FlowSolver.cpp

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#include <algorithm>
#include "Exception.hpp"
#include "ReplicatableVector.hpp"
#include "PetscTools.hpp"
#include "VesselSegment.hpp"
#include "FlowSolver.hpp"
#include "UnitCollection.hpp"
#include "VesselNetworkGraphCalculator.hpp"

template<unsigned DIM>
FlowSolver<DIM>::FlowSolver()
    :   mNodes(),
        mVessels(),
        mpVesselNetwork(),
        mNodeVesselConnectivity(),
        mNodeNodeConnectivity(),
        mBoundaryConditionNodeIndices(),
        mUnconnectedNodeIndices(),
        mpLinearSystem(),
        mUseDirectSolver(true),
        mIsSetUp(false)
{

}

template<unsigned DIM>
FlowSolver<DIM>::~FlowSolver()
{

}

template <unsigned DIM>
boost::shared_ptr<FlowSolver<DIM> > FlowSolver<DIM>::Create()
{
    MAKE_PTR(FlowSolver<DIM>, pSelf);
    return pSelf;
}

template<unsigned DIM>
void FlowSolver<DIM>::SetUp()
{
    if(!mpVesselNetwork)
    {
        EXCEPTION("A vessel network is required before calling SetUp");
    }
    mVessels = mpVesselNetwork->GetVessels();
    mNodes = mpVesselNetwork->GetVesselEndNodes();

    unsigned num_nodes = mNodes.size();
    unsigned max_branches = mpVesselNetwork->GetMaxBranchesOnNode();

    // Set up the system
    mpLinearSystem = boost::shared_ptr<LinearSystem>(new LinearSystem(num_nodes, max_branches + 1));

    // Note: If the network is small the preconditioner is turned off in LinearSystem,
    // so an iterative solver is used instead.
    if (num_nodes >= 6 && mUseDirectSolver)
    {
        mpLinearSystem->SetPcType("lu");
        mpLinearSystem->SetKspType("preonly");
    }

    // Get the boundary condition nodes
    std::vector<boost::shared_ptr<VesselNode<DIM> > > boundary_condition_nodes;
    for (unsigned node_index = 0; node_index < num_nodes; node_index++)
    {
        if (mNodes[node_index]->GetFlowProperties()->IsInputNode()
                || mNodes[node_index]->GetFlowProperties()->IsOutputNode())
        {
            boundary_condition_nodes.push_back(mNodes[node_index]);
            mBoundaryConditionNodeIndices.push_back(node_index);
        }
    }

    // Get the nodes that correspond to segments that are not connected to the rest of the network
    boost::shared_ptr<VesselNetworkGraphCalculator<DIM> > p_graph_calculator = VesselNetworkGraphCalculator<DIM>::Create();
    p_graph_calculator->SetVesselNetwork(mpVesselNetwork);
    mNodeVesselConnectivity = p_graph_calculator->GetNodeVesselConnectivity();
    mNodeNodeConnectivity = p_graph_calculator->GetNodeNodeConnectivity();

    std::vector<bool> connected = p_graph_calculator->IsConnected(boundary_condition_nodes, mNodes);
    mUnconnectedNodeIndices.clear();
    for (unsigned node_index = 0; node_index < num_nodes; node_index++)
    {
        if (!connected[node_index])
        {
            mUnconnectedNodeIndices.push_back(node_index);
        }
    }

    std::cout << "num_connected" << mUnconnectedNodeIndices.size() << std::endl;
    mIsSetUp = true;
    Update(false);
}

template<unsigned DIM>
void FlowSolver<DIM>::SetUseDirectSolver(bool useDirectSolver)
{
    mUseDirectSolver = useDirectSolver;
}

template<unsigned DIM>
void FlowSolver<DIM>::SetVesselNetwork(boost::shared_ptr<VesselNetwork<DIM> > pVesselNetwork)
{
    mpVesselNetwork = pVesselNetwork;
}

template<unsigned DIM>
void FlowSolver<DIM>::Update(bool runSetup)
{
    if(!mIsSetUp or runSetup)
    {
        SetUp();
    }

    mpLinearSystem->SwitchWriteModeLhsMatrix();
    mpLinearSystem->ZeroLhsMatrix();
    mpLinearSystem->ZeroRhsVector();

    // Get the impedances, scale them by the maximum impedance to remove small values from the system matrix
    std::vector<units::quantity<unit::flow_impedance> > scaled_impedances;
    units::quantity<unit::flow_impedance> max_impedance = 0.0 * unit::pascal_second_per_metre_cubed;
    units::quantity<unit::flow_impedance> min_impedance = DBL_MAX * unit::pascal_second_per_metre_cubed;
    for (unsigned vessel_index = 0; vessel_index < mVessels.size(); vessel_index++)
    {
        units::quantity<unit::flow_impedance> impedance = mVessels[vessel_index]->GetFlowProperties()->GetImpedance();
        if (impedance <= 0.0 * unit::pascal_second_per_metre_cubed)
        {
            EXCEPTION("Impedance should be a positive number.");
        }
        if(impedance > max_impedance)
        {
            max_impedance = impedance;
        }
        if(impedance < min_impedance)
        {
            min_impedance = impedance;
        }
        scaled_impedances.push_back(impedance);
    }
    units::quantity<unit::flow_impedance> multiplier = (max_impedance + min_impedance) / 2.0; //scale impedances to avoid floating point problems in PETSC solvers.

    // Set up the system matrix
    for (unsigned node_index = 0; node_index < mNodes.size(); node_index++)
    {
        bool is_bc_node = (std::find(mBoundaryConditionNodeIndices.begin(), mBoundaryConditionNodeIndices.end(),
                                     node_index) != mBoundaryConditionNodeIndices.end());
        bool is_unconnected_node = (std::find(mUnconnectedNodeIndices.begin(), mUnconnectedNodeIndices.end(),
                                              node_index) != mUnconnectedNodeIndices.end());

        if (is_bc_node or is_unconnected_node)
        {
            mpLinearSystem->AddToMatrixElement(node_index, node_index, 1.0);
            if(mNodes[node_index]->GetFlowProperties()->UseVelocityBoundaryCondition())
            {
                // Velocity BC: Assumes only single vessel at inlets
                mpLinearSystem->AddToMatrixElement(node_index, mNodeNodeConnectivity[node_index][0], -1.0);
            }

        }
        else
        {
            for (unsigned vessel_index = 0; vessel_index < mNodeVesselConnectivity[node_index].size(); vessel_index++)
            {
                units::quantity<unit::flow_impedance> impedance = scaled_impedances[mNodeVesselConnectivity[node_index][vessel_index]];
                // Add the inverse impedances to the linear system

                mpLinearSystem->AddToMatrixElement(node_index, node_index, -multiplier / impedance); // Aii
                mpLinearSystem->AddToMatrixElement(node_index, mNodeNodeConnectivity[node_index][vessel_index], multiplier / impedance); // Aij
            }
        }
    }

    mpLinearSystem->AssembleIntermediateLinearSystem();
    // Update the RHS

    for (unsigned bc_index = 0; bc_index < mBoundaryConditionNodeIndices.size(); bc_index++)
    {
        if(mNodes[mBoundaryConditionNodeIndices[bc_index]]->GetFlowProperties()->UseVelocityBoundaryCondition())
        {
            boost::shared_ptr<Vessel<DIM> > p_vessel = mNodes[mBoundaryConditionNodeIndices[bc_index]]->GetSegment(0)->GetVessel();
            units::quantity<unit::flow_rate> flow_rate = boost::units::fabs(p_vessel->GetFlowProperties()->GetFlowRate());
            units::quantity<unit::flow_impedance> impedance = p_vessel->GetFlowProperties()->GetImpedance();
            double pressure_drop = flow_rate * impedance/ unit::pascals;
            mpLinearSystem->SetRhsVectorElement(mBoundaryConditionNodeIndices[bc_index], pressure_drop);
        }
        else
        {
            mpLinearSystem->SetRhsVectorElement(
                    mBoundaryConditionNodeIndices[bc_index],
                    mNodes[mBoundaryConditionNodeIndices[bc_index]]->GetFlowProperties()->GetPressure()/unit::pascals);
        }
    }
}

template<unsigned DIM>
void FlowSolver<DIM>::Solve()
{
    if (!mIsSetUp)
    {
        SetUp();
    }

    // Assemble and solve the final system
    mpLinearSystem->AssembleFinalLinearSystem();
    Vec solution = PetscTools::CreateVec(mNodes.size());
    solution = mpLinearSystem->Solve();

    // Recover the pressure of the vessel nodes
    ReplicatableVector a(solution);

    std::cout << "****************" << std::endl;
    for (unsigned node_index = 0; node_index < mNodes.size(); node_index++)
    {
        std::cout << "pressure" << a[node_index] << std::endl;
        mNodes[node_index]->GetFlowProperties()->SetPressure(a[node_index] * unit::pascals);
    }
    std::cout << "****************" << std::endl;

    // Set the segment flow rates and nodal pressures
    for (unsigned vessel_index = 0; vessel_index < mVessels.size(); vessel_index++)
    {
        units::quantity<unit::pressure> start_node_pressure = mVessels[vessel_index]->GetStartNode()->GetFlowProperties()->GetPressure();
        units::quantity<unit::pressure> end_node_pressure = mVessels[vessel_index]->GetEndNode()->GetFlowProperties()->GetPressure();
        units::quantity<unit::flow_rate> flow_rate = (start_node_pressure - end_node_pressure) / mVessels[vessel_index]->GetFlowProperties()->GetImpedance();

        // Clean up small values as some structural adaptation calculators are sensitive to them.
        if (fabs(flow_rate) < pow(10, -20)*unit::metre_cubed_per_second)
        {
            flow_rate = 0.0 * unit::metre_cubed_per_second;
        }

        std::vector<boost::shared_ptr<VesselSegment<DIM> > > segments = mVessels[vessel_index]->GetSegments();
        units::quantity<unit::pressure> pressure = start_node_pressure;
        for (unsigned segment_index = 0; segment_index < segments.size() - 1; segment_index++)
        {
            pressure -= segments[segment_index]->GetFlowProperties()->GetImpedance() * flow_rate;
            segments[segment_index]->GetNode(1)->GetFlowProperties()->SetPressure(pressure);
            segments[segment_index]->GetFlowProperties()->SetFlowRate(flow_rate);
        }
        segments[segments.size() - 1]->GetFlowProperties()->SetFlowRate(flow_rate);
    }

    // Clean up
    PetscTools::Destroy(solution);
}

// Explicit instantiation
template class FlowSolver<2> ;
template class FlowSolver<3> ;