two_d_adv_diff_adapt.cc

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//LIC//====================================================================
//Driver for a simple 2D adv diff problem with adaptive mesh refinement
 
//Generic routines
#include "generic.h"
 
// The Poisson equations
#include "advection_diffusion.h"
 
// The mesh 
#include "meshes/rectangular_quadmesh.h"
 
using namespace std;
 
using namespace oomph;
 
 
//======start_of_namespace============================================
/// Namespace for exact solution for AdvectionDiffusion equation 
/// with "sharp" step 
//====================================================================
namespace TanhSolnForAdvectionDiffusion
{
 
 /// Peclet number
 double Peclet=200.0;
 
 /// Parameter for steepness of step
 double Alpha;
 
 /// Parameter for angle of step
 double TanPhi;
 
 /// Exact solution as a Vector
 void get_exact_u(const Vector<double>& x, Vector<double>& u)
 {
  u[0]=tanh(1.0-Alpha*(TanPhi*x[0]-x[1]));
 }
 
 /// Exact solution as a scalar
 void get_exact_u(const Vector<double>& x, double& u)
 {
  u=tanh(1.0-Alpha*(TanPhi*x[0]-x[1]));
 }
 
 /// Source function required to make the solution above an exact solution 
 void source_function(const Vector<double>& x_vect, double& source)
 {
  double x=x_vect[0];
  double y=x_vect[1];
  source = 
2.0*tanh(-0.1E1+Alpha*(TanPhi*x-y))*(1.0-pow(tanh(-0.1E1+Alpha*(
TanPhi*x-y)),2.0))*Alpha*Alpha*TanPhi*TanPhi+2.0*tanh(-0.1E1+Alpha*(TanPhi*x-y)
)*(1.0-pow(tanh(-0.1E1+Alpha*(TanPhi*x-y)),2.0))*Alpha*Alpha-Peclet*(-sin(6.0*y
)*(1.0-pow(tanh(-0.1E1+Alpha*(TanPhi*x-y)),2.0))*Alpha*TanPhi+cos(6.0*x)*(1.0-
pow(tanh(-0.1E1+Alpha*(TanPhi*x-y)),2.0))*Alpha);
 }
 
 /// Wind
 void wind_function(const Vector<double>& x, Vector<double>& wind)
 {
  wind[0]=sin(6.0*x[1]);
  wind[1]=cos(6.0*x[0]);
 }
 
} // end of namespace
 
/// ///////////////////////////////////////////////////////////////////
/// ///////////////////////////////////////////////////////////////////
/// ///////////////////////////////////////////////////////////////////
 
//====== start_of_problem_class=======================================
/// 2D AdvectionDiffusion problem on rectangular domain, discretised 
/// with refineable 2D QAdvectionDiffusion elements. The specific type
/// of element is specified via the template parameter.
//====================================================================
template<class ELEMENT> 
class RefineableAdvectionDiffusionProblem : public Problem
{
 
public:
 
 /// Constructor: Pass pointer to source and wind functions
 RefineableAdvectionDiffusionProblem(
  AdvectionDiffusionEquations<2>::AdvectionDiffusionSourceFctPt source_fct_pt,
  AdvectionDiffusionEquations<2>::AdvectionDiffusionWindFctPt wind_fct_pt);
 
 /// Destructor. Empty
 ~RefineableAdvectionDiffusionProblem(){}
 
 /// Update the problem specs before solve: Reset boundary conditions
 /// to the values from the tanh solution.
 void actions_before_newton_solve();
 
 /// Update the problem after solve (empty)
 void actions_after_newton_solve(){}
 
 /// Actions before adapt: Document the solution
 void actions_before_adapt()
  {
   // Doc the solution
   doc_solution();
   
   // Increment label for output files
   Doc_info.number()++;
  }
 
 /// Doc the solution.
 void doc_solution();
 
 /// Overloaded version of the problem's access function to 
 /// the mesh. Recasts the pointer to the base Mesh object to 
 /// the actual mesh type.
 RefineableRectangularQuadMesh<ELEMENT>* mesh_pt() 
  {
   return dynamic_cast<RefineableRectangularQuadMesh<ELEMENT>*>(
    Problem::mesh_pt());
  }
 
private:
 
 /// DocInfo object
 DocInfo Doc_info;
 
 /// Pointer to source function
 AdvectionDiffusionEquations<2>::AdvectionDiffusionSourceFctPt Source_fct_pt;
 
 /// Pointer to wind function
 AdvectionDiffusionEquations<2>::AdvectionDiffusionWindFctPt Wind_fct_pt;
 
}; // end of problem class
 
 
 
//=====start_of_constructor===============================================
/// Constructor for AdvectionDiffusion problem: Pass pointer to 
/// source function.
//========================================================================
template<class ELEMENT>
RefineableAdvectionDiffusionProblem<ELEMENT>::RefineableAdvectionDiffusionProblem(
 AdvectionDiffusionEquations<2>::AdvectionDiffusionSourceFctPt source_fct_pt,
 AdvectionDiffusionEquations<2>::AdvectionDiffusionWindFctPt wind_fct_pt)
       :  Source_fct_pt(source_fct_pt), Wind_fct_pt(wind_fct_pt)
{ 
 
 // Set output directory
 Doc_info.set_directory("RESLT");
 
 // Setup mesh
 
 // # of elements in x-direction
 unsigned n_x=4;
 
 // # of elements in y-direction
 unsigned n_y=4;
 
 // Domain length in x-direction
 double l_x=1.0;
 
 // Domain length in y-direction
 double l_y=2.0;
 
 // Build and assign mesh
 Problem::mesh_pt() = 
  new RefineableRectangularQuadMesh<ELEMENT>(n_x,n_y,l_x,l_y);
 
 // Create/set error estimator
 mesh_pt()->spatial_error_estimator_pt()=new Z2ErrorEstimator;
  
 // Set the boundary conditions for this problem: All nodes are
 // free by default -- only need to 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++)
    {
     mesh_pt()->boundary_node_pt(ibound,inod)->pin(0); 
    }
  } // end loop over boundaries
 
 // Complete the build of all elements so they are fully functional 
 
 // Loop over the elements to set up element-specific 
 // things that cannot be handled by the (argument-free!) ELEMENT 
 // constructor: Pass pointer to source function
 unsigned n_element = mesh_pt()->nelement();
 for(unsigned i=0;i<n_element;i++)
  {
   // Upcast from GeneralsedElement to the present element
   ELEMENT *el_pt = dynamic_cast<ELEMENT*>(mesh_pt()->element_pt(i));
 
   //Set the source function pointer
   el_pt->source_fct_pt() = Source_fct_pt;
 
   //Set the wind function pointer
   el_pt->wind_fct_pt() = Wind_fct_pt;
 
   // Set the Peclet number
   el_pt->pe_pt() = &TanhSolnForAdvectionDiffusion::Peclet;
  }
 
 // Setup equation numbering scheme
 cout <<"Number of equations: " << assign_eqn_numbers() << std::endl; 
 
} // end of constructor
 
 
//========================================start_of_actions_before_newton_solve===
/// Update the problem specs before solve: (Re-)set boundary conditions
/// to the values from the tanh solution.
//========================================================================
template<class ELEMENT>
void RefineableAdvectionDiffusionProblem<ELEMENT>::actions_before_newton_solve()
{
 // How many boundaries are there?
 unsigned num_bound = mesh_pt()->nboundary();
 
 //Loop over the boundaries
 for(unsigned ibound=0;ibound<num_bound;ibound++)
  {
   // How many nodes are there on this boundary?
   unsigned num_nod=mesh_pt()->nboundary_node(ibound);
 
   // Loop over the nodes on boundary
   for (unsigned inod=0;inod<num_nod;inod++)
    {
     // Get pointer to node
     Node* nod_pt=mesh_pt()->boundary_node_pt(ibound,inod);
 
     // Extract nodal coordinates from node:
     Vector<double> x(2);
     x[0]=nod_pt->x(0);
     x[1]=nod_pt->x(1);
 
     // Compute the value of the exact solution at the nodal point
     Vector<double> u(1);
     TanhSolnForAdvectionDiffusion::get_exact_u(x,u);
 
     // Assign the value to the one (and only) nodal value at this node
     nod_pt->set_value(0,u[0]);
    }
  } 
}  // end of actions before solve
 
 
 
//===============start_of_doc=============================================
/// Doc the solution
//========================================================================
template<class ELEMENT>
void RefineableAdvectionDiffusionProblem<ELEMENT>::doc_solution()
{ 
 
 ofstream some_file;
 char filename[100];
 
 // Number of plot points: npts x npts
 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();
 
 // Output exact solution 
 //----------------------
 sprintf(filename,"%s/exact_soln%i.dat",Doc_info.directory().c_str(),
         Doc_info.number());
 some_file.open(filename);
 mesh_pt()->output_fct(some_file,npts,TanhSolnForAdvectionDiffusion::get_exact_u); 
 some_file.close();
 
 // Doc error and return of the square of the L2 error
 //---------------------------------------------------
 double error,norm;
 sprintf(filename,"%s/error%i.dat",Doc_info.directory().c_str(),
         Doc_info.number());
 some_file.open(filename);
 mesh_pt()->compute_error(some_file,TanhSolnForAdvectionDiffusion::get_exact_u,
                          error,norm); 
 some_file.close();
 
 // Doc L2 error and norm of solution
 cout << "\nNorm of error   : " << sqrt(error) << std::endl; 
 cout << "Norm of solution: " << sqrt(norm) << std::endl << std::endl;
 
} // end of doc
 
 
//===== start_of_main=====================================================
/// Driver code for 2D AdvectionDiffusion problem
//========================================================================
int main()
{
 
 //Set up the problem
 //------------------
 
 // Create the problem with 2D nine-node refineable elements from the
 // RefineableQuadAdvectionDiffusionElement family. Pass pointer to 
 // source and wind function. 
 RefineableAdvectionDiffusionProblem<RefineableQAdvectionDiffusionElement<2,
  3> > problem(&TanhSolnForAdvectionDiffusion::source_function,
               &TanhSolnForAdvectionDiffusion::wind_function);
 
 // Check if we're ready to go:
 //----------------------------
 cout << "\n\n\nProblem self-test ";
 if (problem.self_test()==0) 
  {
   cout << "passed: Problem can be solved." << std::endl;
  }
 else 
  {
   throw OomphLibError("Self test failed",
                       OOMPH_CURRENT_FUNCTION,
                       OOMPH_EXCEPTION_LOCATION);
  }
 
 // Set the orientation of the "step" to 45 degrees
 TanhSolnForAdvectionDiffusion::TanPhi=1.0;
 
 // Choose a large value for the steepness of the "step"
 TanhSolnForAdvectionDiffusion::Alpha=50.0; 
 
 // Solve the problem, performing up to 4 adptive refinements
 problem.newton_solve(4);
 
 //Output the solution
 problem.doc_solution();
 
} // end of main