helical_pipe.cc

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//LIC// Copyright (C) 2006-2025 Matthias Heil and Andrew Hazel
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//LIC//====================================================================
/// Driver for a 3D navier stokes steady entry flow problem in a helical
/// tube
 
//Generic routines
#include "generic.h"
#include "navier_stokes.h"
 
// The mesh
#include "meshes/tube_mesh.h"
 
using namespace std;
 
using namespace oomph;
 
 
//=start_of_MyHelicalCylinder==============================================
/// The arguemts are the radius of the tube, its curvature in the x,y plane
/// and the pitch of the helix
//=========================================================================
class MyHelicalCylinder : public GeomObject
{
public:
 
/// Constructor
 MyHelicalCylinder(const double &radius, const double& delta, 
                   const double& pitch) :
  GeomObject(3,3),Radius(radius),Delta(delta),P(pitch)
  {
   //Set the value of pi
   Pi = MathematicalConstants::Pi;
  } 
 
/// Destructor
virtual~MyHelicalCylinder(){}
 
/// Lagrangian coordinate xi
void position (const Vector<double>& xi, Vector<double>& r) const
{
 r[0] = (1.0/Delta)*cos(xi[0]) + xi[2]*Radius*cos(xi[0])*cos(xi[1]);
 r[1] = (1.0/Delta)*sin(xi[0]) + xi[2]*Radius*sin(xi[0])*cos(xi[1]);
 r[2] = P*xi[0]/(2.0*Pi) - xi[2]*Radius*sin(xi[1]);
}
 
 
/// Return the position of the tube as a function of time 
/// (doesn't move as a function of time)
void position(const unsigned& t, 
              const Vector<double>& xi, Vector<double>& r) const
  {
   position(xi,r);
  }
 
private:
 double Pi;
 double Radius;
 double Delta;
 double P;
};
 
//=start_of_namespace================================================
/// Namespace for physical parameters
//===================================================================
namespace Global_Physical_Variables
{
 /// Reynolds number
 double Re=50;
 
 double Delta=0.5;
 double Pitch = 1.0;
} // end_of_namespace
 
 
//=start_of_problem_class=============================================
/// Entry flow problem in tapered tube domain
//====================================================================
template<class ELEMENT>
class SteadyHelicalProblem : public Problem
{
 
public:
 
 /// Constructor: Pass DocInfo object and target errors
 SteadyHelicalProblem(DocInfo& doc_info, const double& min_error_target,
                  const double& max_error_target);
 
 /// Destructor (empty)
 ~SteadyHelicalProblem() {}
 
 /// Update the problem specs before solve 
 void actions_before_newton_solve();
 
 /// After adaptation: Pin redudant pressure dofs.
 void actions_after_adapt()
  {
   // Pin redudant pressure dofs
   RefineableNavierStokesEquations<3>::
    pin_redundant_nodal_pressures(mesh_pt()->element_pt());
  } 
 
 /// Doc the solution
 void doc_solution();
 
 /// Overload generic access function by one that returns
 /// a pointer to the specific  mesh
 RefineableTubeMesh<ELEMENT>* mesh_pt() 
  {
   return dynamic_cast<RefineableTubeMesh<ELEMENT>*>(Problem::mesh_pt());
  }
 
private:
 
 /// Exponent for bluntness of velocity profile
 int Alpha;
 
 /// Doc info object
 DocInfo Doc_info;
 
 /// Pointer to GeomObject that specifies the domain boundary
 GeomObject*Wall_pt;
 
}; // end_of_problem_class
 
 
 
 
//=start_of_constructor===================================================
/// Constructor: Pass DocInfo object and error targets
//========================================================================
template<class ELEMENT>
SteadyHelicalProblem<ELEMENT>::SteadyHelicalProblem(DocInfo& doc_info,
                                            const double& min_error_target,
                                            const double& max_error_target) 
 : Doc_info(doc_info)
{ 
 //Increase the value of the maximum residuals so that the first
 //newton step converges.
 Max_residuals = 100.0;
 
 // Setup mesh:
 //------------
 
 //Build geometric object that forms the domain boundary: a tapered curved tube
 double d=Global_Physical_Variables::Delta;
 double p=Global_Physical_Variables::Pitch;
 
// Create GeomObject that specifies the domain boundary
Wall_pt=new MyHelicalCylinder(1.0,d,p);
 
//Define pi 
 const double pi = MathematicalConstants::Pi;
 
 
//Set the centerline coordinates for the start and end of the helix
 Vector<double> centreline_limits(2);
 centreline_limits[0] = 0.0;
 centreline_limits[1] = pi;
 
 //Set the positions of the angles that divide the outer ring of elements
 Vector<double> theta_positions(4);
 theta_positions[0] = -0.75*pi;
 theta_positions[1] = -0.25*pi;
 theta_positions[2] = 0.25*pi;
 theta_positions[3] = 0.75*pi;
 
 //Define the radial fraction for the central box in the domain
 Vector<double> radial_frac(4,0.5);
 
 // Number of layers in the mesh
 unsigned nlayer=6;
 
 // Build and assign mesh
 Problem::mesh_pt()=
  new RefineableTubeMesh<ELEMENT>(Wall_pt,
                                  centreline_limits,
                                  theta_positions,
                                  radial_frac,
                                  nlayer);
 
 // Set error estimator 
 Z2ErrorEstimator* error_estimator_pt=new Z2ErrorEstimator;
 mesh_pt()->spatial_error_estimator_pt()=error_estimator_pt;
 
 // Error targets for adaptive refinement
 mesh_pt()->max_permitted_error()=max_error_target; 
 mesh_pt()->min_permitted_error()=min_error_target; 
 
 // Set the boundary conditions for this problem: All nodal values are
 // free by default -- just pin the ones that have Dirichlet conditions
 // here. 
 //Choose the conventional form by setting gamma to zero
 //The boundary conditions will be pseudo-traction free (d/dn = 0)
 ELEMENT::Gamma[0] = 0.0;
 ELEMENT::Gamma[1] = 0.0;
 ELEMENT::Gamma[2] = 0.0;
 
 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++)
    {
     // Boundary 0 is the inlet symmetry boundary: 
     // Boundary 1 is the tube wall
     // Pin all values
     if((ibound==0) || (ibound==1))
      {
       mesh_pt()->boundary_node_pt(ibound,inod)->pin(0);
       mesh_pt()->boundary_node_pt(ibound,inod)->pin(1);
       mesh_pt()->boundary_node_pt(ibound,inod)->pin(2);
      }
     
     //Boundary 2 is the outflow boundary, pin z, 
     //leave traction  free
     if(ibound==2)
      {
       //mesh_pt()->boundary_node_pt(ibound,inod)->pin(2);
      }
    }
  } // end loop over boundaries
 
 // Loop over the elements to set up element-specific 
 // things that cannot be handled by constructor
 unsigned n_element = mesh_pt()->nelement();
 for(unsigned i=0;i<n_element;i++)
  {
   // Upcast from GeneralisedElement to the present element
   ELEMENT* el_pt = dynamic_cast<ELEMENT*>(mesh_pt()->element_pt(i));
 
   //Set the Reynolds number, etc
   el_pt->re_pt() = &Global_Physical_Variables::Re;
  }
 
 // Pin redudant pressure dofs
 RefineableNavierStokesEquations<3>::
  pin_redundant_nodal_pressures(mesh_pt()->element_pt());
 
 //Attach the boundary conditions to the mesh
 cout <<"Number of equations: " << assign_eqn_numbers() << std::endl; 
 
} // end_of_constructor
 
 
//=start_of_actions_before_newton_solve==========================================
/// Set the inflow boundary conditions
//========================================================================
template<class ELEMENT>
void SteadyHelicalProblem<ELEMENT>::actions_before_newton_solve()
{
 
 // (Re-)assign velocity profile at inflow values
 //--------------------------------------------
 unsigned ibound=0; 
 unsigned num_nod= mesh_pt()->nboundary_node(ibound); 
 for (unsigned inod=0;inod<num_nod;inod++)
  {
   // Recover coordinates
   double x=mesh_pt()->boundary_node_pt(ibound,inod)->x(0) - 
    1.0/Global_Physical_Variables::Delta;
   double z=mesh_pt()->boundary_node_pt(ibound,inod)->x(2);
   double r=sqrt(x*x+z*z);  
 
   // Bluntish profile for axial velocity (component 1)
   mesh_pt()->boundary_node_pt(ibound,inod)->
    set_value(1,(1.0-pow(r,2.0)));
  }
 
} // end_of_actions_before_newton_solve
 
 
//=start_of_doc_solution==================================================
/// Doc the solution
//========================================================================
template<class ELEMENT>
void SteadyHelicalProblem<ELEMENT>::doc_solution()
{ 
 
 ofstream some_file;
 char filename[100];
 
 // Number of plot points
 unsigned npts;
 npts=5; 
 
 //Need high precision for large radii of curvature
 //some_file.precision(10);
 // Output solution 
 snprintf(filename, sizeof(filename), "%s/soln_Re%g.dat",Doc_info.directory().c_str(),
         Global_Physical_Variables::Re);
 some_file.open(filename);
 mesh_pt()->output(some_file,npts);
 some_file.close();
 
} // end_of_doc_solution
 
 
 
 
////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////
 
 
//=start_of_main=======================================================
/// Driver for 3D entry flow into a tapered tube. If there are
/// any command line arguments, we regard this as a validation run
/// and perform only a single adaptation
//=====================================================================
int main(int argc, char* argv[]) 
{
 
 // Store command line arguments
 CommandLineArgs::setup(argc,argv);
 
 // Allow (up to) two rounds of fully automatic adapation in response to 
 //-----------------------------------------------------------------------
 // error estimate
 //---------------
 unsigned max_adapt;
 double max_error_target,min_error_target;
 
 // Set max number of adaptations in black-box Newton solver and
 // error targets for adaptation
 if (CommandLineArgs::Argc==1)
  {
   // Up to two adaptations
   max_adapt=2;
 
   // Error targets for adaptive refinement
   max_error_target=0.005;
   min_error_target=0.0005;
  } 
 // Validation run: Only one adaptation. Relax error targets
 // to ensure that not all elements are refined so we're getting
 // some hanging nodes.
 else
  {
   // Validation run: Just one round of adaptation
   max_adapt=1;
   
   // Error targets for adaptive refinement
   max_error_target=0.02;
   min_error_target=0.002;
  }
 // end max_adapt setup
 
 
 // Set up doc info
 DocInfo doc_info;
 
 // Do Taylor-Hood elements
 //------------------------
 {
  // Set output directory
  doc_info.set_directory("RESLT_TH");
  
  // Step number
  doc_info.number()=0;
  
  // Build problem
  SteadyHelicalProblem<RefineableQTaylorHoodElement<3> > 
   problem(doc_info,min_error_target,max_error_target);
  
  cout << " Doing Taylor-Hood elements " << std::endl;
  
  // Solve the problem 
  problem.newton_solve(max_adapt);
  // Doc solution after solving
  problem.doc_solution();
 }
 
 // Do Crouzeix-Raviart elements
 //------------------------
 {
  // Set output directory
  doc_info.set_directory("RESLT_CR");
  
  // Step number
  doc_info.number()=0;
  
  // Build problem
  SteadyHelicalProblem<RefineableQCrouzeixRaviartElement<3> > 
   problem(doc_info,min_error_target,max_error_target);
  
  cout << " Doing Crouzeix-Raviart elements " << std::endl;
  
  // Solve the problem 
  problem.newton_solve(max_adapt);
  // Doc solution after solving
  problem.doc_solution();
 }
 
} // end_of_main