body_W(t, zeta_new, f);
      // Vertical coordinate is reflected
      f[1] = -f[1];
    }
 
    /// Southern boundary of lower body macro element zeta \f$\in [-1,1] \f$
    void r_lower_body_S(const unsigned& t,
                        const Vector<double>& zeta,
                        Vector<double>& f)
    {
      // South of lower body is element is north of upper one.
      // Direction of the coordinate stays the same.
      r_upper_body_N(t, zeta, f);
      // Reflect vertical position
      f[1] = -f[1];
    }
 
    /// Boundary of lower body macro element zeta \f$ \in [-1,1] \f$
    void r_lower_body_E(const unsigned& t,
                        const Vector<double>& zeta,
                        Vector<double>& f)
    {
      // East of lower body is element is east of upper one.
      // Direction of the coordinate is inverted.
      Vector<double> zeta_new(1);
      zeta_new[0] = -zeta[0];
      r_upper_body_E(t, zeta_new, f);
      // Vertical coordinate is reflected
      f[1] = -f[1];
    }
 
 
    /// Boundary of lower fin macro element zeta \f$ \in [-1,1] \f$
    void r_lower_fin_N(const unsigned& t,
                       const Vector<double>& zeta,
                       Vector<double>& f)
    {
      // North of lower fin is element is south of upper one.
      // Direction of the coordinate stays the same.
      r_upper_fin_S(t, zeta, f);
      // Reflect vertical position
      f[1] = -f[1];
    }
 
 
    /// Boundary of lower fin macro element zeta \f$ \in [-1,1] \f$
    void r_lower_fin_W(const unsigned& t,
                       const Vector<double>& zeta,
                       Vector<double>& f)
    {
      // West of lower fin is element is west of upper one.
      // Direction of the coordinate is inverted
      Vector<double> zeta_new(1);
      zeta_new[0] = -zeta[0];
      r_upper_fin_W(t, zeta_new, f);
      // Vertical coordinate is reflected
      f[1] = -f[1];
    }
 
    /// Boundary of lower fin macro element zeta \f$ \in [-1,1] \f$
    void r_lower_fin_S(const unsigned& t,
                       const Vector<double>& zeta,
                       Vector<double>& f)
    {
      // South of lower fin is element is north of upper one.
      // Direction of the coordinate stays the same.
      r_upper_fin_N(t, zeta, f);
      // Reflect vertical position
      f[1] = -f[1];
    }
 
    /// Boundary of lower fin macro element zeta \f$ \in [-1,1] \f$
    void r_lower_fin_E(const unsigned& t,
                       const Vector<double>& zeta,
                       Vector<double>& f)
    {
      // East of lower fin is element is east of upper one.
      // Direction of the coordinate is inverted.
      Vector<double> zeta_new(1);
      zeta_new[0] = -zeta[0];
      r_upper_fin_E(t, zeta_new, f);
      // Vertical coordinate is reflected
      f[1] = -f[1];
    }
  };
 
 
  /// //////////////////////////////////////////////////////////////////////
  /// //////////////////////////////////////////////////////////////////////
  /// //////////////////////////////////////////////////////////////////////
 
 
  //==========start_of_macro_element_boundary========================
  /// Vector representation of the  imacro-th macro element
  /// boundary idirect (N/S/W/E) at time level t
  /// (t=0: present; t>0: previous): \f$ {\bf r}({\bf zeta}) \f$
  /// Note that the local coordinate \b zeta is a 1D
  /// Vector rather than a scalar -- this is unavoidable because
  /// this function implements the pure virtual function in the
  /// Domain base class.
  //=================================================================
  void FishDomain::macro_element_boundary(const unsigned& t,
                                          const unsigned& imacro,
                                          const unsigned& idirect,
                                          const Vector<double>& zeta,
                                          Vector<double>& r)
  {
    using namespace QuadTreeNames;
 
 
#ifdef WARN_ABOUT_SUBTLY_CHANGED_OOMPH_INTERFACES
    // Warn about time argument being moved to the front
    OomphLibWarning(
      "Order of function arguments has changed between versions 0.8 and 0.85",
      "FishDomain::macro_element_boundary(...)",
      OOMPH_EXCEPTION_LOCATION);
#endif
 
 
    // Which macro element?
    // --------------------
    switch (imacro)
    {
        // Macro element 0: Lower body
      case 0:
 
        // Which direction?
        if (idirect == N)
        {
          FishDomain::r_lower_body_N(t, zeta, r);
        }
        else if (idirect == S)
        {
          FishDomain::r_lower_body_S(t, zeta, r);
        }
        else if (idirect == W)
        {
          FishDomain::r_lower_body_W(t, zeta, r);
        }
        else if (idirect == E)
        {
          FishDomain::r_lower_body_E(t, zeta, r);
        }
        else
        {
          std::ostringstream error_stream;
          error_stream << "idirect is " << idirect << " not one of N, S, E, W"
                       << std::endl;
 
          throw OomphLibError(error_stream.str(),
                              OOMPH_CURRENT_FUNCTION,
                              OOMPH_EXCEPTION_LOCATION);
        }
 
        break;
 
        // Macro element 1: Lower Fin
      case 1:
 
        // Which direction?
        if (idirect == N)
        {
          FishDomain::r_lower_fin_N(t, zeta, r);
        }
        else if (idirect == S)
        {
          FishDomain::r_lower_fin_S(t, zeta, r);
        }
        else if (idirect == W)
        {
          FishDomain::r_lower_fin_W(t, zeta, r);
        }
        else if (idirect == E)
        {
          FishDomain::r_lower_fin_E(t, zeta, r);
        }
        else
        {
          std::ostringstream error_stream;
          error_stream << "idirect is " << idirect << " not one of N, S, E, W"
                       << std::endl;
 
          throw OomphLibError(error_stream.str(),
                              OOMPH_CURRENT_FUNCTION,
                              OOMPH_EXCEPTION_LOCATION);
        }
 
        break;
 
 
        // Macro element 2: Upper body
      case 2:
 
        // Which direction?
        if (idirect == N)
        {
          FishDomain::r_upper_body_N(t, zeta, r);
        }
        else if (idirect == S)
        {
          FishDomain::r_upper_body_S(t, zeta, r);
        }
        else if (idirect == W)
        {
          FishDomain::r_upper_body_W(t, zeta, r);
        }
        else if (idirect == E)
        {
          FishDomain::r_upper_body_E(t, zeta, r);
        }
        else
        {
          std::ostringstream error_stream;
          error_stream << "idirect is " << idirect << " not one of N, S, E, W"
                       << std::endl;
 
          throw OomphLibError(error_stream.str(),
                              OOMPH_CURRENT_FUNCTION,
                              OOMPH_EXCEPTION_LOCATION);
        }
 
        break;
 
 
        // Macro element 3: Upper Fin
      case 3:
 
        // Which direction?
        if (idirect == N)
        {
          FishDomain::r_upper_fin_N(t, zeta, r);
        }
        else if (idirect == S)
        {
          FishDomain::r_upper_fin_S(t, zeta, r);
        }
        else if (idirect == W)
        {
          FishDomain::r_upper_fin_W(t, zeta, r);
        }
        else if (idirect == E)
        {
          FishDomain::r_upper_fin_E(t, zeta, r);
        }
        else
        {
          std::ostringstream error_stream;
          error_stream << "idirect is " << idirect << " not one of N, S, E, W"
                       << std::endl;
 
          throw OomphLibError(error_stream.str(),
                              OOMPH_CURRENT_FUNCTION,
                              OOMPH_EXCEPTION_LOCATION);
        }
 
        break;
 
      default:
 
        // Error
        std::ostringstream error_stream;
        error_stream << "Wrong imacro " << imacro << std::endl;
 
        throw OomphLibError(
          error_stream.str(), OOMPH_CURRENT_FUNCTION, OOMPH_EXCEPTION_LOCATION);
    }
 
  } // end of macro_element_boundary
 
 
  //=================================================================
  /// Northern edge of upper fin macro element; \f$ \zeta \in [-1,1] \f$
  //=================================================================
  void FishDomain::r_upper_fin_N(const unsigned& t,
                                 const Vector<double>& zeta,
                                 Vector<double>& r)
  {
    // Right end of fish back
    Vector<double> x(1);
    x[0] = Xi_tail;
    Vector<double> r_fish(2);
    Back_pt->position(t, x, r_fish);
 
    // Top end of fin
    Vector<double> r_fin(2);
    r_fin[0] = X_fin;
    r_fin[1] = Y_fin;
 
 
    // Straight line along upper fin
    r[0] = r_fish[0] + (r_fin[0] - r_fish[0]) * 0.5 * (zeta[0] + 1.0);
    r[1] = r_fish[1] + (r_fin[1] - r_fish[1]) * 0.5 * (zeta[0] + 1.0);
  }
 
 
  //=================================================================
  /// Western edge of upper fin macro element; \f$ \zeta \in [-1,1] \f$
  //=================================================================
  void FishDomain::r_upper_fin_W(const unsigned& t,
                                 const Vector<double>& zeta,
                                 Vector<double>& r)
  {
    // Right end of fish back
    Vector<double> x(1);
    x[0] = Xi_tail;
    Vector<double> r_fish(2);
    Back_pt->position(t, x, r_fish);
 
    r[0] = r_fish[0];
    r[1] = r_fish[1] * 0.5 * (zeta[0] + 1.0);
  }
 
 
  //=================================================================
  /// Southern edge of upper fin macro element; \f$ \zeta \in [-1,1] \f$
  //=================================================================
  void FishDomain::r_upper_fin_S(const unsigned& t,
                                 const Vector<double>& zeta,
                                 Vector<double>& r)
  {
    // Right end of fish back
    Vector<double> x(1);
    x[0] = Xi_tail;
    Vector<double> r_fish(2);
    Back_pt->position(t, x, r_fish);
 
 
    r[0] = r_fish[0] * 0.5 * (zeta[0] + 1.0);
    r[1] = 0.0;
  }
 
 
  //=================================================================
  /// Eastern edge of upper fin macro element; \f$ \zeta \in [-1,1] \f$
  //=================================================================
  void FishDomain::r_upper_fin_E(const unsigned& t,
                                 const Vector<double>& zeta,
                                 Vector<double>& r)
  {
    // Straight vertical line from top of fin
    r[0] = X_fin;
    r[1] = Y_fin * 0.5 * (zeta[0] + 1.0);
  }
 
 
  //===============start_of_r_upper_body_N==============================
  /// Northern edge of upper body macro element; \f$ \zeta \in [-1,1] \f$
  //=====================================================================
  void FishDomain::r_upper_body_N(const unsigned& t,
                                  const Vector<double>& zeta,
                                  Vector<double>& r)
  {
    // Lagrangian coordinate along curved "back"
    Vector<double> x(1);
    x[0] = Xi_nose + (Xi_tail - Xi_nose) * 0.5 * (zeta[0] + 1.0);
 
    // Get position on curved back
    Back_pt->position(t, x, r);
 
  } // end of r_upper_body_N
 
 
  //================start_of_r_upper_body_E=============================
  /// Eastern edge of upper body macro element; \f$ \zeta \in [-1,1] \f$
  //=====================================================================
  void FishDomain::r_upper_body_E(const unsigned& t,
                                  const Vector<double>& zeta,
                                  Vector<double>& r)
  {
    // Top right corner (tail end) of body
    Vector<double> r_top(2);
    Vector<double> x(1);
    x[0] = Xi_tail;
    Back_pt->position(t, x, r_top);
 
    // Corresponding point on the x-axis
    Vector<double> r_back(2);
    r_back[0] = r_top[0];
    r_back[1] = 0.0;
 
    r[0] = r_back[0] + (r_top[0] - r_back[0]) * 0.5 * (zeta[0] + 1.0);
    r[1] = r_back[1] + (r_top[1] - r_back[1]) * 0.5 * (zeta[0] + 1.0);
 
 
  } // end of r_upper_body_E
 
 
  //==================start_of_r_upper_body_S============================
  /// Southern edge of upper body macro element; \f$ \zeta \in [-1,1] \f$
  //=====================================================================
  void FishDomain::r_upper_body_S(const unsigned& t,
                                  const Vector<double>& zeta,
                                  Vector<double>& r)
  {
    // Top right (tail) corner of fish body
    Vector<double> r_top(2);
    Vector<double> x(1);
    x[0] = Xi_tail;
    Back_pt->position(t, x, r_top);
 
    // Straight line from mouth to start of fin (=end of body)
    r[0] = X_mouth + (r_top[0] - X_mouth) * 0.5 * (zeta[0] + 1.0);
    r[1] = 0.0;
 
  } // end of r_upper_body_S
 
 
  //===============start_of_r_upper_body_W==============================
  /// Western edge of upper body macro element; \f$ \zeta \in [-1,1] \f$
  //====================================================================
  void FishDomain::r_upper_body_W(const unsigned& t,
                                  const Vector<double>& zeta,
                                  Vector<double>& r)
  {
    // Top left (mouth) corner of curved boundary of upper body
    Vector<double> r_top(2);
    Vector<double> x(1);
    x[0] = Xi_nose;
    Back_pt->position(t, x, r_top);
 
    // The "mouth"
    Vector<double> r_mouth(2);
    r_mouth[0] = X_mouth;
    r_mouth[1] = 0.0;
 
    // Straight line from mouth to leftmost corner on curved boundary
    // of upper body
    r[0] = r_mouth[0] + (r_top[0] - r_mouth[0]) * 0.5 * (zeta[0] + 1.0);
    r[1] = r_mouth[1] + (r_top[1] - r_mouth[1]) * 0.5 * (zeta[0] + 1.0);
 
  } // end of r_upper_body_W
 
 
} // namespace oomph
 
#endif