示例#1
0
文件: main.cpp 项目: haowu80s/IBAMR
void
beam_PK1_dil_stress_function(TensorValue<double>& PP,
                             const TensorValue<double>& FF,
                             const libMesh::Point& /*X*/,
                             const libMesh::Point& /*s*/,
                             Elem* const /*elem*/,
                             const vector<NumericVector<double>*>& /*system_data*/,
                             double /*time*/,
                             void* /*ctx*/)
{
    double J = FF.det();
    J_dil_min = std::min(J, J_dil_min);
    J_dil_max = std::max(J, J_dil_max);
    PP.zero();
    if (!MathUtilities<double>::equalEps(beta_s, 0.0))
    {
        const TensorValue<double> FF_inv_trans = tensor_inverse_transpose(FF, NDIM);
        PP -= 2.0 * beta_s * log(FF.det()) * FF_inv_trans;
    }
    return;
} // beam_PK1_dil_stress_function
示例#2
0
文件: main.cpp 项目: BijanZarif/IBAMR
void
PK1_dil_stress_function(
    TensorValue<double>& PP,
    const TensorValue<double>& FF,
    const libMesh::Point& /*X*/,
    const libMesh::Point& /*s*/,
    Elem* const /*elem*/,
    const std::vector<NumericVector<double>*>& /*system_data*/,
    double /*time*/,
    void* /*ctx*/)
{
    PP = 2.0*(-p0_s + beta_s*log(FF.det()))*tensor_inverse_transpose(FF, NDIM);
    return;
}// PK1_dil_stress_function
示例#3
0
文件: main.cpp 项目: mesnardo/IBAMR
void PK1_stress_function(TensorValue<double>& PP,
                         const TensorValue<double>& FF,
                         const libMesh::Point& /*x*/,
                         const libMesh::Point& /*X*/,
                         subdomain_id_type /*subdomain_id*/,
                         std::vector<double>& /*internal_vars*/,
                         double /*time*/,
                         void* /*ctx*/)
{
    const TensorValue<double> FF_inv_trans = tensor_inverse_transpose(FF, NDIM);
    const TensorValue<double> CC = FF.transpose() * FF;
    PP = 2.0 * c1_s * FF;
    if (!MathUtilities<double>::equalEps(p0_s, 0.0))
    {
        PP -= 2.0 * p0_s * FF_inv_trans;
    }
    if (!MathUtilities<double>::equalEps(beta_s, 0.0))
    {
        PP += beta_s * log(CC.det()) * FF_inv_trans;
    }
    return;
} // PK1_stress_function
示例#4
0
文件: main.cpp 项目: BijanZarif/IBAMR
/*******************************************************************************
 * For each run, the input filename and restart information (if needed) must   *
 * be given on the command line.  For non-restarted case, command line is:     *
 *                                                                             *
 *    executable <input file name>                                             *
 *                                                                             *
 * For restarted run, command line is:                                         *
 *                                                                             *
 *    executable <input file name> <restart directory> <restart number>        *
 *                                                                             *
 *******************************************************************************/
int
main(
    int argc,
    char* argv[])
{
    // Initialize libMesh, PETSc, MPI, and SAMRAI.
    LibMeshInit init(argc, argv);
    SAMRAI_MPI::setCommunicator(PETSC_COMM_WORLD);
    SAMRAI_MPI::setCallAbortInSerialInsteadOfExit();
    SAMRAIManager::startup();

    {// cleanup dynamically allocated objects prior to shutdown

        // Parse command line options, set some standard options from the input
        // file, initialize the restart database (if this is a restarted run),
        // and enable file logging.
        Pointer<AppInitializer> app_initializer = new AppInitializer(argc, argv, "IB.log");
        Pointer<Database> input_db = app_initializer->getInputDatabase();

        // Get various standard options set in the input file.
        const bool dump_viz_data = app_initializer->dumpVizData();
        const int viz_dump_interval = app_initializer->getVizDumpInterval();
        const bool uses_visit = dump_viz_data && app_initializer->getVisItDataWriter();
        const bool uses_exodus = dump_viz_data && !app_initializer->getExodusIIFilename().empty();
        const string exodus_filename = app_initializer->getExodusIIFilename();

        const bool dump_restart_data = app_initializer->dumpRestartData();
        const int restart_dump_interval = app_initializer->getRestartDumpInterval();
        const string restart_dump_dirname = app_initializer->getRestartDumpDirectory();

        const bool dump_postproc_data = app_initializer->dumpPostProcessingData();
        const int postproc_data_dump_interval = app_initializer->getPostProcessingDataDumpInterval();
        const string postproc_data_dump_dirname = app_initializer->getPostProcessingDataDumpDirectory();
        if (dump_postproc_data && (postproc_data_dump_interval > 0) && !postproc_data_dump_dirname.empty())
        {
            Utilities::recursiveMkdir(postproc_data_dump_dirname);
        }

        const bool dump_timer_data = app_initializer->dumpTimerData();
        const int timer_dump_interval = app_initializer->getTimerDumpInterval();

        // Create a simple FE mesh.
        Mesh mesh(NDIM);
        const double dx = input_db->getDouble("DX");
        const double ds = input_db->getDouble("MFAC")*dx;
        string elem_type = input_db->getString("ELEM_TYPE");
        const double R = 0.2;
        if (NDIM == 2 && (elem_type == "TRI3" || elem_type == "TRI6"))
        {
            const int num_circum_nodes = ceil(2.0*M_PI*R/ds);
            for (int k = 0; k < num_circum_nodes; ++k)
            {
                const double theta = 2.0*M_PI*static_cast<double>(k)/static_cast<double>(num_circum_nodes);
                mesh.add_point(libMesh::Point(R*cos(theta), R*sin(theta)));
            }
            TriangleInterface triangle(mesh);
            triangle.triangulation_type() = TriangleInterface::GENERATE_CONVEX_HULL;
            triangle.elem_type() = Utility::string_to_enum<ElemType>(elem_type);
            triangle.desired_area() = 1.5*sqrt(3.0)/4.0*ds*ds;
            triangle.insert_extra_points() = true;
            triangle.smooth_after_generating() = true;
            triangle.triangulate();
        }
        else
        {
            // NOTE: number of segments along boundary is 4*2^r.
            const double num_circum_segments = 2.0*M_PI*R/ds;
            const int r = log2(0.25*num_circum_segments);
            MeshTools::Generation::build_sphere(mesh, R, r, Utility::string_to_enum<ElemType>(elem_type));
        }

        // Ensure nodes on the surface are on the analytic boundary.
        MeshBase::element_iterator el_end = mesh.elements_end();
        for (MeshBase::element_iterator el = mesh.elements_begin();
             el != el_end; ++el)
        {
            Elem* const elem = *el;
            for (unsigned int side = 0; side < elem->n_sides(); ++side)
            {
                const bool at_mesh_bdry = !elem->neighbor(side);
                if (!at_mesh_bdry) continue;
                for (unsigned int k = 0; k < elem->n_nodes(); ++k)
                {
                    if (!elem->is_node_on_side(k,side)) continue;
                    Node& n = *elem->get_node(k);
                    n = R*n.unit();
                }
            }
        }
        mesh.prepare_for_use();

        c1_s   = input_db->getDouble("C1_S");
        p0_s   = input_db->getDouble("P0_S");
        beta_s = input_db->getDouble("BETA_S");

        // Create major algorithm and data objects that comprise the
        // application.  These objects are configured from the input database
        // and, if this is a restarted run, from the restart database.
        Pointer<INSHierarchyIntegrator> navier_stokes_integrator;
        const string solver_type = app_initializer->getComponentDatabase("Main")->getString("solver_type");
        if (solver_type == "STAGGERED")
        {
            navier_stokes_integrator = new INSStaggeredHierarchyIntegrator(
                "INSStaggeredHierarchyIntegrator", app_initializer->getComponentDatabase("INSStaggeredHierarchyIntegrator"));
        }
        else if (solver_type == "COLLOCATED")
        {
            navier_stokes_integrator = new INSCollocatedHierarchyIntegrator(
                "INSCollocatedHierarchyIntegrator", app_initializer->getComponentDatabase("INSCollocatedHierarchyIntegrator"));
        }
        else
        {
            TBOX_ERROR("Unsupported solver type: " << solver_type << "\n" <<
                       "Valid options are: COLLOCATED, STAGGERED");
        }
        Pointer<IBFEMethod> ib_method_ops = new IBFEMethod(
            "IBFEMethod", app_initializer->getComponentDatabase("IBFEMethod"), &mesh, app_initializer->getComponentDatabase("GriddingAlgorithm")->getInteger("max_levels"));
        Pointer<IBHierarchyIntegrator> time_integrator = new IBExplicitHierarchyIntegrator(
            "IBHierarchyIntegrator", app_initializer->getComponentDatabase("IBHierarchyIntegrator"), ib_method_ops, navier_stokes_integrator);
        Pointer<CartesianGridGeometry<NDIM> > grid_geometry = new CartesianGridGeometry<NDIM>(
            "CartesianGeometry", app_initializer->getComponentDatabase("CartesianGeometry"));
        Pointer<PatchHierarchy<NDIM> > patch_hierarchy = new PatchHierarchy<NDIM>(
            "PatchHierarchy", grid_geometry);
        Pointer<StandardTagAndInitialize<NDIM> > error_detector = new StandardTagAndInitialize<NDIM>(
            "StandardTagAndInitialize", time_integrator, app_initializer->getComponentDatabase("StandardTagAndInitialize"));
        Pointer<BergerRigoutsos<NDIM> > box_generator = new BergerRigoutsos<NDIM>();
        Pointer<LoadBalancer<NDIM> > load_balancer = new LoadBalancer<NDIM>(
            "LoadBalancer", app_initializer->getComponentDatabase("LoadBalancer"));
        Pointer<GriddingAlgorithm<NDIM> > gridding_algorithm = new GriddingAlgorithm<NDIM>(
            "GriddingAlgorithm", app_initializer->getComponentDatabase("GriddingAlgorithm"), error_detector, box_generator, load_balancer);

        // Configure the IBFE solver.
        ib_method_ops->registerInitialCoordinateMappingFunction(coordinate_mapping_function);
        IBFEMethod::PK1StressFcnData PK1_dev_stress_data(PK1_dev_stress_function);
        IBFEMethod::PK1StressFcnData PK1_dil_stress_data(PK1_dil_stress_function);
        PK1_dev_stress_data.quad_order = Utility::string_to_enum<libMeshEnums::Order>(input_db->getStringWithDefault("PK1_DEV_QUAD_ORDER","THIRD"));
        PK1_dil_stress_data.quad_order = Utility::string_to_enum<libMeshEnums::Order>(input_db->getStringWithDefault("PK1_DIL_QUAD_ORDER","FIRST"));
        ib_method_ops->registerPK1StressFunction(PK1_dev_stress_data);
        ib_method_ops->registerPK1StressFunction(PK1_dil_stress_data);
        EquationSystems* equation_systems = ib_method_ops->getFEDataManager()->getEquationSystems();

        // Set up post processor to recover computed stresses.
        FEDataManager* fe_data_manager = ib_method_ops->getFEDataManager();
        Pointer<IBFEPostProcessor> ib_post_processor = new IBFECentroidPostProcessor("IBFEPostProcessor", fe_data_manager);

        ib_post_processor->registerTensorVariable(
            "FF", MONOMIAL, CONSTANT, IBFEPostProcessor::FF_fcn);

        std::pair<IBTK::TensorMeshFcnPtr,void*> PK1_dev_stress_fcn_data(PK1_dev_stress_function,static_cast<void*>(NULL));
        ib_post_processor->registerTensorVariable(
            "sigma_dev", MONOMIAL, CONSTANT,
            IBFEPostProcessor::cauchy_stress_from_PK1_stress_fcn,
            std::vector<unsigned int>(), &PK1_dev_stress_fcn_data);

        std::pair<IBTK::TensorMeshFcnPtr,void*> PK1_dil_stress_fcn_data(PK1_dil_stress_function,static_cast<void*>(NULL));
        ib_post_processor->registerTensorVariable(
            "sigma_dil", MONOMIAL, CONSTANT,
            IBFEPostProcessor::cauchy_stress_from_PK1_stress_fcn,
            std::vector<unsigned int>(), &PK1_dil_stress_fcn_data);

        ib_post_processor->registerInterpolatedScalarEulerianVariable(
            "p_f", LAGRANGE, FIRST,
            navier_stokes_integrator->getPressureVariable(),
            navier_stokes_integrator->getCurrentContext());

        // Create Eulerian initial condition specification objects.
        if (input_db->keyExists("VelocityInitialConditions"))
        {
            Pointer<CartGridFunction> u_init = new muParserCartGridFunction(
                "u_init", app_initializer->getComponentDatabase("VelocityInitialConditions"), grid_geometry);
            navier_stokes_integrator->registerVelocityInitialConditions(u_init);
        }

        if (input_db->keyExists("PressureInitialConditions"))
        {
            Pointer<CartGridFunction> p_init = new muParserCartGridFunction(
                "p_init", app_initializer->getComponentDatabase("PressureInitialConditions"), grid_geometry);
            navier_stokes_integrator->registerPressureInitialConditions(p_init);
        }

        // Create Eulerian boundary condition specification objects (when necessary).
        const IntVector<NDIM>& periodic_shift = grid_geometry->getPeriodicShift();
        vector<RobinBcCoefStrategy<NDIM>*> u_bc_coefs(NDIM);
        if (periodic_shift.min() > 0)
        {
            for (unsigned int d = 0; d < NDIM; ++d)
            {
                u_bc_coefs[d] = NULL;
            }
        }
        else
        {
            for (unsigned int d = 0; d < NDIM; ++d)
            {
                ostringstream bc_coefs_name_stream;
                bc_coefs_name_stream << "u_bc_coefs_" << d;
                const string bc_coefs_name = bc_coefs_name_stream.str();

                ostringstream bc_coefs_db_name_stream;
                bc_coefs_db_name_stream << "VelocityBcCoefs_" << d;
                const string bc_coefs_db_name = bc_coefs_db_name_stream.str();

                u_bc_coefs[d] = new muParserRobinBcCoefs(
                    bc_coefs_name, app_initializer->getComponentDatabase(bc_coefs_db_name), grid_geometry);
            }
            navier_stokes_integrator->registerPhysicalBoundaryConditions(u_bc_coefs);
        }

        // Create Eulerian body force function specification objects.
        if (input_db->keyExists("ForcingFunction"))
        {
            Pointer<CartGridFunction> f_fcn = new muParserCartGridFunction(
                "f_fcn", app_initializer->getComponentDatabase("ForcingFunction"), grid_geometry);
            time_integrator->registerBodyForceFunction(f_fcn);
        }

        // Set up visualization plot file writers.
        Pointer<VisItDataWriter<NDIM> > visit_data_writer = app_initializer->getVisItDataWriter();
        if (uses_visit)
        {
            time_integrator->registerVisItDataWriter(visit_data_writer);
        }
        AutoPtr<ExodusII_IO> exodus_io(uses_exodus ? new ExodusII_IO(mesh) : NULL);

        // Initialize hierarchy configuration and data on all patches.
        ib_method_ops->initializeFEData();
        ib_post_processor->initializeFEData();
        time_integrator->initializePatchHierarchy(patch_hierarchy, gridding_algorithm);

        // Deallocate initialization objects.
        app_initializer.setNull();

        // Print the input database contents to the log file.
        plog << "Input database:\n";
        input_db->printClassData(plog);

        // Write out initial visualization data.
        int iteration_num = time_integrator->getIntegratorStep();
        double loop_time = time_integrator->getIntegratorTime();
        if (dump_viz_data)
        {
            pout << "\n\nWriting visualization files...\n\n";
            if (uses_visit)
            {
                time_integrator->setupPlotData();
                visit_data_writer->writePlotData(patch_hierarchy, iteration_num, loop_time);
            }
            if (uses_exodus)
            {
                ib_post_processor->postProcessData(loop_time);
                exodus_io->write_timestep(exodus_filename, *equation_systems, iteration_num/viz_dump_interval+1, loop_time);
            }
        }

        // Open streams to save volume of structure.
        ofstream volume_stream;
        if (SAMRAI_MPI::getRank() == 0)
        {
            volume_stream.open("volume.curve", ios_base::out | ios_base::trunc);
        }

        // Main time step loop.
        double loop_time_end = time_integrator->getEndTime();
        double dt = 0.0;
        while (!MathUtilities<double>::equalEps(loop_time,loop_time_end) &&
               time_integrator->stepsRemaining())
        {
            iteration_num = time_integrator->getIntegratorStep();
            loop_time = time_integrator->getIntegratorTime();

            pout <<                                                    "\n";
            pout << "+++++++++++++++++++++++++++++++++++++++++++++++++++\n";
            pout << "At beginning of timestep # " <<  iteration_num << "\n";
            pout << "Simulation time is " << loop_time              << "\n";

            dt = time_integrator->getMaximumTimeStepSize();
            time_integrator->advanceHierarchy(dt);
            loop_time += dt;

            pout <<                                                    "\n";
            pout << "At end       of timestep # " <<  iteration_num << "\n";
            pout << "Simulation time is " << loop_time              << "\n";
            pout << "+++++++++++++++++++++++++++++++++++++++++++++++++++\n";
            pout <<                                                    "\n";

            // At specified intervals, write visualization and restart files,
            // print out timer data, and store hierarchy data for post
            // processing.
            iteration_num += 1;
            const bool last_step = !time_integrator->stepsRemaining();
            if (dump_viz_data && (iteration_num%viz_dump_interval == 0 || last_step))
            {
                pout << "\nWriting visualization files...\n\n";
                if (uses_visit)
                {
                    time_integrator->setupPlotData();
                    visit_data_writer->writePlotData(patch_hierarchy, iteration_num, loop_time);
                }
                if (uses_exodus)
                {
                    ib_post_processor->postProcessData(loop_time);
                    exodus_io->write_timestep(exodus_filename, *equation_systems, iteration_num/viz_dump_interval+1, loop_time);
                }
            }
            if (dump_restart_data && (iteration_num%restart_dump_interval == 0 || last_step))
            {
                pout << "\nWriting restart files...\n\n";
                RestartManager::getManager()->writeRestartFile(restart_dump_dirname, iteration_num);
            }
            if (dump_timer_data && (iteration_num%timer_dump_interval == 0 || last_step))
            {
                pout << "\nWriting timer data...\n\n";
                TimerManager::getManager()->print(plog);
            }
            if (dump_postproc_data && (iteration_num%postproc_data_dump_interval == 0 || last_step))
            {
                output_data(patch_hierarchy,
                            navier_stokes_integrator, mesh, equation_systems,
                            iteration_num, loop_time, postproc_data_dump_dirname);
            }

            // Compute the volume of the structure.
            double J_integral = 0.0;
            System& X_system = equation_systems->get_system<System>(IBFEMethod::COORDS_SYSTEM_NAME);
            NumericVector<double>* X_vec = X_system.solution.get();
            NumericVector<double>* X_ghost_vec = X_system.current_local_solution.get();
            X_vec->localize(*X_ghost_vec);
            DofMap& X_dof_map = X_system.get_dof_map();
            std::vector<std::vector<unsigned int> > X_dof_indices(NDIM);
            AutoPtr<FEBase> fe(FEBase::build(NDIM, X_dof_map.variable_type(0)));
            AutoPtr<QBase> qrule = QBase::build(QGAUSS, NDIM, FIFTH);
            fe->attach_quadrature_rule(qrule.get());
            const std::vector<double>& JxW = fe->get_JxW();
            const std::vector<std::vector<VectorValue<double> > >& dphi = fe->get_dphi();
            TensorValue<double> FF;
            boost::multi_array<double,2> X_node;
            const MeshBase::const_element_iterator el_begin = mesh.active_local_elements_begin();
            const MeshBase::const_element_iterator el_end   = mesh.active_local_elements_end();
            for (MeshBase::const_element_iterator el_it = el_begin; el_it != el_end; ++el_it)
            {
                Elem* const elem = *el_it;
                fe->reinit(elem);
                for (unsigned int d = 0; d < NDIM; ++d)
                {
                    X_dof_map.dof_indices(elem, X_dof_indices[d], d);
                }
                const int n_qp = qrule->n_points();
                get_values_for_interpolation(X_node, *X_ghost_vec, X_dof_indices);
                for (int qp = 0; qp < n_qp; ++qp)
                {
                    jacobian(FF,qp,X_node,dphi);
                    J_integral += abs(FF.det())*JxW[qp];
                }
            }
            J_integral = SAMRAI_MPI::sumReduction(J_integral);
            if (SAMRAI_MPI::getRank() == 0)
            {
                volume_stream.precision(12);
                volume_stream.setf(ios::fixed,ios::floatfield);
                volume_stream << loop_time << " " << J_integral << endl;
            }
        }

        // Close the logging streams.
        if (SAMRAI_MPI::getRank() == 0)
        {
            volume_stream.close();
        }

        // Cleanup Eulerian boundary condition specification objects (when
        // necessary).
        for (unsigned int d = 0; d < NDIM; ++d) delete u_bc_coefs[d];

    }// cleanup dynamically allocated objects prior to shutdown

    SAMRAIManager::shutdown();
    return 0;
}// main
示例#5
0
文件: main.C 项目: MSV-Project/IBAMR
/*******************************************************************************
 * For each run, the input filename and restart information (if needed) must   *
 * be given on the command line.  For non-restarted case, command line is:     *
 *                                                                             *
 *    executable <input file name>                                             *
 *                                                                             *
 * For restarted run, command line is:                                         *
 *                                                                             *
 *    executable <input file name> <restart directory> <restart number>        *
 *                                                                             *
 *******************************************************************************/
int
main(
    int argc,
    char* argv[])
{
    // Initialize libMesh, PETSc, MPI, and SAMRAI.
    LibMeshInit init(argc, argv);
    SAMRAI_MPI::setCommunicator(PETSC_COMM_WORLD);
    SAMRAI_MPI::setCallAbortInSerialInsteadOfExit();
    SAMRAIManager::startup();

    {// cleanup dynamically allocated objects prior to shutdown

        // Parse command line options, set some standard options from the input
        // file, initialize the restart database (if this is a restarted run),
        // and enable file logging.
        Pointer<AppInitializer> app_initializer = new AppInitializer(argc, argv, "IB.log");
        Pointer<Database> input_db = app_initializer->getInputDatabase();

        // Get various standard options set in the input file.
        const bool dump_viz_data = app_initializer->dumpVizData();
        const int viz_dump_interval = app_initializer->getVizDumpInterval();
        const bool uses_visit = dump_viz_data && !app_initializer->getVisItDataWriter().isNull();
        const bool uses_exodus = dump_viz_data && !app_initializer->getExodusIIFilename().empty();
        const string exodus_filename = app_initializer->getExodusIIFilename();

        const bool dump_restart_data = app_initializer->dumpRestartData();
        const int restart_dump_interval = app_initializer->getRestartDumpInterval();
        const string restart_dump_dirname = app_initializer->getRestartDumpDirectory();

        const bool dump_postproc_data = app_initializer->dumpPostProcessingData();
        const int postproc_data_dump_interval = app_initializer->getPostProcessingDataDumpInterval();
        const string postproc_data_dump_dirname = app_initializer->getPostProcessingDataDumpDirectory();
        if (dump_postproc_data && (postproc_data_dump_interval > 0) && !postproc_data_dump_dirname.empty())
        {
            Utilities::recursiveMkdir(postproc_data_dump_dirname);
        }

        const bool dump_timer_data = app_initializer->dumpTimerData();
        const int timer_dump_interval = app_initializer->getTimerDumpInterval();

        // Create a simple FE mesh with periodic boundary conditions in the "x"
        // direction.
        //
        // Note that boundary condition data must be registered with each FE
        // system before calling IBFEMethod::initializeFEData().
        Mesh mesh(NDIM);
        const double R = 0.25;
        const double w = 0.0625;
        const double dx0 = 1.0/64.0;
        const double dx = input_db->getDouble("DX");
        const double ds0 = input_db->getDouble("MFAC")*dx0;
        string elem_type = input_db->getString("ELEM_TYPE");
        MeshTools::Generation::build_square(mesh,
                                            4*static_cast<int>((dx0/dx)*ceil(2.0*M_PI*R/ds0/4.0)), static_cast<int>((dx0/dx)*ceil(w/ds0)),
                                            0.0, 2.0*M_PI*R,
                                            0.0, w,
                                            Utility::string_to_enum<ElemType>(elem_type));
        VectorValue<double> boundary_translation(2.0*M_PI*R, 0.0, 0.0);
        PeriodicBoundary pbc(boundary_translation);
        pbc.myboundary = 3;
        pbc.pairedboundary = 1;

        // Configure stress tensor options.
        smooth_case = input_db->getBool("SMOOTH_CASE");

        // Create major algorithm and data objects that comprise the
        // application.  These objects are configured from the input database
        // and, if this is a restarted run, from the restart database.
        Pointer<INSHierarchyIntegrator> navier_stokes_integrator;
        const string solver_type = app_initializer->getComponentDatabase("Main")->getString("solver_type");
        if (solver_type == "STAGGERED")
        {
            navier_stokes_integrator = new INSStaggeredHierarchyIntegrator(
                "INSStaggeredHierarchyIntegrator", app_initializer->getComponentDatabase("INSStaggeredHierarchyIntegrator"));
        }
        else if (solver_type == "COLLOCATED")
        {
            navier_stokes_integrator = new INSCollocatedHierarchyIntegrator(
                "INSCollocatedHierarchyIntegrator", app_initializer->getComponentDatabase("INSCollocatedHierarchyIntegrator"));
        }
        else
        {
            TBOX_ERROR("Unsupported solver type: " << solver_type << "\n" <<
                       "Valid options are: COLLOCATED, STAGGERED");
        }
        Pointer<IBFEMethod> ib_method_ops = new IBFEMethod(
            "IBFEMethod", app_initializer->getComponentDatabase("IBFEMethod"), &mesh, app_initializer->getComponentDatabase("GriddingAlgorithm")->getInteger("max_levels"));
        Pointer<IBHierarchyIntegrator> time_integrator = new IBHierarchyIntegrator(
            "IBHierarchyIntegrator", app_initializer->getComponentDatabase("IBHierarchyIntegrator"), ib_method_ops, navier_stokes_integrator);
        Pointer<CartesianGridGeometry<NDIM> > grid_geometry = new CartesianGridGeometry<NDIM>(
            "CartesianGeometry", app_initializer->getComponentDatabase("CartesianGeometry"));
        Pointer<PatchHierarchy<NDIM> > patch_hierarchy = new PatchHierarchy<NDIM>(
            "PatchHierarchy", grid_geometry);
        Pointer<StandardTagAndInitialize<NDIM> > error_detector = new StandardTagAndInitialize<NDIM>(
            "StandardTagAndInitialize", time_integrator, app_initializer->getComponentDatabase("StandardTagAndInitialize"));
        Pointer<BergerRigoutsos<NDIM> > box_generator = new BergerRigoutsos<NDIM>();
        Pointer<LoadBalancer<NDIM> > load_balancer = new LoadBalancer<NDIM>(
            "LoadBalancer", app_initializer->getComponentDatabase("LoadBalancer"));
        Pointer<GriddingAlgorithm<NDIM> > gridding_algorithm = new GriddingAlgorithm<NDIM>(
            "GriddingAlgorithm", app_initializer->getComponentDatabase("GriddingAlgorithm"), error_detector, box_generator, load_balancer);

        // Configure the IBFE solver.
        ib_method_ops->registerInitialCoordinateMappingFunction(&coordinate_mapping_function);
        ib_method_ops->registerPK1StressTensorFunction(&PK1_stress_function);
        EquationSystems* equation_systems = ib_method_ops->getFEDataManager()->getEquationSystems();
        for (unsigned int k = 0; k < equation_systems->n_systems(); ++k)
        {
            System& system = equation_systems->get_system(k);
            system.get_dof_map().add_periodic_boundary(pbc);
        }

        // Create Eulerian initial condition specification objects.  These
        // objects also are used to specify exact solution values for error
        // analysis.
        Pointer<CartGridFunction> u_init = new muParserCartGridFunction(
            "u_init", app_initializer->getComponentDatabase("VelocityInitialConditions"), grid_geometry);
        navier_stokes_integrator->registerVelocityInitialConditions(u_init);

        Pointer<CartGridFunction> p_init = new muParserCartGridFunction(
            "p_init", app_initializer->getComponentDatabase("PressureInitialConditions"), grid_geometry);
        navier_stokes_integrator->registerPressureInitialConditions(p_init);

        // Create Eulerian boundary condition specification objects (when necessary).
        const IntVector<NDIM>& periodic_shift = grid_geometry->getPeriodicShift();
        TinyVector<RobinBcCoefStrategy<NDIM>*,NDIM> u_bc_coefs;
        if (periodic_shift.min() > 0)
        {
            for (unsigned int d = 0; d < NDIM; ++d)
            {
                u_bc_coefs[d] = NULL;
            }
        }
        else
        {
            for (unsigned int d = 0; d < NDIM; ++d)
            {
                ostringstream bc_coefs_name_stream;
                bc_coefs_name_stream << "u_bc_coefs_" << d;
                const string bc_coefs_name = bc_coefs_name_stream.str();

                ostringstream bc_coefs_db_name_stream;
                bc_coefs_db_name_stream << "VelocityBcCoefs_" << d;
                const string bc_coefs_db_name = bc_coefs_db_name_stream.str();

                u_bc_coefs[d] = new muParserRobinBcCoefs(
                    bc_coefs_name, app_initializer->getComponentDatabase(bc_coefs_db_name), grid_geometry);
            }
            navier_stokes_integrator->registerPhysicalBoundaryConditions(u_bc_coefs);
        }

        // Create Eulerian body force function specification objects.
        if (input_db->keyExists("ForcingFunction"))
        {
            Pointer<CartGridFunction> f_fcn = new muParserCartGridFunction(
                "f_fcn", app_initializer->getComponentDatabase("ForcingFunction"), grid_geometry);
            time_integrator->registerBodyForceFunction(f_fcn);
        }

        // Set up visualization plot file writers.
        Pointer<VisItDataWriter<NDIM> > visit_data_writer = app_initializer->getVisItDataWriter();
        if (uses_visit)
        {
            time_integrator->registerVisItDataWriter(visit_data_writer);
        }
        AutoPtr<ExodusII_IO> exodus_io(uses_exodus ? new ExodusII_IO(mesh) : NULL);

        // Initialize hierarchy configuration and data on all patches.
        ib_method_ops->initializeFEData();
        time_integrator->initializePatchHierarchy(patch_hierarchy, gridding_algorithm);

        // Deallocate initialization objects.
        app_initializer.setNull();

        // Print the input database contents to the log file.
        plog << "Input database:\n";
        input_db->printClassData(plog);

        // Setup data used to determine the accuracy of the computed solution.
        VariableDatabase<NDIM>* var_db = VariableDatabase<NDIM>::getDatabase();

        const Pointer<hier::Variable<NDIM> > u_var = navier_stokes_integrator->getVelocityVariable();
        const Pointer<VariableContext> u_ctx = navier_stokes_integrator->getCurrentContext();

        const int u_idx = var_db->mapVariableAndContextToIndex(u_var, u_ctx);
        const int u_cloned_idx = var_db->registerClonedPatchDataIndex(u_var, u_idx);

        const Pointer<hier::Variable<NDIM> > p_var = navier_stokes_integrator->getPressureVariable();
        const Pointer<VariableContext> p_ctx = navier_stokes_integrator->getCurrentContext();

        const int p_idx = var_db->mapVariableAndContextToIndex(p_var, p_ctx);
        const int p_cloned_idx = var_db->registerClonedPatchDataIndex(p_var, p_idx);
        visit_data_writer->registerPlotQuantity("P error", "SCALAR", p_cloned_idx);

        const int coarsest_ln = 0;
        const int finest_ln = patch_hierarchy->getFinestLevelNumber();
        for (int ln = coarsest_ln; ln <= finest_ln; ++ln)
        {
            patch_hierarchy->getPatchLevel(ln)->allocatePatchData(u_cloned_idx);
            patch_hierarchy->getPatchLevel(ln)->allocatePatchData(p_cloned_idx);
        }

        // Write out initial visualization data.
        int iteration_num = time_integrator->getIntegratorStep();
        double loop_time = time_integrator->getIntegratorTime();
        if (dump_viz_data)
        {
            pout << "\n\nWriting visualization files...\n\n";
            if (uses_visit)
            {
                time_integrator->setupPlotData();
                visit_data_writer->writePlotData(patch_hierarchy, iteration_num, loop_time);
            }
            if (uses_exodus)
            {
                exodus_io->write_timestep(exodus_filename, *equation_systems, iteration_num/viz_dump_interval+1, loop_time);
            }
        }

        // Open streams to save volume of structure.
        ofstream volume_stream;
        if (SAMRAI_MPI::getRank() == 0)
        {
            volume_stream.open("volume.curve", ios_base::out | ios_base::trunc);
        }

        // Main time step loop.
        double loop_time_end = time_integrator->getEndTime();
        double dt = 0.0;
        while (!MathUtilities<double>::equalEps(loop_time,loop_time_end) &&
               time_integrator->stepsRemaining())
        {
            iteration_num = time_integrator->getIntegratorStep();
            loop_time = time_integrator->getIntegratorTime();

            pout <<                                                    "\n";
            pout << "+++++++++++++++++++++++++++++++++++++++++++++++++++\n";
            pout << "At beginning of timestep # " <<  iteration_num << "\n";
            pout << "Simulation time is " << loop_time              << "\n";

            dt = time_integrator->getTimeStepSize();
            time_integrator->advanceHierarchy(dt);
            loop_time += dt;

            pout <<                                                    "\n";
            pout << "At end       of timestep # " <<  iteration_num << "\n";
            pout << "Simulation time is " << loop_time              << "\n";
            pout << "+++++++++++++++++++++++++++++++++++++++++++++++++++\n";
            pout <<                                                    "\n";

            // At specified intervals, write visualization and restart files,
            // print out timer data, and store hierarchy data for post
            // processing.
            iteration_num += 1;
            const bool last_step = !time_integrator->stepsRemaining();
            if (dump_viz_data && (iteration_num%viz_dump_interval == 0 || last_step))
            {
                pout << "\nWriting visualization files...\n\n";
                if (uses_visit)
                {
                    time_integrator->setupPlotData();
                    visit_data_writer->writePlotData(patch_hierarchy, iteration_num, loop_time);
                }
                if (uses_exodus)
                {
                    exodus_io->write_timestep(exodus_filename, *equation_systems, iteration_num/viz_dump_interval+1, loop_time);
                }
            }
            if (dump_restart_data && (iteration_num%restart_dump_interval == 0 || last_step))
            {
                pout << "\nWriting restart files...\n\n";
                RestartManager::getManager()->writeRestartFile(restart_dump_dirname, iteration_num);
            }
            if (dump_timer_data && (iteration_num%timer_dump_interval == 0 || last_step))
            {
                pout << "\nWriting timer data...\n\n";
                TimerManager::getManager()->print(plog);
            }
            if (dump_postproc_data && (iteration_num%postproc_data_dump_interval == 0 || last_step))
            {
                pout << "\nWriting state data...\n\n";
                output_data(patch_hierarchy,
                            navier_stokes_integrator, mesh, equation_systems,
                            iteration_num, loop_time, postproc_data_dump_dirname);
            }

            // Compute velocity and pressure error norms.
            const int coarsest_ln = 0;
            const int finest_ln = patch_hierarchy->getFinestLevelNumber();
            for (int ln = coarsest_ln; ln <= finest_ln; ++ln)
            {
                Pointer<PatchLevel<NDIM> > level = patch_hierarchy->getPatchLevel(ln);
                if (!level->checkAllocated(u_cloned_idx)) level->allocatePatchData(u_cloned_idx);
                if (!level->checkAllocated(p_cloned_idx)) level->allocatePatchData(p_cloned_idx);
            }

            pout << "\n"
                 << "+++++++++++++++++++++++++++++++++++++++++++++++++++\n"
                 << "Computing error norms.\n\n";

            u_init->setDataOnPatchHierarchy(u_cloned_idx, u_var, patch_hierarchy, loop_time);
            p_init->setDataOnPatchHierarchy(p_cloned_idx, p_var, patch_hierarchy, loop_time-0.5*dt);

            HierarchyMathOps hier_math_ops("HierarchyMathOps", patch_hierarchy);
            hier_math_ops.setPatchHierarchy(patch_hierarchy);
            hier_math_ops.resetLevels(coarsest_ln, finest_ln);
            const double volume  = hier_math_ops.getVolumeOfPhysicalDomain();
            const int wgt_cc_idx = hier_math_ops.getCellWeightPatchDescriptorIndex();
            const int wgt_sc_idx = hier_math_ops.getSideWeightPatchDescriptorIndex();

            Pointer<CellVariable<NDIM,double> > u_cc_var = u_var;
            if (!u_cc_var.isNull())
            {
                HierarchyCellDataOpsReal<NDIM,double> hier_cc_data_ops(patch_hierarchy, coarsest_ln, finest_ln);
                hier_cc_data_ops.subtract(u_cloned_idx, u_idx, u_cloned_idx);
                pout << "Error in u at time " << loop_time << ":\n"
                     << "  L1-norm:  " << hier_cc_data_ops. L1Norm(u_cloned_idx,wgt_cc_idx)  << "\n"
                     << "  L2-norm:  " << hier_cc_data_ops. L2Norm(u_cloned_idx,wgt_cc_idx)  << "\n"
                     << "  max-norm: " << hier_cc_data_ops.maxNorm(u_cloned_idx,wgt_cc_idx) << "\n";
            }

            Pointer<SideVariable<NDIM,double> > u_sc_var = u_var;
            if (!u_sc_var.isNull())
            {
                HierarchySideDataOpsReal<NDIM,double> hier_sc_data_ops(patch_hierarchy, coarsest_ln, finest_ln);
                hier_sc_data_ops.subtract(u_cloned_idx, u_idx, u_cloned_idx);
                pout << "Error in u at time " << loop_time << ":\n"
                     << "  L1-norm:  " << hier_sc_data_ops. L1Norm(u_cloned_idx,wgt_sc_idx)  << "\n"
                     << "  L2-norm:  " << hier_sc_data_ops. L2Norm(u_cloned_idx,wgt_sc_idx)  << "\n"
                     << "  max-norm: " << hier_sc_data_ops.maxNorm(u_cloned_idx,wgt_sc_idx) << "\n";
            }

            HierarchyCellDataOpsReal<NDIM,double> hier_cc_data_ops(patch_hierarchy, coarsest_ln, finest_ln);
            const double p_mean = (1.0/volume)*hier_cc_data_ops.integral(p_idx, wgt_cc_idx);
            hier_cc_data_ops.addScalar(p_idx, p_idx, -p_mean);
            const double p_cloned_mean = (1.0/volume)*hier_cc_data_ops.integral(p_cloned_idx, wgt_cc_idx);
            hier_cc_data_ops.addScalar(p_cloned_idx, p_cloned_idx, -p_cloned_mean);
            hier_cc_data_ops.subtract(p_cloned_idx, p_idx, p_cloned_idx);
            pout << "Error in p at time " << loop_time-0.5*dt << ":\n"
                 << "  L1-norm:  " << hier_cc_data_ops. L1Norm(p_cloned_idx,wgt_cc_idx)  << "\n"
                 << "  L2-norm:  " << hier_cc_data_ops. L2Norm(p_cloned_idx,wgt_cc_idx)  << "\n"
                 << "  max-norm: " << hier_cc_data_ops.maxNorm(p_cloned_idx,wgt_cc_idx) << "\n"
                 << "+++++++++++++++++++++++++++++++++++++++++++++++++++\n";

            // Compute the volume of the structure.
            double J_integral = 0.0;
            System& X_system = equation_systems->get_system<System>(IBFEMethod::COORDS_SYSTEM_NAME);
            NumericVector<double>* X_vec = X_system.solution.get();
            NumericVector<double>* X_ghost_vec = X_system.current_local_solution.get();
            X_vec->localize(*X_ghost_vec);
            DofMap& X_dof_map = X_system.get_dof_map();
            blitz::Array<std::vector<unsigned int>,1> X_dof_indices(NDIM);
            AutoPtr<FEBase> fe(FEBase::build(NDIM, X_dof_map.variable_type(0)));
            AutoPtr<QBase> qrule = QBase::build(QGAUSS, NDIM, FIFTH);
            fe->attach_quadrature_rule(qrule.get());
            const std::vector<double>& JxW = fe->get_JxW();
            const std::vector<std::vector<VectorValue<double> > >& dphi = fe->get_dphi();
            TensorValue<double> FF;
            blitz::Array<double,2> X_node;
            const MeshBase::const_element_iterator el_begin = mesh.active_local_elements_begin();
            const MeshBase::const_element_iterator el_end   = mesh.active_local_elements_end();
            for (MeshBase::const_element_iterator el_it = el_begin; el_it != el_end; ++el_it)
            {
                Elem* const elem = *el_it;
                fe->reinit(elem);
                for (unsigned int d = 0; d < NDIM; ++d)
                {
                    X_dof_map.dof_indices(elem, X_dof_indices(d), d);
                }
                const int n_qp = qrule->n_points();
                get_values_for_interpolation(X_node, *X_ghost_vec, X_dof_indices);
                for (int qp = 0; qp < n_qp; ++qp)
                {
                    jacobian(FF,qp,X_node,dphi);
                    J_integral += abs(FF.det())*JxW[qp];
                }
            }
            J_integral = SAMRAI_MPI::sumReduction(J_integral);
            if (SAMRAI_MPI::getRank() == 0)
            {
                volume_stream.precision(12);
                volume_stream.setf(ios::fixed,ios::floatfield);
                volume_stream << loop_time << " " << J_integral << endl;
            }
        }

        // Close the logging streams.
        if (SAMRAI_MPI::getRank() == 0)
        {
            volume_stream.close();
        }

        // Cleanup Eulerian boundary condition specification objects (when
        // necessary).
        for (unsigned int d = 0; d < NDIM; ++d) delete u_bc_coefs[d];

    }// cleanup dynamically allocated objects prior to shutdown

    SAMRAIManager::shutdown();
    return 0;
}// main