elastic_poisson.cc

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// Solve Poisson equation in deformable fish-shaped domain.
// Mesh deformation is driven by pseudo-elasticity approach.
 
// Generic oomph-lib headers
#include "generic.h"  
 
// Poisson equations
#include "poisson.h"
 
// Solid mechanics
#include "solid.h"
 
// The fish mesh 
#include "meshes/fish_mesh.h" 
 
// Circle as generalised element:
#include "circle_as_generalised_element.h"
 
using namespace std;
 
using namespace oomph;
 
///////////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////////
 
 
 
//====================================================================
/// Namespace for const source term in Poisson equation
//====================================================================
namespace ConstSourceForPoisson
{
 /// Strength of source function: default value 1.0
 double Strength=1.0;
 
/// Const source function
 void get_source(const Vector<double>& x, double& source)
 {
  source = -Strength;
 }
 
}
 
///////////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////////
 
//=========================================================================
/// Refineable fish mesh upgraded to become a solid mesh
//=========================================================================
template<class ELEMENT>
class ElasticFishMesh : public virtual RefineableFishMesh<ELEMENT>, 
                        public virtual SolidMesh 
{
 
public:
 
 /// Constructor: Build underlying adaptive fish mesh and then 
 /// set current Eulerian coordinates to be the Lagrangian ones.
 /// Pass pointer to geometric objects that specify the 
 /// fish's back in the "current" and "undeformed" configurations,
 /// and pointer to timestepper (defaults to Static)
 // Note: FishMesh is virtual base and its constructor is automatically
 // called first! --> this is where we need to build the mesh;
 // the constructors of the derived meshes don't call the
 // base constructor again and simply add the extra functionality.
 ElasticFishMesh(GeomObject* back_pt, GeomObject* undeformed_back_pt, 
                 TimeStepper* time_stepper_pt=&Mesh::Default_TimeStepper) : 
  FishMesh<ELEMENT>(back_pt,time_stepper_pt), 
  RefineableFishMesh<ELEMENT>(back_pt,time_stepper_pt)
  {
   // Mesh has been built, adaptivity etc has been set up --> 
   // assign the Lagrangian coordinates so that the current
   // configuration becomes the stress-free initial configuration 
   set_lagrangian_nodal_coordinates();
 
   // Build "undeformed" domain: This is a "deep" copy of the
   // Domain that we used to create set the Eulerian coordinates
   // in the initial mesh -- the original domain (accessible via 
   // the private member data Domain_pt) will be used to update
   // the position of boundary nodes; the copy that we're
   // creating here will be used to determine the Lagrangian coordinates
   // of any newly created SolidNodes during mesh refinement
   double xi_nose = this->Domain_pt->xi_nose(); 
   double xi_tail = this->Domain_pt->xi_tail();
   Undeformed_domain_pt=new FishDomain(undeformed_back_pt,xi_nose,xi_tail);
 
   // Loop over all elements and set the undeformed macro element pointer
   unsigned n_element=this->nelement();
   for (unsigned e=0;e<n_element;e++)
    {
     // Get pointer to full element type 
     ELEMENT* el_pt=dynamic_cast<ELEMENT*>(this->element_pt(e));
     
     // Set pointer to macro element so the curvlinear boundaries
     // of the undeformed mesh/domain get picked up during adaptive
     // mesh refinement
     el_pt->set_undeformed_macro_elem_pt(
      Undeformed_domain_pt->macro_element_pt(e));
    }
   
  }
 
 /// Destructor: Kill "undeformed" Domain
 virtual ~ElasticFishMesh()
  {
   delete Undeformed_domain_pt;
  }
 
private:
 
 /// Pointer to "undeformed" Domain -- used to determine the
 /// Lagrangian coordinates of any newly created SolidNodes during
 /// Mesh refinement
 Domain* Undeformed_domain_pt;
 
};
 
 
 
 
///////////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////////
 
 
 
 
//================================================================
/// Global variables
//================================================================
namespace Global_Physical_Variables
{
 /// Pointer to constitutive law
 ConstitutiveLaw* Constitutive_law_pt;
 
 /// Poisson's ratio
 double Nu=0.3;
 
}
 
 
///////////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////////
 
 
 
//====================================================================== 
/// Solve Poisson equation on deforming fish-shaped domain.
/// Mesh update via pseudo-elasticity.
//====================================================================== 
template<class ELEMENT>
class DeformableFishPoissonProblem : public Problem
{
 
public:
 
 /// Constructor:
 DeformableFishPoissonProblem();
 
 /// Run simulation
 void run();
 
 /// Access function for the specific mesh
 ElasticFishMesh<ELEMENT>* mesh_pt() 
  {return dynamic_cast<ElasticFishMesh<ELEMENT>*>(Problem::mesh_pt());} 
 
 /// Doc the solution
 void doc_solution(DocInfo& doc_info);
 
 /// Update function (empty)
 void actions_after_newton_solve() {}
 
 /// Update before solve: We're dealing with a static problem so
 /// the nodal positions before the next solve merely serve as
 /// initial conditions. For meshes that are very strongly refined
 /// near the boundary, the update of the displacement boundary
 /// conditions (which only moves the SolidNodes *on* the boundary),
 /// can lead to strongly distorted meshes. This can cause the
 /// Newton method to fail --> the overall method is actually more robust
 /// if we use the nodal positions as determined by the Domain/MacroElement-
 /// based mesh update as initial guesses. 
 void actions_before_newton_solve()
  { 
   bool update_all_solid_nodes=true;
   mesh_pt()->node_update(update_all_solid_nodes);
  }   
 
 /// Update after adapt: Pin all redundant solid pressure nodes (if required)
 void actions_after_adapt()
  { 
   // Pin the redundant solid pressures (if any)
   PVDEquationsBase<2>::pin_redundant_nodal_solid_pressures(
    mesh_pt()->element_pt());
  }
 
private:
 
 
 /// Node at which the solution of the Poisson equation is documented
 Node* Doc_node_pt;
 
 /// Trace file
 ofstream Trace_file;
 
 // Geometric object/generalised element that represents the deformable 
 // fish back
 ElasticallySupportedRingElement* Fish_back_pt;
 
};
 
 
 
//====================================================================== 
/// Constructor: 
//====================================================================== 
template<class ELEMENT>
DeformableFishPoissonProblem<ELEMENT>::DeformableFishPoissonProblem() 
{
 
 // Set coordinates and radius for the circle that will become the fish back
 double x_c=0.5;
 double y_c=0.0;
 double r_back=1.0;
 
 // Build geometric object/generalised element that will become the 
 // deformable fish back
 Fish_back_pt=new ElasticallySupportedRingElement(x_c,y_c,r_back);
 
 // Build geometric object/generalised that specifies the fish back in the
 // undeformed configuration (basically a deep copy of the previous one)
 GeomObject* undeformed_fish_back_pt=new 
  ElasticallySupportedRingElement(x_c,y_c,r_back);
 
 // Build fish mesh with geometric object that specifies the deformable
 // and undeformed fish back 
 Problem::mesh_pt()=new ElasticFishMesh<ELEMENT>(Fish_back_pt,
                                                 undeformed_fish_back_pt);
 
 
 // Choose a node at which the solution is documented: Choose
 // the central node that is shared by all four elements in
 // the base mesh because it exists at all refinement levels.
 
 // How many nodes does element 0 have?
 unsigned nnod=mesh_pt()->finite_element_pt(0)->nnode();
 
 // The central node is the last node in element 0:
 Doc_node_pt=mesh_pt()->finite_element_pt(0)->node_pt(nnod-1);
 
 // Doc
 cout << std::endl <<  "Control node is located at: " 
      << Doc_node_pt->x(0) << " " << Doc_node_pt->x(1) << std::endl << std::endl;
 
 
 // Set error estimator
 Z2ErrorEstimator* error_estimator_pt=new Z2ErrorEstimator;
 mesh_pt()->spatial_error_estimator_pt()=error_estimator_pt;
 
 // Change/doc targets for mesh adaptation
 if (CommandLineArgs::Argc>1) 
  {
   mesh_pt()->max_permitted_error()=0.05;
   mesh_pt()->min_permitted_error()=0.005;
  }
 mesh_pt()->doc_adaptivity_targets(cout);
 
 
 // Specify BC/source fct for Poisson problem:
 //-------------------------------------------
 
 // Set the Poisson 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++)
    {
     mesh_pt()->boundary_node_pt(ibound,inod)->pin(0); 
    }
  }
 
 // Set homogeneous boundary conditions for the Poisson equation 
 // on all boundaries 
 for(unsigned ibound=0;ibound<num_bound;ibound++)
  {
   // Loop over the nodes on boundary
   unsigned num_nod=mesh_pt()->nboundary_node(ibound);
   for (unsigned inod=0;inod<num_nod;inod++)
    {
     mesh_pt()->boundary_node_pt(ibound,inod)->set_value(0,0.0);
    }
  }
 
 /// Loop over elements and set pointers to source function
 unsigned n_element = mesh_pt()->nelement();
 for(unsigned i=0;i<n_element;i++)
  {
   // Upcast from FiniteElement 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() = &ConstSourceForPoisson::get_source;
  }
 
 
 // Specify BC/source fct etc for (pseudo-)Solid problem
 //-----------------------------------------------------
 
 // Pin all nodal positions
 for(unsigned ibound=0;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)->pin_position(i); 
      }
    }
  }
 
 //Loop over the elements in the mesh to set Solid parameters/function pointers
 for(unsigned i=0;i<n_element;i++)
  {
   //Cast to a solid element
   ELEMENT *el_pt = dynamic_cast<ELEMENT*>(mesh_pt()->element_pt(i));
   
   // Set the constitutive law
   el_pt->constitutive_law_pt() =
    Global_Physical_Variables::Constitutive_law_pt;
     
  }
 
 // Pin the redundant solid pressures (if any)
 PVDEquationsBase<2>::pin_redundant_nodal_solid_pressures(
  mesh_pt()->element_pt());
 
 //Attach the boundary conditions to the mesh
 cout << assign_eqn_numbers() << std::endl; 
 
 // Refine the problem uniformly (this automatically passes the
 // function pointers/parameters to the finer elements
 refine_uniformly();
 
 // The non-pinned positions of the newly SolidNodes will have been
 // determined by interpolation. Update all solid nodes based on 
 // the Mesh's Domain/MacroElement representation.
 bool update_all_solid_nodes=true;
 mesh_pt()->node_update(update_all_solid_nodes);
 
 // Now set the Eulerian equal to the Lagrangian coordinates
 mesh_pt()->set_lagrangian_nodal_coordinates();
 
} 
 
 
//==================================================================
/// Doc the solution
//==================================================================
template<class ELEMENT>
void DeformableFishPoissonProblem<ELEMENT>::doc_solution(DocInfo& doc_info)
{
 ofstream some_file;
 char filename[100];
 
 // Number of plot points
 unsigned npts = 5; 
 
 // Call output function for all elements
 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();
 
 
 // Write vertical position of the fish back, and solution at 
 // control node to trace file
 Trace_file 
  << static_cast<Circle*>(mesh_pt()->fish_back_pt())->y_c()
  << " " << Doc_node_pt->value(0) << std::endl;
 
}
 
 
//==================================================================
/// Run the problem
//==================================================================
template<class ELEMENT>
void DeformableFishPoissonProblem<ELEMENT>::run()
{
 
 // Output
 DocInfo doc_info;
 
 // Set output directory
 doc_info.set_directory("RESLT");
 
 // Step number
 doc_info.number()=0;
 
 // Open trace file
 char filename[100];
 snprintf(filename, sizeof(filename), "%s/trace.dat",doc_info.directory().c_str());
 Trace_file.open(filename);
 
 Trace_file << "VARIABLES=\"y<sub>circle</sub>\",\"u<sub>control</sub>\""
            << std::endl;
 
  //Parameter incrementation
 unsigned nstep=5; 
 for(unsigned i=0;i<nstep;i++)
  {
   //Solve the problem with Newton's method, allowing for up to 2
   //rounds of adaptation
   newton_solve(2);
 
   // Doc solution
   doc_solution(doc_info);
   doc_info.number()++;
 
   // Increment width of fish domain
   Fish_back_pt->y_c()+=0.03;
  }
 
}
 
//======================================================================
/// Driver for simple elastic problem.
/// If there are any command line arguments, we regard this as a 
/// validation run and perform only a single step.
//======================================================================
int main(int argc, char* argv[])
{
 
 // Store command line arguments
 CommandLineArgs::setup(argc,argv);
 
 //Set physical parameters
 Global_Physical_Variables::Nu = 0.4; 
 
 // Define a constitutive law (based on strain energy function)
  Global_Physical_Variables::Constitutive_law_pt = 
   new GeneralisedHookean(&Global_Physical_Variables::Nu);
 
 
  // Set up the problem: Choose a hybrid element that combines the
  // 3x3 node refineable quad Poisson element with a displacement-based
  // solid-mechanics element (for the pseudo-elastic mesh update in response
  // to changes in the boundary shape)
  DeformableFishPoissonProblem<
   RefineablePseudoSolidNodeUpdateElement<RefineableQPoissonElement<2,3>,
   RefineableQPVDElement<2,3>  > 
                              > problem;
  
  problem.run(); 
 
 
}