unstructured_acoustic_fsi.cc

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//LIC// ====================================================================
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//LIC// multi-physics finite-element library, available 
//LIC// at http://www.oomph-lib.org.
//LIC// 
//LIC// Copyright (C) 2006-2025 Matthias Heil and Andrew Hazel
//LIC// 
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//LIC// License as published by the Free Software Foundation; either
//LIC// version 2.1 of the License, or (at your option) any later version.
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//LIC//====================================================================
// Driver for Helmholtz/TimeHarmonicTimeHarmonicLinElast coupling
 
//Oomph-lib includes
#include "generic.h"
#include "helmholtz.h"
#include "time_harmonic_linear_elasticity.h"
#include "multi_physics.h"
 
//The meshes
#include "meshes/annular_mesh.h"
#include "meshes/triangle_mesh.h"
 
using namespace std;
using namespace oomph;
 
///////////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////////
// Straight line as geometric object
///////////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////////
 
 
 
//=========================================================================
/// Straight 1D line in 2D space 
//=========================================================================
class MyStraightLine : public GeomObject
{
 
public:
 
 /// Constructor:  Pass start and end points
 MyStraightLine(const Vector<double>& r_start, const Vector<double>& r_end) 
  :  GeomObject(1,2), R_start(r_start), R_end(r_end)
  { }
 
 
 /// Broken copy constructor
 MyStraightLine(const MyStraightLine& dummy) 
  { 
   BrokenCopy::broken_copy("MyStraightLine");
  } 
 
 /// Broken assignment operator
 void operator=(const MyStraightLine&) 
  {
   BrokenCopy::broken_assign("MyStraightLine");
  }
 
 
 /// Destructor:  Empty
 ~MyStraightLine(){}
 
 /// Position Vector at Lagrangian coordinate zeta 
 void position(const Vector<double>& zeta, Vector<double>& r) const
  {
   // Position Vector
   r[0] = R_start[0]+(R_end[0]-R_start[0])*zeta[0];
   r[1] = R_start[1]+(R_end[1]-R_start[1])*zeta[0];
  }
 
private:
 
 /// Start point of line
 Vector<double> R_start;
 
 /// End point of line
 Vector<double> R_end;
 
};
 
 
 
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////
 
 
//=======start_namespace==========================================
/// Global variables
//================================================================
namespace Global_Parameters
{
 
 /// Square of wavenumber for the Helmholtz equation
 double K_squared=10.0;
 
 /// Radius of outer boundary of Helmholtz domain
 double Outer_radius=4.0; 
 
 /// Order of absorbing/appproximate boundary condition
 unsigned ABC_order=3;
 
 /// FSI parameter
 double Q=0.0;
 
 /// Non-dim thickness of elastic coating
 double H_coating=0.1; 
 
 /// Poisson's ratio
 double Nu = 0.3;
 
 /// Square of non-dim frequency for the two regions -- dependent variable!
 Vector<double> Omega_sq(2,0.0);
  
 /// Density ratio for the two regions: solid to fluid
 Vector<double> Density_ratio(2,0.1);
 
 /// The elasticity tensors for the two regions
 Vector<TimeHarmonicIsotropicElasticityTensor*> E_pt;
 
 /// Function to update dependent parameter values
 void update_parameter_values()
 {
  Omega_sq[0]=Density_ratio[0]*Q;
  Omega_sq[1]=Density_ratio[1]*Q;
 }
 
 /// Uniform pressure
 double P = 0.1;
 
 /// Peakiness parameter for pressure load
 double Alpha=200.0;
 
 /// Pressure load (real and imag part)
 void pressure_load(const Vector<double> &x,
                    const Vector<double> &n, 
                    Vector<std::complex<double> >&traction)
 {
  double phi=atan2(x[1],x[0]);
  double magnitude=exp(-Alpha*pow(phi-0.25*MathematicalConstants::Pi,2));
 
  unsigned dim = traction.size();
  for(unsigned i=0;i<dim;i++)
   {
    traction[i] = complex<double>(-magnitude*P*n[i],magnitude*P*n[i]);
   }
 } // end_of_pressure_load
 
 // Output directory
 string Directory="RESLT";
 
 // Multiplier for number of elements
 unsigned El_multiplier=1;
 
} //end namespace
 
 
 
//=============begin_problem============================================ 
/// Coated disk FSI
//====================================================================== 
template<class ELASTICITY_ELEMENT, class HELMHOLTZ_ELEMENT>
class CoatedDiskProblem : public Problem
{
 
public:
 
 /// Constructor:
 CoatedDiskProblem();
 
 /// Update function (empty)
 void actions_before_newton_solve() {}
 
 /// Update function (empty)
 void actions_after_newton_solve() {}
 
 /// Actions before adapt: Wipe the face meshes
 void actions_before_adapt();
 
 /// Actions after adapt: Rebuild the face meshes
 void actions_after_adapt();
 
 /// Doc the solution
 void doc_solution();
 
private:
 
 // Complete problem setup
 void complete_problem_setup(); 
 
 /// Create solid traction elements
 void create_solid_traction_elements();
 
 /// Create FSI traction elements
 void create_fsi_traction_elements();
 
 /// Create Helmholtz FSI flux elements
 void create_helmholtz_fsi_flux_elements();
 
 /// Delete (face) elements in specified mesh 
 void delete_face_elements(Mesh* const & boundary_mesh_pt);
 
 /// Create ABC face elements 
 void create_helmholtz_ABC_elements();
 
 /// Setup interaction
 void setup_interaction();
 
 /// Pointer to refineable solid mesh
 RefineableTriangleMesh<ELASTICITY_ELEMENT>* Solid_mesh_pt;
 
 /// Pointer to mesh of solid traction elements
 Mesh* Solid_traction_mesh_pt;
 
 /// Pointer to mesh of FSI traction elements
 Mesh* FSI_traction_mesh_pt;
 
 /// Pointer to Helmholtz mesh
 TreeBasedRefineableMeshBase* Helmholtz_mesh_pt;
 
 /// Pointer to mesh of Helmholtz FSI flux elements
 Mesh* Helmholtz_fsi_flux_mesh_pt;
 
 /// Pointer to mesh containing the ABC elements
 Mesh* Helmholtz_outer_boundary_mesh_pt;
 
 /// Boundary ID of upper symmetry boundary
 unsigned Upper_symmetry_boundary_id;
 
 /// Boundary ID of lower symmetry boundary
 unsigned Lower_symmetry_boundary_id;
 
 /// Boundary ID of upper inner boundary
 unsigned Upper_inner_boundary_id;
 
 /// Boundary ID of lower inner boundary
 unsigned Lower_inner_boundary_id;
 
 /// Boundary ID of outer boundary
 unsigned Outer_boundary_id;
 
 // Boundary ID of rib divider
 unsigned Rib_divider_boundary_id;
 
 /// DocInfo object for output
 DocInfo Doc_info;
 
 /// Trace file
 ofstream Trace_file;
 
};
 
 
//===========start_of_constructor======================================= 
/// Constructor
//====================================================================== 
template<class ELASTICITY_ELEMENT, class HELMHOLTZ_ELEMENT>
CoatedDiskProblem<ELASTICITY_ELEMENT, HELMHOLTZ_ELEMENT>::CoatedDiskProblem() 
{
 // To suppress boundary warnings (to avoid a lot of warnings) uncomment
 // the following code:
 //UnstructuredTwoDMeshGeometryBase::
 // Suppress_warning_about_regions_and_boundaries=true;
 
 // Solid mesh
 //-----------
 
 // Start and end coordinates
 Vector<double> r_start(2);
 Vector<double> r_end(2);
 
 // Outer radius of hull
 double r_outer = 1.0;
 
 // Inner radius of hull
 double r_inner = r_outer-Global_Parameters::H_coating;
 
 // Thickness of rib
 double rib_thick=0.05;
 
 // Depth of rib
 double rib_depth=0.2;
 
 // Total width of T
 double t_width=0.2;
 
 // Thickness of T
 double t_thick=0.05;
 
 // Half-opening angle of rib
 double half_phi_rib=asin(0.5*rib_thick/r_inner);
 
 // Pointer to the closed curve that defines the outer boundary
 TriangleMeshClosedCurve* closed_curve_pt=0;
 
 // Provide storage for pointers to the parts of the curvilinear boundary
 Vector<TriangleMeshCurveSection*> curvilinear_boundary_pt;
 
 // Outer boundary
 //---------------
 Ellipse* outer_boundary_circle_pt = new Ellipse(r_outer,r_outer);
 double zeta_start=-0.5*MathematicalConstants::Pi;
 double zeta_end=0.5*MathematicalConstants::Pi;
 unsigned nsegment=50;
 unsigned boundary_id=curvilinear_boundary_pt.size();
 curvilinear_boundary_pt.push_back(
  new TriangleMeshCurviLine(
   outer_boundary_circle_pt,zeta_start,zeta_end,nsegment,boundary_id));
 
 // Remember it
 Outer_boundary_id=boundary_id;
 
 
 // Upper straight line segment on symmetry axis
 //---------------------------------------------
 r_start[0]=0.0;
 r_start[1]=r_outer;
 r_end[0]=0.0;
 r_end[1]=r_inner;
 MyStraightLine* upper_sym_pt = new MyStraightLine(r_start,r_end);
 zeta_start=0.0;
 zeta_end=1.0;
 nsegment=1;
 boundary_id=curvilinear_boundary_pt.size();
 curvilinear_boundary_pt.push_back(
  new TriangleMeshCurviLine(
   upper_sym_pt,zeta_start,zeta_end,nsegment,boundary_id));
                                                        
 // Remember it
 Upper_symmetry_boundary_id=boundary_id;
 
 // Upper part of inner boundary
 //-----------------------------
 Ellipse* upper_inner_boundary_pt = 
  new Ellipse(r_inner,r_inner);
 zeta_start=0.5*MathematicalConstants::Pi;
 zeta_end=half_phi_rib;
 nsegment=20;
 boundary_id=curvilinear_boundary_pt.size();
 curvilinear_boundary_pt.push_back(
  new TriangleMeshCurviLine(
   upper_inner_boundary_pt,
   zeta_start,zeta_end,nsegment,boundary_id));
 
 // Remember it
 Upper_inner_boundary_id=boundary_id;
 
 // Data associated with rib
 MyStraightLine* upper_inward_rib_pt=0;
 MyStraightLine* lower_inward_rib_pt=0;
 TriangleMeshCurviLine* upper_inward_rib_curviline_pt=0;
 Vector<TriangleMeshOpenCurve*> inner_boundary_pt;
 TriangleMeshCurviLine* lower_inward_rib_curviline_pt=0;
 Vector<double> rib_center(2);
 
 // Upper half of inward rib
 //-------------------------
 r_start[0]=r_inner*cos(half_phi_rib);
 r_start[1]=r_inner*sin(half_phi_rib);
 r_end[0]=r_start[0]-rib_depth;
 r_end[1]=r_start[1];
 upper_inward_rib_pt = new MyStraightLine(r_start,r_end);
 zeta_start=0.0;
 zeta_end=1.0;
 nsegment=1;
 boundary_id=curvilinear_boundary_pt.size();
 upper_inward_rib_curviline_pt=
  new TriangleMeshCurviLine(
   upper_inward_rib_pt,zeta_start,zeta_end,nsegment,boundary_id);
 curvilinear_boundary_pt.push_back(upper_inward_rib_curviline_pt);
 
 // Vertical upper bit of T
 //------------------------
 r_start[0]=r_end[0];
 r_start[1]=r_end[1];
 r_end[0]=r_start[0];
 r_end[1]=r_start[1]+0.5*(t_width-rib_thick);
 MyStraightLine* vertical_upper_t_rib_pt = new MyStraightLine(r_start,r_end);
 zeta_start=0.0;
 zeta_end=1.0;
 nsegment=1;
 boundary_id=curvilinear_boundary_pt.size();
 curvilinear_boundary_pt.push_back(
  new TriangleMeshCurviLine(
   vertical_upper_t_rib_pt,zeta_start,zeta_end,nsegment,boundary_id));
 
 
 // Horizontal upper bit of T
 //-----------==-------------
 r_start[0]=r_end[0];
 r_start[1]=r_end[1];
 r_end[0]=r_start[0]-t_thick;
 r_end[1]=r_start[1];
 MyStraightLine* horizontal_upper_t_rib_pt = new MyStraightLine(r_start,r_end);
 zeta_start=0.0;
 zeta_end=1.0;
 nsegment=1;
 boundary_id=curvilinear_boundary_pt.size();
 curvilinear_boundary_pt.push_back(
  new TriangleMeshCurviLine(
   horizontal_upper_t_rib_pt,zeta_start,zeta_end,nsegment,boundary_id));
 
 // Vertical end of rib end
 //------------------------
 r_start[0]=r_end[0];
 r_start[1]=r_end[1];
 r_end[0]=r_start[0];
 r_end[1]=-r_start[1];
 MyStraightLine* inner_vertical_rib_pt = new MyStraightLine(r_start,r_end);
 zeta_start=0.0;
 zeta_end=1.0;
 nsegment=1;
 boundary_id=curvilinear_boundary_pt.size();
 curvilinear_boundary_pt.push_back(
  new TriangleMeshCurviLine(
   inner_vertical_rib_pt,zeta_start,zeta_end,nsegment,boundary_id));
 
 
 // Horizontal lower bit of T
 //-----------==-------------
 r_start[0]=r_end[0];
 r_start[1]=r_end[1];
 r_end[0]=r_start[0]+t_thick;
 r_end[1]=r_start[1];
 MyStraightLine* horizontal_lower_t_rib_pt = new MyStraightLine(r_start,r_end);
 zeta_start=0.0;
 zeta_end=1.0;
 nsegment=1;
 boundary_id=curvilinear_boundary_pt.size();
 curvilinear_boundary_pt.push_back(
  new TriangleMeshCurviLine(
   horizontal_lower_t_rib_pt,zeta_start,zeta_end,nsegment,boundary_id));
 
 
 // Vertical lower bit of T
 //------------------------
 r_start[0]=r_end[0];
 r_start[1]=r_end[1];
 r_end[0]=r_start[0];
 r_end[1]=r_start[1]+0.5*(t_width-rib_thick);
 MyStraightLine* vertical_lower_t_rib_pt = new MyStraightLine(r_start,r_end);
 zeta_start=0.0;
 zeta_end=1.0;
 nsegment=1;
 boundary_id=curvilinear_boundary_pt.size();
 curvilinear_boundary_pt.push_back(
  new TriangleMeshCurviLine(
   vertical_lower_t_rib_pt,zeta_start,zeta_end,nsegment,boundary_id));
 
 
 // Lower half of inward rib
 //-------------------------
 r_end[0]=r_inner*cos(half_phi_rib);
 r_end[1]=-r_inner*sin(half_phi_rib);
 r_start[0]=r_end[0]-rib_depth;
 r_start[1]=r_end[1];
 lower_inward_rib_pt = new MyStraightLine(r_start,r_end);
 zeta_start=0.0;
 zeta_end=1.0;
 nsegment=1;
 boundary_id=curvilinear_boundary_pt.size();
 lower_inward_rib_curviline_pt=
  new TriangleMeshCurviLine(
   lower_inward_rib_pt,zeta_start,zeta_end,nsegment,boundary_id);
 curvilinear_boundary_pt.push_back(lower_inward_rib_curviline_pt);
 
 
 // Lower part of inner boundary
 //-----------------------------
 Ellipse* lower_inner_boundary_circle_pt = new Ellipse(r_inner,r_inner);
 zeta_start=-half_phi_rib;
 zeta_end=-0.5*MathematicalConstants::Pi;
 nsegment=20;
 boundary_id=curvilinear_boundary_pt.size();
 curvilinear_boundary_pt.push_back(
  new TriangleMeshCurviLine(
   lower_inner_boundary_circle_pt,zeta_start,zeta_end,nsegment,boundary_id)); 
 
 // Remember it
 Lower_inner_boundary_id=boundary_id;
 
 // Lower straight line segment on symmetry axis
 //---------------------------------------------
 r_start[0]=0.0;
 r_start[1]=-r_inner;
 r_end[0]=0.0;
 r_end[1]=-r_outer;
 MyStraightLine* lower_sym_pt = new MyStraightLine(r_start,r_end);
 zeta_start=0.0;
 zeta_end=1.0;
 nsegment=1;
 boundary_id=curvilinear_boundary_pt.size();
 curvilinear_boundary_pt.push_back(
  new TriangleMeshCurviLine(
   lower_sym_pt,zeta_start,zeta_end,nsegment,boundary_id));
      
 // Remember it
 Lower_symmetry_boundary_id=boundary_id;
 
 // Combine to curvilinear boundary
 //--------------------------------
 closed_curve_pt=
  new TriangleMeshClosedCurve(curvilinear_boundary_pt); 
 
 // Vertical dividing line across base of T-rib
 //--------------------------------------------
 Vector<TriangleMeshCurveSection*> internal_polyline_pt(1);
 r_start[0]=r_inner*cos(half_phi_rib);
 r_start[1]=r_inner*sin(half_phi_rib);
 r_end[0]=r_inner*cos(half_phi_rib);
 r_end[1]=-r_inner*sin(half_phi_rib);
 
 Vector<Vector<double> > boundary_vertices(2);
 boundary_vertices[0]=r_start;
 boundary_vertices[1]=r_end;
 boundary_id=100;
 TriangleMeshPolyLine* rib_divider_pt=
  new TriangleMeshPolyLine(boundary_vertices,boundary_id); 
 internal_polyline_pt[0]=rib_divider_pt;
 
 // Remember it
 Rib_divider_boundary_id=boundary_id;
 
 // Make connection
 double s_connect=0.0;
 internal_polyline_pt[0]->connect_initial_vertex_to_curviline(
  upper_inward_rib_curviline_pt,s_connect);
 
 // Make connection
 s_connect=1.0;
 internal_polyline_pt[0]->connect_final_vertex_to_curviline(
  lower_inward_rib_curviline_pt,s_connect);
 
 // Create open curve that defines internal bondary
 inner_boundary_pt.push_back(new TriangleMeshOpenCurve(internal_polyline_pt));
 
 // Define coordinates of a point inside the rib
 rib_center[0]=r_inner-rib_depth;
 rib_center[1]=0.0;
 
 
 // Now build the mesh
 //===================
 
 // Use the TriangleMeshParameters object for helping on the manage of the
 // TriangleMesh parameters. The only parameter that needs to take is the
 // outer boundary.
 TriangleMeshParameters triangle_mesh_parameters(closed_curve_pt);
 
 // Target area
 triangle_mesh_parameters.element_area()=0.2;
 
 // Specify the internal open boundary
 triangle_mesh_parameters.internal_open_curves_pt()=inner_boundary_pt;
 
 // Define the region
 triangle_mesh_parameters.add_region_coordinates(1,rib_center);
 
 // Build the mesh
 Solid_mesh_pt=new 
  RefineableTriangleMesh<ELASTICITY_ELEMENT>(triangle_mesh_parameters);
 
 // Helmholtz mesh
 //---------------
 
 // Number of elements in azimuthal direction in Helmholtz mesh
 unsigned ntheta_helmholtz=11*Global_Parameters::El_multiplier;
 
 // Number of elements in radial direction in Helmholtz mesh
 unsigned nr_helmholtz=3*Global_Parameters::El_multiplier;
 
 // Innermost radius of Helmholtz mesh
 double a=1.0;
 
 // Thickness of Helmholtz mesh
 double h_thick_helmholtz=Global_Parameters::Outer_radius-a;
 
 // Build mesh
 bool periodic=false;
 double azimuthal_fraction=0.5;
 double phi=MathematicalConstants::Pi/2.0;
 Helmholtz_mesh_pt = new 
  RefineableTwoDAnnularMesh<HELMHOLTZ_ELEMENT>
  (periodic,azimuthal_fraction,
   ntheta_helmholtz,nr_helmholtz,a,h_thick_helmholtz,phi);
 
 // Set error estimators
 Solid_mesh_pt->spatial_error_estimator_pt()=new Z2ErrorEstimator;
 Helmholtz_mesh_pt->spatial_error_estimator_pt()=new Z2ErrorEstimator;
 
 // Mesh containing the Helmholtz ABC
 // elements. 
 Helmholtz_outer_boundary_mesh_pt = new Mesh;
 
 // Create elasticity tensors
 Global_Parameters::E_pt.resize(2);
 Global_Parameters::E_pt[0]=new TimeHarmonicIsotropicElasticityTensor(
    Global_Parameters::Nu);
 Global_Parameters::E_pt[1]=new TimeHarmonicIsotropicElasticityTensor(
  Global_Parameters::Nu);
 
 // Complete build of solid elements
 complete_problem_setup();
 
 // Same for Helmholtz mesh
 unsigned n_element =Helmholtz_mesh_pt->nelement();
 for(unsigned i=0;i<n_element;i++)
  {
   //Cast to a solid element
   HELMHOLTZ_ELEMENT *el_pt = 
    dynamic_cast<HELMHOLTZ_ELEMENT*>(Helmholtz_mesh_pt->element_pt(i));
 
   //Set the pointer to square of Helmholtz wavenumber
   el_pt->k_squared_pt() = &Global_Parameters::K_squared;
  }
 
 // Output meshes and their boundaries so far so we can double 
 // check the boundary enumeration
 Solid_mesh_pt->output("solid_mesh.dat");
 Helmholtz_mesh_pt->output("helmholtz_mesh.dat");
 Solid_mesh_pt->output_boundaries("solid_mesh_boundary.dat");
 Helmholtz_mesh_pt->output_boundaries("helmholtz_mesh_boundary.dat");
 
 // Create FaceElement meshes for boundary conditions
 //---------------------------------------------------
 
 // Construct the solid traction element mesh
 Solid_traction_mesh_pt=new Mesh;
 create_solid_traction_elements(); 
 
 // Construct the fsi traction element mesh
 FSI_traction_mesh_pt=new Mesh;
 create_fsi_traction_elements(); 
 
 // Construct the Helmholtz fsi flux element mesh
 Helmholtz_fsi_flux_mesh_pt=new Mesh;
 create_helmholtz_fsi_flux_elements();
 
 // Create ABC elements on outer boundary of Helmholtz mesh
 create_helmholtz_ABC_elements();
 
 
 // Combine sub meshes
 //-------------------
 
 // Solid mesh is first sub-mesh
 add_sub_mesh(Solid_mesh_pt);
 
 // Add solid traction sub-mesh
 add_sub_mesh(Solid_traction_mesh_pt);
 
 // Add FSI traction sub-mesh
 add_sub_mesh(FSI_traction_mesh_pt);
 
 // Add Helmholtz mesh
 add_sub_mesh(Helmholtz_mesh_pt);
 
 // Add Helmholtz FSI flux mesh
 add_sub_mesh(Helmholtz_fsi_flux_mesh_pt);
 
 // Add Helmholtz ABC mesh
 add_sub_mesh(Helmholtz_outer_boundary_mesh_pt); 
 
 // Build combined "global" mesh
 build_global_mesh();
 
 
 // Setup fluid-structure interaction
 //----------------------------------
 setup_interaction();
 
 // Assign equation  numbers
 oomph_info << "Number of unknowns: " << assign_eqn_numbers() << std::endl; 
 
 // Set output directory
 Doc_info.set_directory(Global_Parameters::Directory);
 
 // Open trace file
 char filename[100];
 snprintf(filename, sizeof(filename), "%s/trace.dat",Doc_info.directory().c_str());
 Trace_file.open(filename);
  
 
} //end of constructor
 
 
//=====================start_of_actions_before_adapt======================
/// Actions before adapt: Wipe the meshes face elements
//========================================================================
template<class ELASTICITY_ELEMENT, class HELMHOLTZ_ELEMENT>
void CoatedDiskProblem<ELASTICITY_ELEMENT,HELMHOLTZ_ELEMENT>::
actions_before_adapt()
{
 // Kill the solid traction elements and wipe surface mesh
 delete_face_elements(Solid_traction_mesh_pt);
 
 // Kill the fsi traction elements and wipe surface mesh
 delete_face_elements(FSI_traction_mesh_pt);
 
 // Kill Helmholtz FSI flux elements
 delete_face_elements(Helmholtz_fsi_flux_mesh_pt);
 
 // Kill Helmholtz BC elements 
 delete_face_elements(Helmholtz_outer_boundary_mesh_pt);
 
 // Rebuild the Problem's global mesh from its various sub-meshes
 rebuild_global_mesh();
 
}// end of actions_before_adapt
 
 
 
//=====================start_of_actions_after_adapt=======================
///  Actions after adapt: Rebuild the meshes of face elements
//========================================================================
template<class ELASTICITY_ELEMENT, class HELMHOLTZ_ELEMENT>
void CoatedDiskProblem<ELASTICITY_ELEMENT,HELMHOLTZ_ELEMENT>::
actions_after_adapt()
{
 // Complete problem setup
 complete_problem_setup(); 
 
 // Construct the solid traction elements
 create_solid_traction_elements(); 
 
 // Create fsi traction elements from all elements that are 
 // adjacent to FSI boundaries and add them to surface meshes
 create_fsi_traction_elements();
 
 // Create Helmholtz fsi flux elements
 create_helmholtz_fsi_flux_elements();
 
 // Create ABC elements from all elements that are 
 // adjacent to the outer boundary of Helmholtz mesh
 create_helmholtz_ABC_elements();
   
 // Setup interaction
 setup_interaction();
 
 // Rebuild the Problem's global mesh from its various sub-meshes
 rebuild_global_mesh();
 
}// end of actions_after_adapt
 
 
 
 
//=====================start_of_complete_problem_setup=======================
/// Complete problem setup: Apply boundary conditions and set
/// physical properties
//========================================================================
template<class ELASTICITY_ELEMENT, class HELMHOLTZ_ELEMENT>
void CoatedDiskProblem<ELASTICITY_ELEMENT,HELMHOLTZ_ELEMENT>::
complete_problem_setup()
{
 
 // Solid boundary conditions:
 //---------------------------
 // Pin real and imag part of horizontal displacement components 
 //-------------------------------------------------------------
 // on vertical boundaries
 //-----------------------
 {  
  //Loop over the nodes to pin and assign boundary displacements on 
  //solid boundary
  unsigned n_node = Solid_mesh_pt->nboundary_node(Upper_symmetry_boundary_id);
  for(unsigned i=0;i<n_node;i++)
   {
    Node* nod_pt=Solid_mesh_pt->boundary_node_pt(Upper_symmetry_boundary_id,i);
    
    // Real part of x-displacement 
    nod_pt->pin(0);
    nod_pt->set_value(0,0.0);
    
    // Imag part of x-displacement
    nod_pt->pin(2);
    nod_pt->set_value(2,0.0);
   }
 }
 {
  //Loop over the nodes to pin and assign boundary displacements on 
  //solid boundary
  unsigned n_node = Solid_mesh_pt->nboundary_node(Lower_symmetry_boundary_id);
  for(unsigned i=0;i<n_node;i++)
   {
    Node* nod_pt=Solid_mesh_pt->boundary_node_pt(Lower_symmetry_boundary_id,i);
 
    // Real part of x-displacement 
    nod_pt->pin(0);
    nod_pt->set_value(0,0.0);
    
    // Imag part of x-displacement
    nod_pt->pin(2);
    nod_pt->set_value(2,0.0);
   }
 }
 
 
 
 //Assign the physical properties to the elements
 //----------------------------------------------
 unsigned nreg=Solid_mesh_pt->nregion();
 for (unsigned r=0;r<nreg;r++)
  {
   unsigned nel=Solid_mesh_pt->nregion_element(r);
   for (unsigned e=0;e<nel;e++)
    {     
     //Cast to a solid element
     ELASTICITY_ELEMENT *el_pt = 
      dynamic_cast<ELASTICITY_ELEMENT*>(Solid_mesh_pt->
                                        region_element_pt(r,e));
     
     // Set the constitutive law
     el_pt->elasticity_tensor_pt() = Global_Parameters::E_pt[r];
     
     // Square of non-dim frequency
     el_pt->omega_sq_pt()= &Global_Parameters::Omega_sq[r];
    }
  }    
}
 
//============start_of_delete_face_elements================
/// Delete face elements and wipe the mesh
//==========================================================
template<class ELASTICITY_ELEMENT, class HELMHOLTZ_ELEMENT>
void CoatedDiskProblem<ELASTICITY_ELEMENT,HELMHOLTZ_ELEMENT>::
delete_face_elements(Mesh* const & boundary_mesh_pt)
{
 // How many surface elements are in the surface mesh
 unsigned n_element = boundary_mesh_pt->nelement();
 
 // Loop over the surface elements
 for(unsigned e=0;e<n_element;e++)
  {
   //   Kill surface element
   delete boundary_mesh_pt->element_pt(e);
  }
 
 // Wipe the mesh
 boundary_mesh_pt->flush_element_and_node_storage();
 
} // end of delete_face_elements
 
 
 
//============start_of_create_solid_traction_elements====================
/// Create solid traction elements 
//=======================================================================
template<class ELASTICITY_ELEMENT, class HELMHOLTZ_ELEMENT>
void CoatedDiskProblem<ELASTICITY_ELEMENT,HELMHOLTZ_ELEMENT>::
create_solid_traction_elements()
{
 // Loop over pressure loaded boundaries
 unsigned b=0;
 unsigned nb=3;
 for (unsigned i=0;i<nb;i++) 
  {
   switch(i)
    {
    case 0:
     b=Upper_inner_boundary_id;
     break;
     
    case 1:
     b=Lower_inner_boundary_id;
     break;
     
    case 2:
     b=Rib_divider_boundary_id;
     break;
    }
   
   // We're attaching face elements to region 0
   unsigned r=0;
   
   // How many bulk elements are adjacent to boundary b?
   unsigned n_element = Solid_mesh_pt->nboundary_element_in_region(b,r);
   
   // Loop over the bulk elements adjacent to boundary b
   for(unsigned e=0;e<n_element;e++)
    {
     // Get pointer to the bulk element that is adjacent to boundary b
     ELASTICITY_ELEMENT* bulk_elem_pt = dynamic_cast<ELASTICITY_ELEMENT*>(
      Solid_mesh_pt->boundary_element_in_region_pt(b,r,e));
     
     //Find the index of the face of element e along boundary b
     int face_index = Solid_mesh_pt->face_index_at_boundary_in_region(b,r,e);
     
     // Create element
     TimeHarmonicLinearElasticityTractionElement<ELASTICITY_ELEMENT>* el_pt=
      new TimeHarmonicLinearElasticityTractionElement<ELASTICITY_ELEMENT>
      (bulk_elem_pt,face_index);   
     
     // Add to mesh
     Solid_traction_mesh_pt->add_element_pt(el_pt);
     
     // Associate element with bulk boundary (to allow it to access
     // the boundary coordinates in the bulk mesh)
     el_pt->set_boundary_number_in_bulk_mesh(b); 
     
     //Set the traction function
     el_pt->traction_fct_pt() = Global_Parameters::pressure_load;  
    }
  }
} // end of create_traction_elements
 
 
 
 
//============start_of_create_fsi_traction_elements======================
/// Create fsi traction elements 
//=======================================================================
template<class ELASTICITY_ELEMENT, class HELMHOLTZ_ELEMENT>
void CoatedDiskProblem<ELASTICITY_ELEMENT,HELMHOLTZ_ELEMENT>::
create_fsi_traction_elements()
{
 // We're on the outer boundary of the solid mesh
 unsigned b=Outer_boundary_id;
 
 // How many bulk elements are adjacent to boundary b?
 unsigned n_element = Solid_mesh_pt->nboundary_element(b);
 
 // Loop over the bulk elements adjacent to boundary b
 for(unsigned e=0;e<n_element;e++)
  {
   // Get pointer to the bulk element that is adjacent to boundary b
   ELASTICITY_ELEMENT* bulk_elem_pt = dynamic_cast<ELASTICITY_ELEMENT*>(
    Solid_mesh_pt->boundary_element_pt(b,e));
   
   //Find the index of the face of element e along boundary b
   int face_index = Solid_mesh_pt->face_index_at_boundary(b,e);
   
   // Create element
   TimeHarmonicLinElastLoadedByHelmholtzPressureBCElement
    <ELASTICITY_ELEMENT,HELMHOLTZ_ELEMENT>* el_pt=
    new TimeHarmonicLinElastLoadedByHelmholtzPressureBCElement
    <ELASTICITY_ELEMENT,HELMHOLTZ_ELEMENT>(bulk_elem_pt,
                                           face_index);   
   // Add to mesh
   FSI_traction_mesh_pt->add_element_pt(el_pt);
   
   // Associate element with bulk boundary (to allow it to access
   // the boundary coordinates in the bulk mesh)
   el_pt->set_boundary_number_in_bulk_mesh(b); 
   
   // Set FSI parameter
   el_pt->q_pt()=&Global_Parameters::Q;          
  }
 
} // end of create_traction_elements
 
 
 
 
 
//============start_of_create_helmholtz_fsi_flux_elements================
/// Create Helmholtz fsi flux elements 
//=======================================================================
template<class ELASTICITY_ELEMENT, class HELMHOLTZ_ELEMENT>
void CoatedDiskProblem<ELASTICITY_ELEMENT,HELMHOLTZ_ELEMENT>::
create_helmholtz_fsi_flux_elements()
{
 
 // Attach to inner boundary of Helmholtz mesh (0)
 unsigned b=0;
 
 // How many bulk elements are adjacent to boundary b?
 unsigned n_element = Helmholtz_mesh_pt->nboundary_element(b);
 
 // Loop over the bulk elements adjacent to boundary b
 for(unsigned e=0;e<n_element;e++)
  {
   // Get pointer to the bulk element that is adjacent to boundary b
   HELMHOLTZ_ELEMENT* bulk_elem_pt = dynamic_cast<HELMHOLTZ_ELEMENT*>(
    Helmholtz_mesh_pt->boundary_element_pt(b,e));
   
   //Find the index of the face of element e along boundary b
   int face_index = Helmholtz_mesh_pt->face_index_at_boundary(b,e);
   
   // Create element
   HelmholtzFluxFromNormalDisplacementBCElement
    <HELMHOLTZ_ELEMENT,ELASTICITY_ELEMENT>* el_pt=
    new HelmholtzFluxFromNormalDisplacementBCElement
    <HELMHOLTZ_ELEMENT,ELASTICITY_ELEMENT>(bulk_elem_pt,
                                           face_index);
   
   // Add to mesh
   Helmholtz_fsi_flux_mesh_pt->add_element_pt(el_pt);
   
   // Associate element with bulk boundary (to allow it to access
   // the boundary coordinates in the bulk mesh)
   el_pt->set_boundary_number_in_bulk_mesh(b); 
  }  
  
} // end of create_helmholtz_flux_elements
 
 
 
//============start_of_create_ABC_elements==============================
/// Create ABC elements on the outer boundary of 
/// the Helmholtz mesh
//===========================================================================
template<class ELASTICITY_ELEMENT, class HELMHOLTZ_ELEMENT>
void CoatedDiskProblem<ELASTICITY_ELEMENT,HELMHOLTZ_ELEMENT>::
create_helmholtz_ABC_elements()
{
 // We're on boundary 2 of the Helmholtz mesh
 unsigned b=2;
 
 // How many bulk elements are adjacent to boundary b?
 unsigned n_element = Helmholtz_mesh_pt->nboundary_element(b);
 
 // Loop over the bulk elements adjacent to boundary b?
 for(unsigned e=0;e<n_element;e++)
  {
   // Get pointer to the bulk element that is adjacent to boundary b
   HELMHOLTZ_ELEMENT* bulk_elem_pt = dynamic_cast<HELMHOLTZ_ELEMENT*>(
    Helmholtz_mesh_pt->boundary_element_pt(b,e));
   
   //Find the index of the face of element e along boundary b 
   int face_index = Helmholtz_mesh_pt->face_index_at_boundary(b,e);
   
   // Build the corresponding ABC element
   HelmholtzAbsorbingBCElement<HELMHOLTZ_ELEMENT>* flux_element_pt = new 
    HelmholtzAbsorbingBCElement<HELMHOLTZ_ELEMENT>(bulk_elem_pt,face_index);
 
   // Set pointer to outer radius of artificial boundary
   flux_element_pt->outer_radius_pt()=&Global_Parameters::Outer_radius;
   
   // Set order of absorbing boundary condition
   flux_element_pt->abc_order_pt()=&Global_Parameters::ABC_order;   
 
   //Add the flux boundary element to the  helmholtz_outer_boundary_mesh
   Helmholtz_outer_boundary_mesh_pt->add_element_pt(flux_element_pt);
  }
 
} // end of create_helmholtz_ABC_elements
 
 
 
//=====================start_of_setup_interaction======================
/// Setup interaction between two fields
//========================================================================
template<class ELASTICITY_ELEMENT, class HELMHOLTZ_ELEMENT>
void CoatedDiskProblem<ELASTICITY_ELEMENT,HELMHOLTZ_ELEMENT>::
setup_interaction()
{
 
 // Setup Helmholtz "pressure" load on traction elements
 unsigned boundary_in_helmholtz_mesh=0;
 
 // Doc boundary coordinate for Helmholtz
 ofstream the_file;
 the_file.open("boundary_coordinate_hh.dat");
 Helmholtz_mesh_pt->Mesh::doc_boundary_coordinates<HELMHOLTZ_ELEMENT>
  (boundary_in_helmholtz_mesh, the_file);
 the_file.close();
 
  Multi_domain_functions::setup_bulk_elements_adjacent_to_face_mesh
  <HELMHOLTZ_ELEMENT,2>
  (this,boundary_in_helmholtz_mesh,Helmholtz_mesh_pt,FSI_traction_mesh_pt);
 
 // Setup Helmholtz flux from normal displacement interaction
 unsigned boundary_in_solid_mesh=Outer_boundary_id;
 
 // Doc boundary coordinate for solid mesh
 the_file.open("boundary_coordinate_solid.dat");
 Solid_mesh_pt->Mesh::template doc_boundary_coordinates<ELASTICITY_ELEMENT>
  (boundary_in_solid_mesh, the_file);
 the_file.close();
 
 Multi_domain_functions::setup_bulk_elements_adjacent_to_face_mesh
  <ELASTICITY_ELEMENT,2>(
   this,boundary_in_solid_mesh,Solid_mesh_pt,Helmholtz_fsi_flux_mesh_pt);
}
 
 
 
//==============start_doc===========================================
/// Doc the solution
//==================================================================
template<class ELASTICITY_ELEMENT, class HELMHOLTZ_ELEMENT>
void CoatedDiskProblem<ELASTICITY_ELEMENT,HELMHOLTZ_ELEMENT>::doc_solution()
{
 
 ofstream some_file,some_file2;
 char filename[100];
 
 // Number of plot points
 unsigned n_plot=5; 
 
 // Compute/output the radiated power
 //----------------------------------
 snprintf(filename, sizeof(filename), "%s/power%i.dat",Doc_info.directory().c_str(),
         Doc_info.number());
 some_file.open(filename);
 
 // Accumulate contribution from elements
 double power=0.0;
 unsigned nn_element=Helmholtz_outer_boundary_mesh_pt->nelement(); 
 for(unsigned e=0;e<nn_element;e++)
  {
   HelmholtzBCElementBase<HELMHOLTZ_ELEMENT> *el_pt = 
    dynamic_cast<HelmholtzBCElementBase<HELMHOLTZ_ELEMENT>*>(
     Helmholtz_outer_boundary_mesh_pt->element_pt(e)); 
   power += el_pt->global_power_contribution(some_file);
  }
 some_file.close();
 oomph_info << "Step: " << Doc_info.number() 
            << ": Q=" << Global_Parameters::Q  << "\n"
            << " k_squared=" << Global_Parameters::K_squared  << "\n"
            << " density ratio (annulus) =" 
            << Global_Parameters::Density_ratio[0]  << "\n"
            << " density ratio (rib)     =" 
            << Global_Parameters::Density_ratio[1]  << "\n"
            << " omega_sq (annulus)=" << Global_Parameters::Omega_sq[0]  << "\n"
            << " omega_sq (rib    )=" << Global_Parameters::Omega_sq[1]  << "\n"
            << " Total radiated power " << power  << "\n"
            << std::endl; 
 
 
 // Write trace file
 Trace_file << Global_Parameters::Q << " " 
            << Global_Parameters::K_squared << " "
            << Global_Parameters::Density_ratio[0] << " "
            << Global_Parameters::Density_ratio[1] << " "
            << Global_Parameters::Omega_sq[0] << " "
            << Global_Parameters::Omega_sq[1] << " "
            << power << " " 
            << std::endl;
  
 std::ostringstream case_string;
 case_string << "TEXT X=10,Y=90, T=\"Q=" 
             <<  Global_Parameters::Q 
             << ",  k<sup>2</sup> = "
             <<  Global_Parameters::K_squared
             << ",  density ratio = "
             <<  Global_Parameters::Density_ratio[0] << " and "
             <<  Global_Parameters::Density_ratio[1] 
             << ",  omega_sq = "
             <<  Global_Parameters::Omega_sq[0] << " and " 
             <<  Global_Parameters::Omega_sq[1] << " " 
             << "\"\n";
 
 
 // Output displacement field
 //--------------------------
 snprintf(filename, sizeof(filename), "%s/elast_soln%i.dat",Doc_info.directory().c_str(),
         Doc_info.number());
 some_file.open(filename);
 Solid_mesh_pt->output(some_file,n_plot);
 some_file.close();
 
 // Output solid traction elements
 //--------------------------------
 snprintf(filename, sizeof(filename), "%s/solid_traction_soln%i.dat",Doc_info.directory().c_str(),
         Doc_info.number());
 some_file.open(filename);
 Solid_traction_mesh_pt->output(some_file,n_plot);
 some_file.close();
 
 // Output fsi traction elements
 //----------------------------- 
 snprintf(filename, sizeof(filename), "%s/traction_soln%i.dat",Doc_info.directory().c_str(),
         Doc_info.number());
 some_file.open(filename);
 FSI_traction_mesh_pt->output(some_file,n_plot);
 some_file.close();
 
 
 // Output Helmholtz fsi flux elements
 //----------------------------------- 
 snprintf(filename, sizeof(filename), "%s/flux_bc_soln%i.dat",Doc_info.directory().c_str(),
         Doc_info.number());
 some_file.open(filename);
 Helmholtz_fsi_flux_mesh_pt->output(some_file,n_plot);
 some_file.close();
 
 
 // Output Helmholtz
 //-----------------
 snprintf(filename, sizeof(filename), "%s/helmholtz_soln%i.dat",Doc_info.directory().c_str(),
         Doc_info.number());
 some_file.open(filename);
 Helmholtz_mesh_pt->output(some_file,n_plot);
 some_file << case_string.str();
 some_file.close();
 
 // Output regions of solid mesh
 //-----------------------------
 unsigned nreg=Solid_mesh_pt->nregion();
 for (unsigned r=0;r<nreg;r++)
  {
   snprintf(filename, sizeof(filename), "%s/region%i_%i.dat",Doc_info.directory().c_str(),
           r,Doc_info.number());   
   some_file.open(filename);   
   unsigned nel=Solid_mesh_pt->nregion_element(r);
   for (unsigned e=0;e<nel;e++)
    {     
     FiniteElement* el_pt=Solid_mesh_pt->region_element_pt(r,e);
     el_pt->output(some_file,n_plot);
    }
   some_file.close();
  }
 
 
 // Do animation of Helmholtz solution
 //-----------------------------------
 unsigned nstep=40;
 for (unsigned i=0;i<nstep;i++)
  {
   snprintf(filename, sizeof(filename), "%s/helmholtz_animation%i_frame%i.dat",
           Doc_info.directory().c_str(),
           Doc_info.number(),i);
   some_file.open(filename);
   double phi=2.0*MathematicalConstants::Pi*double(i)/double(nstep-1);
   unsigned nelem=Helmholtz_mesh_pt->nelement();
   for (unsigned e=0;e<nelem;e++)
    {
     HELMHOLTZ_ELEMENT* el_pt=dynamic_cast<HELMHOLTZ_ELEMENT*>(
      Helmholtz_mesh_pt->element_pt(e));
     el_pt->output_real(some_file,phi,n_plot);    
    }
   some_file.close();
  }
 
 cout << "Doced for Q=" << Global_Parameters::Q << " (step "
      << Doc_info.number() << ")\n";
 
// Increment label for output files
 Doc_info.number()++;
 
} //end doc
 
 
 
//=======start_of_main==================================================
/// Driver for acoustic fsi problem
//======================================================================
int main(int argc, char **argv)
{
 
 // Store command line arguments
 CommandLineArgs::setup(argc,argv);
 
 // Define possible command line arguments and parse the ones that
 // were actually specified
 
 // Output directory
 CommandLineArgs::specify_command_line_flag("--dir",
                                            &Global_Parameters::Directory);
 
 // Peakiness parameter for loading
 CommandLineArgs::specify_command_line_flag("--alpha",
                                            &Global_Parameters::Alpha);
 
 // Multiplier for number of elements in solid mesh
 CommandLineArgs::specify_command_line_flag("--el_multiplier",
                            &Global_Parameters::El_multiplier);
 
 // Outer radius of Helmholtz domain
 CommandLineArgs::specify_command_line_flag("--outer_radius",
                            &Global_Parameters::Outer_radius);
  
 // Validaton run?
 CommandLineArgs::specify_command_line_flag("--validation");
 
 // Max. number of adaptations
 unsigned max_adapt=3;
 CommandLineArgs::specify_command_line_flag("--max_adapt",&max_adapt);
 
 // Parse command line
 CommandLineArgs::parse_and_assign(); 
 
 // Doc what has actually been specified on the command line
 CommandLineArgs::doc_specified_flags();
 
 //Set up the problem
 CoatedDiskProblem<ProjectableTimeHarmonicLinearElasticityElement
                   <TTimeHarmonicLinearElasticityElement<2,3> >,
                   RefineableQHelmholtzElement<2,3> > problem; 
 
 
 // Set values for parameter values
 Global_Parameters::Q=5.0; 
 Global_Parameters::Density_ratio[0]=0.1; 
 Global_Parameters::Density_ratio[1]=0.1; 
 Global_Parameters::update_parameter_values();
 
 //Parameter study
 unsigned nstep=3; 
 if (CommandLineArgs::command_line_flag_has_been_set("--validation"))
  {
   nstep=1;
   max_adapt=2;
  }
 for(unsigned i=0;i<nstep;i++)
  {
   // Solve the problem with Newton's method, allowing
   // up to max_adapt mesh adaptations after every solve.
   problem.newton_solve(max_adapt);
 
   // Doc solution
   problem.doc_solution();
 
   // Make rib a lot heavier but keep its stiffness
   if (i==0)
    {
     Global_Parameters::E_pt[1]->update_constitutive_parameters(
      Global_Parameters::Nu,1.0);
     Global_Parameters::Density_ratio[1]=10.0; 
     Global_Parameters::update_parameter_values();
    }
 
   // Make rib very soft and inertia-less
   if (i==1)
    {
     Global_Parameters::E_pt[1]->update_constitutive_parameters(
      Global_Parameters::Nu,1.0e-16);
     Global_Parameters::Density_ratio[1]=0.0; 
     Global_Parameters::update_parameter_values();
    }
   
   
  }
 
} //end of main