driven_cavity.cc

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//LIC// ====================================================================
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//LIC// Copyright (C) 2006-2025 Matthias Heil and Andrew Hazel
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//LIC//====================================================================
//Driver for 2D rectangular driven cavity
 
//Generic includes
#include "generic.h"
#include "navier_stokes.h"
 
#include "meshes/simple_rectangular_quadmesh.h"
 
 
using namespace std;
 
using namespace oomph;
 
 
//==start_of_namespace==============================
/// Namespace for physical parameters
//==================================================
namespace Global_Physical_Variables
{
 
 /// Reynolds number
 double Re=100;
 
} // end_of_namespace
 
 
 
////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////
 
 
 
//==start_of_problem_class============================================
/// Driven cavity problem in rectangular domain
//====================================================================
template<class ELEMENT>
class RectangularDrivenCavityProblem : public Problem
{
 
public:
 
 
 /// Constructor
 RectangularDrivenCavityProblem();
 
 /// Destructor (empty)
 ~RectangularDrivenCavityProblem(){}
 
 /// Fix pressure in element e at pressure dof pdof and set to pvalue
 void fix_pressure(const unsigned &e, const unsigned &pdof, 
                   const double &pvalue)
  {
   //Cast to full element type and fix the pressure at that element
   dynamic_cast<ELEMENT*>(mesh_pt()->element_pt(e))->
                          fix_pressure(pdof,pvalue);
  } // end of fix_pressure
 
 
 /// Update the after solve (empty)
 void actions_after_newton_solve(){}
 
 
 /// Update the problem specs before solve. 
 /// Re-set velocity boundary conditions just to be on the safe side...
 void actions_before_newton_solve()
 {
  // Setup tangential flow along boundary 0:
  unsigned ibound=0; 
  unsigned num_nod= mesh_pt()->nboundary_node(ibound);
  for (unsigned inod=0;inod<num_nod;inod++)
   {
    // Tangential flow
    unsigned i=0;
    mesh_pt()->boundary_node_pt(ibound,inod)->set_value(i,1.0);
    // No penetration
    i=1;
    mesh_pt()->boundary_node_pt(ibound,inod)->set_value(i,0.0);
   }
  
  // Overwrite with no flow along the other boundaries
  unsigned num_bound = mesh_pt()->nboundary();
  for(unsigned ibound=1;ibound<num_bound;ibound++)
   {
    unsigned num_nod= mesh_pt()->nboundary_node(ibound);
    for (unsigned inod=0;inod<num_nod;inod++)
     {
      for (unsigned i=0;i<2;i++)
       {
        mesh_pt()->boundary_node_pt(ibound,inod)->set_value(i,0.0);
       }
     }
   }
 } // end_of_actions_before_newton_solve
 
 // Access function for the specific mesh
 SimpleRectangularQuadMesh<ELEMENT>* mesh_pt() 
  {
   // Upcast from pointer to the Mesh base class to the specific 
   // element type that we're using here.
   return dynamic_cast<SimpleRectangularQuadMesh<ELEMENT>*>(
    Problem::mesh_pt());
  }
 
 
 /// Doc the solution
 void doc_solution(DocInfo& doc_info);
 
}; // end_of_problem_class
 
 
//==start_of_constructor==================================================
/// Constructor for RectangularDrivenCavity problem 
//========================================================================
template<class ELEMENT>
RectangularDrivenCavityProblem<ELEMENT>::RectangularDrivenCavityProblem()
{ 
 
 // Setup mesh
 
 // # of elements in x-direction
 unsigned n_x=10;
 
 // # of elements in y-direction
 unsigned n_y=10;
 
 // Domain length in x-direction
 double l_x=1.0;
 
 // Domain length in y-direction
 double l_y=1.0;
 
 // Build and assign mesh
 Problem::mesh_pt() = new SimpleRectangularQuadMesh<ELEMENT>(n_x,n_y,l_x,l_y);
 
 // Set the boundary conditions for this problem: All nodes are
 // free by default -- just pin the ones that have Dirichlet conditions
 // here. 
 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++)
    {
     // Loop over values (u and v velocities)
     for (unsigned i=0;i<2;i++)
      {
       mesh_pt()->boundary_node_pt(ibound,inod)->pin(i); 
      }
    }
  } // end loop over boundaries
 
 // Complete the build of all elements so they are fully functional
 
 //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
 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_Variables::Re;
  } // end loop over elements
 
 // Now set the first pressure value in element 0 to 0.0
 fix_pressure(0,0,0.0);
 
 // 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 RectangularDrivenCavityProblem<ELEMENT>::doc_solution(DocInfo& doc_info)
{ 
 ofstream some_file;
 char filename[100];
 
 // Number of plot points
 unsigned npts;
 npts=5; 
 
 // Output solution 
 snprintf(filename, sizeof(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 RectangularDrivenCavity test problem -- test drive
/// with two different types of element.
//=====================================================================
int main()
{
 
 // Set up doc info
 // ---------------
 
 // Label for output
 DocInfo doc_info;
 
 // Set output directory
 doc_info.set_directory("RESLT");
 
 // Step number
 doc_info.number()=0;
 
 // ---------------
 // end of Set up doc info
 
 // Doing QCrouzeixRaviartElements
 {
  
  // Build the problem with QCrouzeixRaviartElements
  RectangularDrivenCavityProblem<QCrouzeixRaviartElement<2> > problem;
  cout << "Doing QCrouzeixRaviartElement<2>" << std::endl;
  
  // Solve the problem
  problem.newton_solve();
  
  // Outpt the solution
  problem.doc_solution(doc_info);
 
  // Step number
  doc_info.number()++;
 
 } // end of QCrouzeixRaviartElements
 
 // Doing QTaylorHoodElements
 {
  
  // Build the problem with QTaylorHoodElements
  RectangularDrivenCavityProblem<QTaylorHoodElement<2> > problem;
  cout << "Doing QTaylorHoodElement<2>" << std::endl;
  
  // Solve the problem
  problem.newton_solve();
  
  // Outpt the solution
  problem.doc_solution(doc_info);
 
  // Step number
  doc_info.number()++;
 
 } // end of QTaylorHoodElements
 
 
} // end_of_main