QInflow.cpp

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///////////////////////////////////////////////////////////////////////////////
//
// File QInflow.cpp
//
// For more information, please see: http://www.nektar.info
//
// The MIT License
//
// Copyright (c) 2006 Division of Applied Mathematics, Brown University (USA),
// Department of Aeronautics, Imperial College London (UK), and Scientific
// Computing and Imaging Institute, University of Utah (USA).
//
// License for the specific language governing rights and limitations under
// Permission is hereby granted, free of charge, to any person obtaining a
// copy of this software and associated documentation files (the "Software"),
// to deal in the Software without restriction, including without limitation
// the rights to use, copy, modify, merge, publish, distribute, sublicense,
// and/or sell copies of the Software, and to permit persons to whom the
// Software is furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included
// in all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
// OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
// THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
// DEALINGS IN THE SOFTWARE.
//
// Description: QInflow class
//
///////////////////////////////////////////////////////////////////////////////

#include <PulseWaveSolver/EquationSystems/QInflow.h>

namespace Nektar
{

    std::string QInflow::className
    = GetBoundaryFactory().RegisterCreatorFunction(
        "Q-inflow",
        QInflow::create,
        "Inflow boundary condition");

    /**
     *
     */
    QInflow::QInflow(Array<OneD, MultiRegions::ExpListSharedPtr> pVessel, 
                     const LibUtilities::SessionReaderSharedPtr pSession,
                     PulseWavePressureAreaSharedPtr pressureArea)
        : PulseWaveBoundary(pVessel,pSession,pressureArea)
    {
    }

    /**
     *
     */
    QInflow::~QInflow()
    {

    }

    void QInflow::v_DoBoundary(
        const Array<OneD,const Array<OneD, NekDouble> > &inarray,
        Array<OneD, Array<OneD, NekDouble> > &A_0,
        Array<OneD, Array<OneD, NekDouble> > &beta,
        const NekDouble time,
        int omega,
        int offset, 
        int n)
    { 
    NekDouble Q, A_u, u_u;
        NekDouble A_r, u_r, A_l, u_l;
        Array<OneD, MultiRegions::ExpListSharedPtr>     vessel(2);

        vessel[0] = m_vessels[2*omega];
        vessel[1] = m_vessels[2*omega+1];

        vessel[0]->EvaluateBoundaryConditions(time);

        // Note: The Q value is contained in A in the
        // inputfile, the value in u has to be 1.0
        //ASSERTL0((vessel[1]->UpdateBndCondExpansion(n))->UpdatePhys()[0] == 1.0, "For the Q-inflow BC the value in u must be 1.0");
                    
        // Get the values of all variables needed for the Riemann problem
        Q = (vessel[0]->UpdateBndCondExpansion(n))->GetCoeffs()[0];

        A_r = inarray[0][offset];
        u_r = inarray[1][offset];

        // Call the Q-inflow Riemann solver
        Q_RiemannSolver(Q,A_r,u_r,A_0[omega][0],beta[omega][0],A_u,u_u);

        // Set the boundary conditions to  prescribe
        A_l=A_r;
        u_l=2*u_u-u_r;
                        
        // Store the updated values in the boundary condition
        (vessel[0]->UpdateBndCondExpansion(n))->UpdatePhys()[0] = A_l;
        (vessel[1]->UpdateBndCondExpansion(n))->UpdatePhys()[0] = u_l;
    }

    /**
     *  Q-inflow Riemann solver for pulse wave propagation. This Riemann solver is called
     *  by DoOdeProjection in case of a Q-inflow boundary condition. It is based on the 
     *  conservation of mass and total pressure and on the characteristic information. For
     *  further details see "Pulse wave propagation in the human vascular system", section 3.4.1
     *  Returns the upwinded quantities \f$(A_u,u_u)\f$ and stores them into the boundary values
     */
    void QInflow::Q_RiemannSolver(NekDouble Q,NekDouble A_r,NekDouble u_r,NekDouble A_0, NekDouble beta,
                                                     NekDouble &Au,NekDouble &uu)
    {       
        NekDouble W2 = 0.0;
        NekDouble A_calc = 0.0;
        NekDouble fa = 0.0;
        NekDouble dfa = 0.0;
        NekDouble delta_A_calc = 0.0;
        NekDouble rho = m_rho; 
    
        int proceed = 1;
        int iter = 0;
        int MAX_ITER = 200;
    
        // Tolerances for the algorithm
        NekDouble Tol = 1.0e-10;
    
        // Riemann invariant \f$W_2(Ar,ur)\f$
        W2 = u_r - 4*sqrt(beta/(2*rho))*sqrt(sqrt(A_r));
    
        // Newton Iteration (Area only)
        A_calc = A_r;
        while ((proceed) && (iter < MAX_ITER))
        {   
            iter =iter+1;
            
            fa = Q - W2*A_calc - A_calc*4*sqrt(beta/(2*rho))*sqrt(sqrt(A_calc));
            dfa = -W2 - 5*sqrt(beta/(2*rho))*sqrt(sqrt(A_calc));
            delta_A_calc = fa/dfa;
            A_calc = A_calc - delta_A_calc;
            
            if (sqrt(delta_A_calc*delta_A_calc) < Tol)
                proceed = 0;
        }
    
        // Obtain u_u and A_u
        uu = W2+4*sqrt(beta/(2*rho))*sqrt(sqrt(A_calc)); 
        Au = A_calc;
    }

}