spine_channel2.cc

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//LIC// at http://www.oomph-lib.org.
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//LIC// Copyright (C) 2006-2023 Matthias Heil and Andrew Hazel
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//LIC//====================================================================
// Driver for 2-D Channel with changing width, using Taylor Hood 
// and Crouzeix Raviart elements.
 
// Generic oomph-lib header
#include "generic.h"
 
// Navier Stokes headers
#include "navier_stokes.h"
 
// The mesh
#include "meshes/channel_spine_mesh.h"
 
using namespace std;
 
using namespace oomph;
 
//==start_of_namespace===================================================
/// Namespace for physical parameters
//=======================================================================
namespace Global_Physical_Variables2
{
 /// Reynolds number
 double Re=100;
} // end_of_namespace
 
 
/// ////////////////////////////////////////////////////////////////////
/// ////////////////////////////////////////////////////////////////////
// Deflected line as geometric object
/// ////////////////////////////////////////////////////////////////////
/// ////////////////////////////////////////////////////////////////////
 
 
 
//=========================================================================
/// Steady, spiked 1D line in 2D space 
///  \f[ x = \zeta \f]
///  \f[ y = \left\{
///  \begin{array}{cl}
///  H + 2A\left(\frac{\zeta - \zeta_{\mbox{min}}}
///                   {\zeta_{\mbox{max}} - \zeta_{\mbox{min}}}\right) & 
/// \mbox{for } \zeta \leq \frac{1}{2}
///            \left(\zeta_{\mbox{max}} + \zeta_{\mbox{min}}\right)\\H +
///  2A\left(\frac{\zeta - \zeta_{\mbox{max}}}
///                   {\zeta_{\mbox{min}} - \zeta_{\mbox{max}}}\right) & 
/// \mbox{for } \zeta > \frac{1}{2}
///            \left(\zeta_{\mbox{max}} 
///  + \zeta_{\mbox{min}}\right)\\   \end{array}
///                          \right.\f]
//=========================================================================
class SpikedLine : public GeomObject
{
 
public:
 
 /// Constructor:  Four item of geometric data: 
 /// \code
 ///  Geom_data_pt[0]->value(0) = height
 ///  Geom_data_pt[0]->value(1) = amplitude
 ///  Geom_data_pt[0]->value(2) = zeta_min
 ///  Geom_data_pt[0]->value(3) = zeta_max
 /// \endcode
 SpikedLine(const Vector<Data*>& geom_data_pt) : GeomObject(1,2)
  {
#ifdef PARANOID
   if (geom_data_pt.size()!=1)
    {
     std::ostringstream error_stream;
     error_stream 
      << "Wrong size for geom_data_pt " << geom_data_pt.size() << std::endl;
     if (geom_data_pt[0]->nvalue()!=1)
      {
       error_stream << "Wrong geom_data_pt[0]->nvalue() " 
                    << geom_data_pt[0]->nvalue() << std::endl;
      }
     
     throw OomphLibError(error_stream.str(),
                         OOMPH_CURRENT_FUNCTION,
                         OOMPH_EXCEPTION_LOCATION);
    }
#endif
   Geom_data_pt.resize(1);
   Geom_data_pt[0]=geom_data_pt[0];
 
   // Data has been created externally: Must not clean up
   Must_clean_up=false;
  }
 
 
 /// Constructor:  Pass height, amplitude, zeta min and zeta max
 /// (all are pinned by default)
 SpikedLine(const double& height, const double& amplitude,
            const double& zeta_min, const double& zeta_max)
  : GeomObject(1,2)
  {
   // Create Data for deflected-line object
   Geom_data_pt.resize(1);
   
   // Create data: Four value, no timedependence, free by default
   Geom_data_pt[0] = new Data(4);
 
   // I've created the data, I need to clean up
   Must_clean_up=true;
   
   // Pin the data
   for (unsigned i=0;i<4;i++) {Geom_data_pt[0]->pin(i);}
   
   // Give it a value: Initial height
   Geom_data_pt[0]->set_value(0,height);
   Geom_data_pt[0]->set_value(1,amplitude);
   Geom_data_pt[0]->set_value(2,zeta_min);
   Geom_data_pt[0]->set_value(3,zeta_max);
  }
 
 
 /// Destructor:  Clean up if necessary
 ~SpikedLine()
  {
   // Do I need to clean up?
   if (Must_clean_up)
    {
     delete Geom_data_pt[0];
     Geom_data_pt[0]=0;
    }
  }
 
 
 /// Position Vector at Lagrangian coordinate zeta 
 void position(const Vector<double>& zeta, Vector<double>& r) const
  {
#ifdef PARANOID
   if (r.size()!=Ndim)
    {
     throw OomphLibError("The vector r has the wrong dimension\n",
                         OOMPH_CURRENT_FUNCTION,
                         OOMPH_EXCEPTION_LOCATION);
    }
#endif
   // Get parametres
   double H = Geom_data_pt[0]->value(0);
   double A = Geom_data_pt[0]->value(1);
   double zeta_min = Geom_data_pt[0]->value(2);
   double zeta_max = Geom_data_pt[0]->value(3);
   double halfLz = (zeta_max-zeta_min)/2.0;
   
   // Position Vector
   r[0] = zeta[0];
   if (zeta[0]-zeta_min<=halfLz)
    {
     r[1] = H + A*(zeta[0]-zeta_min)/halfLz;
    }
   else
    {
     r[1] = H - A*(zeta[0]-zeta_max)/halfLz;
    }
  }
 
 
 /// Parametrised position on object: r(zeta). Evaluated at
 /// previous timestep. t=0: current time; t>0: previous
 /// timestep. 
 void position(const unsigned& t, const Vector<double>& zeta,
               Vector<double>& r) const
  {
#ifdef PARANOID
   if (t>Geom_data_pt[0]->time_stepper_pt()->nprev_values())
    {
     std::ostringstream error_stream;
     error_stream 
      << "t > nprev_values() in SpikedLine:  " << t << " " 
      << Geom_data_pt[0]->time_stepper_pt()->nprev_values() << std::endl;
 
     throw OomphLibError(error_stream.str(),
                         OOMPH_CURRENT_FUNCTION,
                         OOMPH_EXCEPTION_LOCATION);
    }
#endif
 
   // Get parametres
   double H = Geom_data_pt[0]->value(t,0);
   double A = Geom_data_pt[0]->value(t,1);
   double zeta_min = Geom_data_pt[0]->value(t,2);
   double zeta_max = Geom_data_pt[0]->value(t,3);
   double halfLz = (zeta_max-zeta_min)/2.0;
   
   // Position Vector
   r[0] = zeta[0];
   if (zeta[0]-zeta_min<=halfLz)
    {
     r[1] = H + A*(zeta[0]-zeta_min)/halfLz;
    }
   else
    {
     r[1] = H - A*(zeta[0]-zeta_max)/halfLz;
    }
  }
 
 
 /// Derivative of position Vector w.r.t. to coordinates: 
 /// \f$ \frac{dR_i}{d \zeta_\alpha}\f$ = drdzeta(alpha,i). 
 /// Evaluated at current time.
 virtual void dposition(const Vector<double>& zeta, 
                        DenseMatrix<double> &drdzeta) const
  {
   // Get parametres
   double A = Geom_data_pt[0]->value(1);
   double zeta_min = Geom_data_pt[0]->value(2);
   double zeta_max = Geom_data_pt[0]->value(3);
   double halfLz = (zeta_max-zeta_min)/2.0;
 
   // Tangent vector
   drdzeta(0,0)=1.0;
   if (zeta[0]-zeta_min<=halfLz)
    {
     drdzeta(0,1)=A/halfLz;
    }
   else
    {
     drdzeta(0,1)=-A/halfLz;
    }
  }
 
 
 /// 2nd derivative of position Vector w.r.t. to coordinates: 
 /// \f$ \frac{d^2R_i}{d \zeta_\alpha d \zeta_\beta}\f$ = ddrdzeta(alpha,beta,i). 
 /// Evaluated at current time.
 virtual void d2position(const Vector<double>& zeta, 
                         RankThreeTensor<double> &ddrdzeta) const
  {
   // Derivative of tangent vector
   ddrdzeta(0,0,0)=0.0;
   ddrdzeta(0,0,1)=0.0;
  }
 
 
 /// Posn Vector and its  1st & 2nd derivatives
 /// w.r.t. to coordinates:
 /// \f$ \frac{dR_i}{d \zeta_\alpha}\f$ = drdzeta(alpha,i). 
 /// \f$ \frac{d^2R_i}{d \zeta_\alpha d \zeta_\beta}\f$ = ddrdzeta(alpha,beta,i). 
 /// Evaluated at current time.
 virtual void d2position(const Vector<double>& zeta, Vector<double>& r,
                         DenseMatrix<double> &drdzeta,
                         RankThreeTensor<double> &ddrdzeta) const
  {
   // Get parametres
   double H = Geom_data_pt[0]->value(0);
   double A = Geom_data_pt[0]->value(1);
   double zeta_min = Geom_data_pt[0]->value(2);
   double zeta_max = Geom_data_pt[0]->value(3);
   double halfLz = (zeta_max-zeta_min)/2.0;
 
   // Position Vector
   r[0] = zeta[0];
   if (zeta[0]-zeta_min<=halfLz)
    {
     r[1] = H + A*(zeta[0]-zeta_min)/halfLz;
    }
   else
    {
     r[1] = H - A*(zeta[0]-zeta_max)/halfLz;
    }
 
   // Tangent vector
   drdzeta(0,0)=1.0;
   if (zeta[0]-zeta_min<=halfLz)
    {
     drdzeta(0,1)=A/halfLz;
    }
   else
    {
     drdzeta(0,1)=-A/halfLz;
    }
 
   // Derivative of tangent vector
   ddrdzeta(0,0,0)=0.0;
   ddrdzeta(0,0,1)=0.0;
  }
 
 /// How many items of Data does the shape of the object depend on?
 unsigned ngeom_data() const {return Geom_data_pt.size();}
 
 /// Return pointer to the j-th Data item that the object's 
 /// shape depends on 
 Data* geom_data_pt(const unsigned& j) {return Geom_data_pt[j];}
 
 
private:
 
 /// Vector of pointers to Data items that affects the object's shape
 Vector<Data*> Geom_data_pt;
 
 /// Do I need to clean up?
 bool Must_clean_up;
 
};
 
/// ////////////////////////////////////////////////////////////////////
/// ////////////////////////////////////////////////////////////////////
/// ////////////////////////////////////////////////////////////////////
 
 
 
//==start_of_problem_class============================================
/// Channel flow, through a non-uniform channel, using Spines.
//====================================================================
template<class ELEMENT>
class SpikedChannelSpineFlowProblem : public Problem
{
private:
 
 /// Width of channel
 double Ly;
 
public:
 
 /// Destructor: Empty
 ~SpikedChannelSpineFlowProblem(){}
 
 /// Update the after solve (empty)
 void actions_after_newton_solve() {}
 
 /// Update the problem specs before solve. 
 /// set velocity boundary conditions just to be on the safe side...
 void actions_before_newton_solve()
  { 
   // Update the mesh
   mesh_pt()->node_update();
 
   // Setup inflow flow along boundary 3:
   unsigned ibound=3; 
   unsigned num_nod= mesh_pt()->nboundary_node(ibound);
   for (unsigned inod=0;inod<num_nod;inod++)
    {
     double y=mesh_pt()->boundary_node_pt(ibound,inod)->x(1);
     // parabolic inflow
     unsigned i=0;
     mesh_pt()->boundary_node_pt(ibound,inod)->set_value(i,y*(Ly-y));
     // 0 Tangential flow
     i=1;
     mesh_pt()->boundary_node_pt(ibound,inod)->set_value(i,0);
    }
  
   // Overwrite with no flow along top & bottom boundaries and
   // parallel outflow
   unsigned num_bound = mesh_pt()->nboundary();
   for(unsigned ibound=0;ibound<num_bound-1;ibound++)
    {
     unsigned num_nod= mesh_pt()->nboundary_node(ibound);
     for (unsigned inod=0;inod<num_nod;inod++)
      {
       for (unsigned i=0;i<2;i++)
        {
         if (ibound!=1)
          {
           mesh_pt()->boundary_node_pt(ibound,inod)->set_value(i,0.0);
          }
         else
          {
           mesh_pt()->boundary_node_pt(ibound,inod)->set_value(1,0.0);
          }
        }
      }
    }
   // Leave boundary 1 free!
  } // end_of_actions_before_newton_solve
 
 /// Upcasted access function for the mesh
 ChannelSpineMesh<ELEMENT>* mesh_pt()
  {
   return dynamic_cast<ChannelSpineMesh<ELEMENT>*>(Problem::mesh_pt());
  }
 
 /// Constructor
 SpikedChannelSpineFlowProblem();
 
 /// Doc the solution
 void doc_solution(DocInfo& doc_info);
 
}; // end_of_problem_class
 
 
 
//==start_of_constructor==================================================
/// Constructor for SpikedChannelSpineFlow problem 
///
//========================================================================
template<class ELEMENT>
SpikedChannelSpineFlowProblem<ELEMENT>::SpikedChannelSpineFlowProblem()
{ 
 
 // Setup mesh
 
 // # of elements in x-direction in left region 
 unsigned Nx0=3;
 // # of elements in x-direction in centre region
 unsigned Nx1=12;
 // # of elements in x-direction in right region
 unsigned Nx2=8;
 
 // # of elements in y-direction
 unsigned Ny=10;
 
 // Domain length in x-direction in left region
 double Lx0=0.5;
 // Domain length in x-direction in centre region
 double Lx1=0.7;
 // Domain length in x-direction in right region
 double Lx2=1.5;
 
 // Domain length in y-direction
 Ly=1.0;
 
 double amplitude_upper = -0.4*Ly;
 double zeta_min=Lx0;
 double zeta_max=Lx0+Lx1;
 GeomObject* UpperWall = 
  new SpikedLine(Ly,amplitude_upper,zeta_min,zeta_max);
 
 // Build and assign mesh
 Problem::mesh_pt() = new ChannelSpineMesh<ELEMENT>(Nx0,Nx1,Nx2,Ny,
                                                    Lx0,Lx1,Lx2,Ly,
                                                    UpperWall);
 
 // Set the boundary conditions for this problem: All nodes are
 // free by default -- just pin the ones that have Dirichlet conditions
 // here: All boundaries are Dirichlet boundaries, except on boundary 1
 unsigned num_bound = mesh_pt()->nboundary();
 for(unsigned ibound=0;ibound<num_bound;ibound++)
  {
   unsigned num_nod= mesh_pt()->nboundary_node(ibound);
   for (unsigned inod=0;inod<num_nod;inod++)
    {
     if (ibound!=1)
      {
       // Loop over values (u and v velocities)
       for (unsigned i=0;i<2;i++)
        {
         mesh_pt()->boundary_node_pt(ibound,inod)->pin(i); 
        }
      }
     else
      {
       // Parallel outflow ==> no-slip
       mesh_pt()->boundary_node_pt(ibound,inod)->pin(1); 
      }
    }
  } // end loop over boundaries
 
 // Find number of elements in mesh
 unsigned n_element = mesh_pt()->nelement();
 
 // Loop over the elements to set up element-specific 
 // things that cannot be handled by constructor: Pass pointer to Reynolds
 // number
 for(unsigned e=0;e<n_element;e++)
  {
   // Upcast from GeneralisedElement to the present element
   ELEMENT* el_pt = dynamic_cast<ELEMENT*>(mesh_pt()->element_pt(e));
   //Set the Reynolds number
   el_pt->re_pt() = &Global_Physical_Variables2::Re;
  } // end loop over elements
 
 // Setup equation numbering scheme
 cout <<"Number of equations: " << assign_eqn_numbers() << std::endl; 
 
} // end_of_constructor
 
 
 
//==start_of_doc_solution=================================================
/// Doc the solution
//========================================================================
template<class ELEMENT>
void SpikedChannelSpineFlowProblem<ELEMENT>::doc_solution(DocInfo& doc_info)
{ 
 
 ofstream some_file;
 char filename[100];
 
 // Number of plot points
 unsigned npts=5; 
 
 // Output solution 
 sprintf(filename,"%s/soln%i.dat",doc_info.directory().c_str(),
         doc_info.number());
 some_file.open(filename);
 mesh_pt()->output(some_file,npts);
 some_file.close();
 
} // end_of_doc_solution
 
 
//==start_of_main======================================================
/// Driver for SpikedChannelSpineFlow test problem 
//=====================================================================
int main()
{
 // Set output directory
 DocInfo doc_info;
 doc_info.set_directory("RESLT");
 doc_info.number()=0;
 
 // Solve problem with Taylor Hood elements
 //---------------------------------------
 {
  //Build problem
  SpikedChannelSpineFlowProblem<SpineElement<QTaylorHoodElement<2> > >
   problem;
  
  // Solve the problem with automatic adaptation
  problem.newton_solve();
  
  //Output solution
  problem.doc_solution(doc_info);
  // Step number
  doc_info.number()++;
 
 } // end of Taylor Hood elements
 
 
 // Solve problem with Crouzeix Raviart elements
 //--------------------------------------------
 {
  // Build problem
  SpikedChannelSpineFlowProblem<SpineElement<QCrouzeixRaviartElement<2> > >
   problem;
  
  // Solve the problem with automatic adaptation
  problem.newton_solve();
  
  //Output solution
  problem.doc_solution(doc_info);
  // Step number
  doc_info.number()++;
  
 } // end of Crouzeix Raviart elements
      
     
} // end_of_main