TestMatrixVentilationProblem.hpp

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#ifndef _TESTMATRIXVENTILATIONPROBLEM_HPP_
#define _TESTMATRIXVENTILATIONPROBLEM_HPP_

#include <cxxtest/TestSuite.h>
#include <queue>

#include "TetrahedralMesh.hpp"
#include "TrianglesMeshReader.hpp"
#include "PetscSetupAndFinalize.hpp"
#include "MatrixVentilationProblem.hpp"
#include "Warnings.hpp"

void LinearTimeBCs(AbstractVentilationProblem* pProblem, TimeStepper& rTimeStepper, const Node<3>& rNode)
{
    double time = rTimeStepper.GetTime();
    pProblem->SetPressureAtBoundaryNode(rNode, 15*time);
}

void SineBCs(AbstractVentilationProblem* pProblem, TimeStepper& rTimeStepper, const Node<3>& rNode)
{
    double time = rTimeStepper.GetTime();
    pProblem->SetPressureAtBoundaryNode(rNode, 15.0*sin(time*5.0/(2.0*M_PI)));
}


void GravitationalBCs(AbstractVentilationProblem* pProblem, TimeStepper& rTimeStepper, const Node<3>& rNode)
{
    double x_max =  6.0;
    double x_min = -6.0;
    double delta_p = 0.5;

    double x = rNode.rGetLocation()[0];

    double pressure = delta_p * (x - x_min)/(x_max - x_min);

    pProblem->SetPressureAtBoundaryNode(rNode, pressure);
}

class TestMatrixVentilationProblem : public CxxTest::TestSuite
{
private:

public:
    void TestOnBranch()
    {
        MatrixVentilationProblem problem("mesh/test/data/y_branch_3d_mesh", 0u);
        problem.SetMeshInMilliMetres();
        TS_ASSERT_DELTA(problem.GetViscosity(), 1.92e-5, 1e-12);
        problem.SetViscosity(1.0);
        problem.SetOutflowPressure(100);
        problem.SetConstantInflowPressures(0.0);
        problem.Solve();

        std::vector<double> flux, pressure;
        problem.GetSolutionAsFluxesAndPressures(flux, pressure);
        TS_ASSERT_DELTA(flux[0], 0.092813610, 1e-8);
        TS_ASSERT_DELTA(flux[1], 0.046406805, 1e-8);
        TS_ASSERT_DELTA(flux[2], 0.046406805, 1e-8);
        TS_ASSERT_DELTA(pressure[0], 100.0, 1e-6); //BC
        TS_ASSERT_DELTA(pressure[1], 84.5107, 1e-4);
        TS_ASSERT_DELTA(pressure[2], 0.0, 1e-6); //BC
        TS_ASSERT_DELTA(pressure[3], 0.0, 1e-6); //BC
#ifdef CHASTE_VTK
        problem.WriteVtk("TestVentilation", "small_conical");
#endif
    }
    void TestOnBranchCylindrical()
    {
        MatrixVentilationProblem problem("mesh/test/data/y_branch_3d_mesh");
        problem.SetMeshInMilliMetres();
        //These values are equivalent to Swan et al. 2012. 10.1016/j.jtbi.2012.01.042 (page 224)
        TS_ASSERT_DELTA(problem.GetViscosity(), 1.92e-5, 1e-12);
        problem.SetViscosity(1.0);
        TS_ASSERT_DELTA(problem.GetDensity(), 1.15, 1e-10);
        problem.SetDensity(1.0);
        problem.SetRadiusOnEdge();
        problem.SetOutflowPressure(100);
        problem.SetConstantInflowPressures(0.0);
        problem.Solve();

        std::vector<double> flux, pressure;
        problem.GetSolutionAsFluxesAndPressures(flux, pressure);
        TS_ASSERT_DELTA(flux[0], 0.019932007, 1e-8);
        TS_ASSERT_DELTA(flux[1], 0.009966003, 1e-8);
        TS_ASSERT_DELTA(flux[2], 0.009966003, 1e-8);
        TS_ASSERT_DELTA(pressure[0], 100.0, 1e-6); //BC
        TS_ASSERT_DELTA(pressure[1], 91.8789, 1e-4);
        TS_ASSERT_DELTA(pressure[2], 0.0, 1e-6); //BC
        TS_ASSERT_DELTA(pressure[3], 0.0, 1e-6); //BC

#ifdef CHASTE_VTK
        problem.WriteVtk("TestVentilation", "small_cylindrical");
#endif
    }

    void TestThreeBifurcationsWithRadiusOnEdgeFile()
    {
        MatrixVentilationProblem problem("lung/test/data/three_bifurcations", 0u);
        problem.SetMeshInMilliMetres();
        problem.SetRadiusOnEdge();
        problem.SetOutflowPressure(0.0);
        problem.SetConstantInflowPressures(0.00148608);
        problem.Solve();
#ifdef CHASTE_VTK
        problem.WriteVtk("TestVentilation", "three_bifurcations");
#endif
        std::vector<double> flux, pressure;
        problem.GetSolutionAsFluxesAndPressures(flux, pressure);
        TS_ASSERT_DELTA(pressure[0], 0.0, 1e-8); //BC
        TS_ASSERT_DELTA(pressure[1], 0.0006,   1e-4);
        TS_ASSERT_DELTA(pressure[2], 0.001274, 1e-4);
        TS_ASSERT_DELTA(pressure[3], 0.001274, 1e-4);
        TS_ASSERT_DELTA(pressure[4], 0.00148608, 1e-8); //BC
        TS_ASSERT_DELTA(pressure[5], 0.00148608, 1e-8); //BC
        TS_ASSERT_DELTA(pressure[6], 0.00148608, 1e-8); //BC
        TS_ASSERT_DELTA(pressure[7], 0.00148608, 1e-8); //BC

        // Total flux
        // TS_ASSERT_DELTA(flux[0], -2.8143e-5, 1e-8); // Mesh in meters
        TS_ASSERT_DELTA(flux[0], -2.8143e-14, 1e-15); //Mesh in millimeters
        TS_ASSERT_DELTA(problem.GetFluxAtOutflow(), -2.8143e-14, 1e-15);
    }

    void TestThreeBifurcations()
    {
        MatrixVentilationProblem problem("lung/test/data/three_bifurcations", 0u);
        problem.SetMeshInMilliMetres();
        problem.SetOutflowPressure(0.0);
        problem.SetConstantInflowPressures(15.0);
        problem.Solve();

        std::vector<double> flux, pressure;
        problem.GetSolutionAsFluxesAndPressures(flux, pressure);
        TS_ASSERT_DELTA(pressure[0], 0.0, 1e-8); //BC
        TS_ASSERT_DELTA(pressure[1], 6.66666,   1e-4);
        TS_ASSERT_DELTA(pressure[2], 12.22223, 1e-4);
        TS_ASSERT_DELTA(pressure[3], 12.22222, 1e-4);
        TS_ASSERT_DELTA(pressure[4], 15.0, 1e-8); //BC
        TS_ASSERT_DELTA(pressure[5], 15.0, 1e-8); //BC
        TS_ASSERT_DELTA(pressure[6], 15.0, 1e-8); //BC
        TS_ASSERT_DELTA(pressure[7], 15.0, 1e-8); //BC
        TS_ASSERT_DELTA(flux[0], -2.8407e-10 , 1e-13); // (Outflow flux)
        TS_ASSERT_DELTA(flux[3], -7.102e-11, 1e-13); // (Inflow flux)
        TS_ASSERT_DELTA(flux[4], -7.102e-11, 1e-13); // (Inflow flux)
        TS_ASSERT_DELTA(flux[5], -7.102e-11, 1e-13); // (Inflow flux)
        TS_ASSERT_DELTA(flux[6], -7.102e-11, 1e-13); // (Inflow flux)
    }


    void TestThreeBifurcationsExtraLinksDirect()
    {
        MatrixVentilationProblem problem("lung/test/data/three_bifurcations_extra_links", 0u);
        problem.SetMeshInMilliMetres();
        problem.SetOutflowPressure(0.0 + 1.0);
        problem.SetConstantInflowFluxes(-7.102e-11);
        problem.Solve();

        std::vector<double> flux, pressure;
        problem.GetSolutionAsFluxesAndPressures(flux, pressure);
        TS_ASSERT_DELTA(pressure[0], 0.0 + 1.0, 1e-8); // BC
        TS_ASSERT_DELTA(flux[10], -7.102e-11, 1e-20); // BC
        TS_ASSERT_DELTA(flux[11], -7.102e-11, 1e-20); // BC
        TS_ASSERT_DELTA(flux[12], -7.102e-11, 1e-20); // BC
        TS_ASSERT_DELTA(flux[13], -7.102e-11, 1e-20); // BC
        TS_ASSERT_DELTA(pressure[1], 6.66666 + 1.0,   1e-3);
        TS_ASSERT_DELTA(pressure[2], 12.22223 + 1.0, 1e-3);
        TS_ASSERT_DELTA(pressure[3], 12.22223 + 1.0, 1e-3);
        TS_ASSERT_DELTA(pressure[4], 15 + 1.0, 1e-3);
        TS_ASSERT_DELTA(pressure[5], 15 + 1.0, 1e-3);
        TS_ASSERT_DELTA(pressure[6], 15 + 1.0, 1e-3);
        TS_ASSERT_DELTA(pressure[7], 15 + 1.0, 1e-3);
        TS_ASSERT_DELTA(flux[0], 2.8407e-10, 1e-4); // (Outflow flux)
        //This is the extra node at the Trachea
        TS_ASSERT_DELTA(pressure[8], 3.33335 + 1.0, 1e-4); //Between root and first bifurcation

    }

    void TestThreeBifurcationsExtraLinks()
    {
        MatrixVentilationProblem problem("lung/test/data/three_bifurcations_extra_links", 0u);
        problem.SetMeshInMilliMetres();
        problem.SetOutflowPressure(0.0 + 1.0);
        problem.SetConstantInflowPressures(15.0 + 1.0);
        problem.Solve();

        std::vector<double> flux, pressure;
        problem.GetSolutionAsFluxesAndPressures(flux, pressure);
        TS_ASSERT_DELTA(pressure[0], 0.0 + 1.0, 1e-8); //BC
        TS_ASSERT_DELTA(pressure[1], 6.66666 + 1.0,   1e-4);
        TS_ASSERT_DELTA(pressure[2], 12.22223 + 1.0, 1e-4);
        TS_ASSERT_DELTA(pressure[3], 12.22223 + 1.0, 1e-4);
        TS_ASSERT_DELTA(pressure[4], 15 + 1.0, 1e-7); //BC
        TS_ASSERT_DELTA(pressure[5], 15 + 1.0, 1e-7); //BC
        TS_ASSERT_DELTA(pressure[6], 15 + 1.0, 1e-7); //BC
        TS_ASSERT_DELTA(pressure[7], 15 + 1.0, 1e-7); //BC
        TS_ASSERT_DELTA(flux[0], 2.8407e-10, 1e-4); // (Outflow flux)
        TS_ASSERT_DELTA(flux[10], -7.102e-11, 1e-13); // (Inflow flux)
        TS_ASSERT_DELTA(flux[11], -7.102e-11, 1e-13); // (Inflow flux)
        TS_ASSERT_DELTA(flux[12], -7.102e-11, 1e-13); // (Inflow flux)
        TS_ASSERT_DELTA(flux[13], -7.102e-11, 1e-13); // (Inflow flux)
        //This is the extra node at the Trachea
        TS_ASSERT_DELTA(pressure[8], 3.33335 + 1.0, 1e-4); //Between root and first bifurcation

#ifdef CHASTE_VTK
        problem.WriteVtk("TestVentilation", "three_bifurcations_extra_links");
#endif
    }

    void TestThreeBifurcationsFluxBoundaries()
    {
        MatrixVentilationProblem problem("lung/test/data/three_bifurcations", 0u);
        problem.SetMeshInMilliMetres();
        problem.SetOutflowPressure(0.0);
        problem.SetConstantInflowFluxes(-7.10176e-11);
        problem.Solve();

        std::vector<double> flux, pressure;
        problem.GetSolutionAsFluxesAndPressures(flux, pressure);
        TS_ASSERT_DELTA(pressure[0], 0.0, 1e-8); //BC
        TS_ASSERT_DELTA(pressure[1], 6.6666,   2e-3);
        TS_ASSERT_DELTA(pressure[2], 12.2222, 2e-4);
        TS_ASSERT_DELTA(pressure[3], 12.2222, 2e-4);
        TS_ASSERT_DELTA(pressure[4], 15, 2e-4);
        TS_ASSERT_DELTA(pressure[5], 15, 2e-4);
        TS_ASSERT_DELTA(pressure[6], 15, 2e-4);
        TS_ASSERT_DELTA(pressure[7], 15, 2e-4);
        TS_ASSERT_DELTA(flux[0], -2.840704e-10, 1e-13); // (Outflow flux)
        TS_ASSERT_DELTA(flux[3],  -7.10176e-11, 1e-16); // BC (Inflow flux)
        TS_ASSERT_DELTA(flux[4],  -7.10176e-11, 1e-16); // BC (Inflow flux)
        TS_ASSERT_DELTA(flux[5],  -7.10176e-11, 1e-16); // BC (Inflow flux)
        TS_ASSERT_DELTA(flux[6],  -7.10176e-11, 1e-16); // BC (Inflow flux)
    }

    void TestThreeBifurcationsWithDynamicResistance()
    {
        /*
         * HOW_TO_TAG Continuum mechanics/Ventilation
         * Solve a simple ventilation problem with no time variation.
         *
         * Pressure is prescribed at the root (trachea) and at the leaves (acini).
         * Dynamic (Pedley) resistance is used at higher Reynolds numbers.
         * There is no coupled acinus compliance model in this version.
         */
        EXIT_IF_PARALLEL; ///\todo #2300 There is a problem with the Windows parallel implementation
        MatrixVentilationProblem problem("lung/test/data/three_bifurcations", 0u);
        problem.SetMeshInMilliMetres();
        problem.SetOutflowPressure(0.0);
        problem.SetConstantInflowPressures(150000); //Needed to increase the resistance in these artificial airways
        problem.SetDynamicResistance();
        problem.Solve();
        std::vector<double> flux, pressure;
        problem.GetSolutionAsFluxesAndPressures(flux, pressure);
        TS_ASSERT_DELTA(pressure[0], 0.0, 1e-8); //BC
        TS_ASSERT_DELTA(pressure[1], 91108.7409,   1e-1);
        TS_ASSERT_DELTA(pressure[2], 132694.0014, 1e-2);
        TS_ASSERT_DELTA(pressure[3], 132694.0014, 1e-2);
        TS_ASSERT_DELTA(pressure[4], 1.5e5, 1e-8); //BC
        TS_ASSERT_DELTA(pressure[5], 1.5e5, 1e-8); //BC
        TS_ASSERT_DELTA(pressure[6], 1.5e5, 1e-8); //BC
        TS_ASSERT_DELTA(pressure[7], 1.5e5, 1e-8); //BC
        TS_ASSERT_DELTA(flux[6], -4.424511e-7, 1e-11);
#ifdef CHASTE_VTK
        problem.WriteVtk("TestVentilation", "three_bifurcations_pedley");
#endif
    }
   void TestThreeBifurcationsExtraLinksWithDynamicResistance()
    {
        /*
         * As previous but with every segment divided into two segments
         */
        MatrixVentilationProblem problem("lung/test/data/three_bifurcations_extra_links", 0u);
        problem.SetMeshInMilliMetres();
        problem.SetOutflowPressure(0.0);
        problem.SetConstantInflowPressures(150000); //Needed to increase the resistance in these artificial airways
        problem.SetDynamicResistance();
        problem.Solve();
        std::vector<double> flux, pressure;
        problem.GetSolutionAsFluxesAndPressures(flux, pressure);
        TS_ASSERT_DELTA(pressure[0], 0.0, 1e-8); //BC
        TS_ASSERT_DELTA(pressure[1], 91108.7409,   1e-1);
        TS_ASSERT_DELTA(pressure[2], 132694.0014, 1e-2);
        TS_ASSERT_DELTA(pressure[3], 132694.0014, 1e-2);
        TS_ASSERT_DELTA(pressure[4], 1.5e5, 1e-8); //BC
        TS_ASSERT_DELTA(pressure[5], 1.5e5, 1e-8); //BC
        TS_ASSERT_DELTA(pressure[6], 1.5e5, 1e-8); //BC
        TS_ASSERT_DELTA(pressure[7], 1.5e5, 1e-8); //BC
        TS_ASSERT_DELTA(flux[6], -4.424511e-7, 1e-11);
#ifdef CHASTE_VTK
        problem.WriteVtk("TestVentilation", "three_bifurcations_pedley");
#endif
    }

    void TestThreeBifurcationsWithPerElementDynamicResistance()
    {
        MatrixVentilationProblem problem("lung/test/data/three_bifurcations", 0u);
        problem.SetMeshInMilliMetres();
        problem.SetOutflowPressure(0.0);
        problem.SetConstantInflowPressures(150000); //Needed to increase the resistance in these artificial airways
        // Here's the set-up function with applies van Ertbruggen 2005
        problem.SetPerGenerationDynamicResistance();

        problem.Solve();
        std::vector<double> flux, pressure;
        problem.GetSolutionAsFluxesAndPressures(flux, pressure);
        TS_ASSERT_DELTA(pressure[0], 0.0, 1e-8); //BC
        TS_ASSERT_DELTA(pressure[1], 75114.3782,   1e-1);
        TS_ASSERT_DELTA(pressure[2], 125695.1375, 1e-2);
        TS_ASSERT_DELTA(pressure[3], 125695.1375, 1e-2);
        TS_ASSERT_DELTA(pressure[4], 1.5e5, 1e-8); //BC
        TS_ASSERT_DELTA(pressure[5], 1.5e5, 1e-8); //BC
        TS_ASSERT_DELTA(pressure[6], 1.5e5, 1e-8); //BC
        TS_ASSERT_DELTA(pressure[7], 1.5e5, 1e-8); //BC
        TS_ASSERT_DELTA(flux[6], -6.2138e-7, 1e-11);  // -4.424511e-7 with Pedley. -7.1017e-7 with static
#ifdef CHASTE_VTK
        problem.WriteVtk("TestVentilation", "three_bifurcations_pedley");
#endif
    }

    void TestTimeVaryingThreeBifurcations()
    {
        MatrixVentilationProblem problem("lung/test/data/three_bifurcations", 0u);
        problem.SetRadiusOnEdge();
        problem.SetOutflowPressure(0.0);
        TimeStepper stepper(0.0, 1.0, 0.1);
        problem.SolveOverTime(stepper, &LinearTimeBCs, "TestVentilation", "three_bifurcations_time");
    }

    void TestSineThreeBifurcations()
    {
        MatrixVentilationProblem problem("lung/test/data/three_bifurcations", 0u);
        problem.SetRadiusOnEdge();
        problem.SetOutflowPressure(0.0);
        TimeStepper stepper(0.0, 25.0, 0.1);
        problem.SolveOverTime(stepper, &SineBCs, "TestVentilation", "three_bifurcations_sine");
        std::vector<double> flux, pressure;
        problem.GetSolutionAsFluxesAndPressures(flux, pressure); //check pressure at end time @ 25
        TS_ASSERT_DELTA(pressure[0], 0.0,     1e-8); //BC
        TS_ASSERT_DELTA(pressure[1], 5.7655,  1e-4);
        TS_ASSERT_DELTA(pressure[2], 10.5701, 1e-4);
        TS_ASSERT_DELTA(pressure[3], 10.5701, 1e-4);
        TS_ASSERT_DELTA(pressure[4], 12.972452, 1e-5); //BC
        TS_ASSERT_DELTA(pressure[5], 12.972452, 1e-5); //BC
    }

    void TestGravitationalVaryingThreeBifurcations()
    {
        MatrixVentilationProblem problem("lung/test/data/three_bifurcations", 0u);
        problem.SetRadiusOnEdge();
        problem.SetOutflowPressure(0.0);
        TimeStepper stepper(0.0, 1.0, 0.1);
        problem.SolveOverTime(stepper, &GravitationalBCs, "TestVentilation", "three_bifurcations_gravity");
    }

    /*
     * HOW_TO_TAG Continuum mechanics/Ventilation
     * Solve a simple ventilation problem defined in a file.
     *
     * The file prescribes pressure at the root (trachea) and at the leaves (acini).
     * The file sets density and viscosity
     *
     * Output file names are given to the function (but might instead be given in the file)
     *
     */
    void TestSolveProblemDefinedInFile()
    {
        MatrixVentilationProblem problem("lung/test/data/three_bifurcations");
        problem.SolveProblemFromFile("lung/test/data/ChasteVentilationInput.txt", "VentilationOutput", "3_bifurcations");
    }

    void TestTopOfAirwaysPatientData()
    {
        MatrixVentilationProblem problem("lung/test/data/top_of_tree", 0u);
        PetscTools::SetOption("-ksp_monitor", "");
        problem.SetOutflowPressure(0.0);
        problem.SetConstantInflowPressures(50.0);
        //problem.SetConstantInflowFluxes(100.0);
        TetrahedralMesh<1, 3>& r_mesh=problem.rGetMesh();
        TS_ASSERT_EQUALS(r_mesh.GetNumNodes(), 31u);
        TS_ASSERT_EQUALS(r_mesh.GetNumElements(), 30u);
        problem.Solve();
        problem.Solve();

        std::vector<double> flux, pressure;
        problem.GetSolutionAsFluxesAndPressures(flux, pressure);
        TS_ASSERT_DELTA(pressure[27], 43.7415, 1e-4);
        TS_ASSERT_DELTA(pressure[28], 50.0,    1e-4); //BC
    }


    void TestTopOfAirwaysPatientDataOutflowFlux()
    {
        MatrixVentilationProblem problem("lung/test/data/top_of_tree", 0u);
        PetscTools::SetOption("-ksp_monitor", "");
        problem.SetOutflowFlux(0.001);
        problem.SetConstantInflowPressures(50.0);
        //problem.SetConstantInflowFluxes(100.0);
        TetrahedralMesh<1, 3>& r_mesh=problem.rGetMesh();
        TS_ASSERT_EQUALS(r_mesh.GetNumNodes(), 31u);
        TS_ASSERT_EQUALS(r_mesh.GetNumElements(), 30u);
        problem.Solve();

        std::vector<double> flux, pressure;
        problem.GetSolutionAsFluxesAndPressures(flux, pressure);
        TS_ASSERT_DELTA(flux[0], 0.001, 1e-5);
    }

    void OnlyWorksWithUMFPACKTestPatientData()
    {
        MatrixVentilationProblem problem("notforrelease_lung/test/data/Novartis002", 0u);
        PetscTools::SetOption("-ksp_monitor", "");

        problem.SetOutflowPressure(0.);
        problem.SetConstantInflowPressures(50.0);
//        problem.SetConstantInflowFluxes(100.0);
        //TetrahedralMesh<1, 3>& r_mesh=problem.rGetMesh();
       // TS_ASSERT_EQUALS(r_mesh.GetNumNodes(), 31u);
     //   TS_ASSERT_EQUALS(r_mesh.GetNumElements(), 30u);
        //problem.SetRadiusOnEdge();
        problem.SetMeshInMilliMetres();
        //problem.SetDynamicResistance();
        problem.Solve();

//        std::vector<double> flux, pressure;
//        problem.GetSolutionAsFluxesAndPressures(flux, pressure); //check pressure at time @ 25
//
//        VtkMeshWriter<1, 3> vtk_writer("TestMatrixVentilation", "flow_solution", false);
//        vtk_writer.AddCellData("Flux", flux);
//        vtk_writer.AddPointData("Pressure", pressure);
//
//        std::vector<double> radii(problem.rGetMesh().GetNumElements());
//        for (TetrahedralMesh<1,3>::ElementIterator iter = problem.rGetMesh().GetElementIteratorBegin();
//             iter != problem.rGetMesh().GetElementIteratorEnd();
//             ++iter)
//        {
//            radii[(*iter).GetIndex()] = (*iter).GetAttribute();
//        }
//
//        vtk_writer.AddCellData("Radii", radii);
//        vtk_writer.WriteFilesUsingMesh(problem.rGetMesh());
    }
    void TestExceptions()
    {
        TS_ASSERT_THROWS_THIS(MatrixVentilationProblem bad_problem("mesh/test/data/y_branch_3d_mesh", 1u),
                "Outlet node is not a boundary node");

        MatrixVentilationProblem problem("lung/test/data/three_bifurcations");
        TS_ASSERT_THROWS_THIS(problem.SolveProblemFromFile("DoesNotExist.txt", "out", "out"), "Could not open file DoesNotExist.txt");

        TS_ASSERT_THROWS_THIS(problem.SetPressureAtBoundaryNode(3u, 0.0), "Boundary conditions cannot be set at internal nodes");
        TS_ASSERT_THROWS_THIS(problem.SetFluxAtBoundaryNode(3u, 0.0), "Boundary conditions cannot be set at internal nodes");

    }
};

#endif /*_TESTMATRIXVENTILATIONPROBLEM_HPP_*/