TemplatePressureArea.cpp

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///////////////////////////////////////////////////////////////////////////////
//
// File: TemplatePressureArea.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
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
// DEALINGS IN THE SOFTWARE.
//
// Description: TemplatePressureArea class
//
///////////////////////////////////////////////////////////////////////////////
 
#include <PulseWaveSolver/EquationSystems/TemplatePressureArea.h>
 
namespace Nektar
{
 
std::string TemplatePressureArea::className =
    GetPressureAreaFactory().RegisterCreatorFunction(
        "Template", TemplatePressureArea::create,
        "Template to add a new Pressure-Area relation");
 
TemplatePressureArea::TemplatePressureArea(
    Array<OneD, MultiRegions::ExpListSharedPtr> pVessel,
    const LibUtilities::SessionReaderSharedPtr pSession)
    : PulseWavePressureArea(pVessel, pSession)
{
}
 
void TemplatePressureArea::v_GetPressure(NekDouble &P, const NekDouble &beta,
                                         const NekDouble &A,
                                         const NekDouble &A0,
                                         const NekDouble &dAUdx,
                                         const NekDouble &gamma,
                                         const NekDouble &alpha)
{
    // Relation here
 
    /*
    NOTE: to add a new relation, you also need to add the name of the .h and
    .cpp files to the CMakeLists.txt file in the PulseWaveSolver folder.
    */
}
 
void TemplatePressureArea::v_GetC(NekDouble &c, const NekDouble beta,
                                  const NekDouble A, const NekDouble A0,
                                  const NekDouble alpha)
{
    // PWV here
}
 
void TemplatePressureArea::v_GetW1(NekDouble &W1, const NekDouble u,
                                   const NekDouble beta, const NekDouble A,
                                   const NekDouble A0, const NekDouble alpha)
{
    NekDouble I = 0.0;
    GetCharIntegral(I, beta, A, A0);
 
    W1 = u + I; // Elastic and assumes u0 = 0
}
 
void TemplatePressureArea::v_GetW2(NekDouble &W2, const NekDouble u,
                                   const NekDouble beta, const NekDouble A,
                                   const NekDouble A0, const NekDouble alpha)
{
    NekDouble I = 0.0;
    GetCharIntegral(I, beta, A, A0);
 
    W2 = u - I; // Elastic and assumes u0 = 0
}
 
void TemplatePressureArea::v_GetAFromChars(NekDouble &A, const NekDouble W1,
                                           const NekDouble W2,
                                           const NekDouble beta,
                                           const NekDouble A0,
                                           const NekDouble alpha)
{
    /*
    If an anayltical formula exists for this, then it should be used here. If
    not, a numerical method is used.
    */
 
    // Iterative Newton-Raphson
    NekDouble I    = 0.0;
    NekDouble c    = 0.0;
    NekDouble FA   = 0.0;
    NekDouble dFdA = 0.0;
    NekDouble dA   = 0.0;
 
    int proceed   = 1;
    int iter      = 0;
    int MAX_ITER  = 200;
    NekDouble Tol = 1.0E-10;
 
    while ((proceed) && (iter < MAX_ITER))
    {
        iter += 1;
 
        GetCharIntegral(I, beta, A, A0, alpha);
        GetC(c, beta, A, A0, alpha);
 
        FA   = I - ((W1 - W2) / 2);
        dFdA = c / A;
 
        dA = FA / dFdA;
        A -= dA;
 
        if (sqrt(dA * dA) < Tol)
        {
            proceed = 0;
        }
    }
}
 
void TemplatePressureArea::v_GetUFromChars(NekDouble &u, const NekDouble W1,
                                           const NekDouble W2)
{
    u = (W1 + W2) / 2; // Necessarily the case for all tube laws
}
 
void TemplatePressureArea::v_GetCharIntegral(NekDouble &I, const NekDouble beta,
                                             const NekDouble A,
                                             const NekDouble A0,
                                             const NekDouble alpha)
{
    /*
    If an anayltical formula exists for this, then it should be used here. If
    not, a numerical method is used.
    */
 
    // Numerical integration via the trapezium rule
    // f(x) = c / A, x1 = A0, x2 = A
 
    int n         = 500;
    NekDouble h   = (A - A0) / n;
    NekDouble A_n = A0;
    NekDouble c_n = 0.0;
 
    for (int i = 1; i < n; ++i)
    {
        A_n += h;
        GetC(c_n, beta, A_n, A0, alpha);
        I += c_n / A_n;
    }
 
    NekDouble c  = 0.0;
    NekDouble c0 = 0.0;
    GetC(c, beta, A, A0, alpha);
    GetC(c0, beta, A0, A0, alpha);
 
    I += ((c / A) + (c0 / A0)) / 2;
    I *= h;
}
 
void TemplatePressureArea::v_GetJacobianInverse(
    NekMatrix<NekDouble> &invJ, const Array<OneD, NekDouble> Au,
    const Array<OneD, NekDouble> uu, const Array<OneD, NekDouble> beta,
    const Array<OneD, NekDouble> A0, const Array<OneD, NekDouble> alpha,
    const std::string type)
{
    /*
    This is a general method that will work for all tube laws. Simulations will
    run faster if specific analytical formulae are derived as in the case of the
    beta law, but it's not necessary.
    */
 
    // General formulation
    if (type == "Bifurcation")
    {
        NekMatrix<NekDouble> J(6, 6);
        Array<OneD, NekDouble> c(3);
 
        for (int i = 0; i < 3; ++i)
        {
            GetC(c[i], beta[i], Au[i], A0[i], alpha[i]);
        }
 
        J.SetValue(0, 0, 1);
        J.SetValue(0, 1, 0);
        J.SetValue(0, 2, 0);
        J.SetValue(0, 3, c[0] / Au[0]);
        J.SetValue(0, 4, 0);
        J.SetValue(0, 5, 0);
 
        J.SetValue(1, 0, 0);
        J.SetValue(1, 1, 1);
        J.SetValue(1, 2, 0);
        J.SetValue(1, 3, 0);
        J.SetValue(1, 4, -c[1] / Au[1]);
        J.SetValue(1, 5, 0);
 
        J.SetValue(2, 0, 0);
        J.SetValue(2, 1, 0);
        J.SetValue(2, 2, 1);
        J.SetValue(2, 3, 0);
        J.SetValue(2, 4, 0);
        J.SetValue(2, 5, -c[2] / Au[2]);
 
        J.SetValue(3, 0, Au[0]);
        J.SetValue(3, 1, -Au[1]);
        J.SetValue(3, 2, -Au[2]);
        J.SetValue(3, 3, uu[0]);
        J.SetValue(3, 4, -uu[1]);
        J.SetValue(3, 5, -uu[2]);
 
        J.SetValue(4, 0, 2 * uu[0]);
        J.SetValue(4, 1, -2 * uu[1]);
        J.SetValue(4, 2, 0);
        J.SetValue(4, 3, 2 * c[0] * c[0] / Au[0]);
        J.SetValue(4, 4, -2 * c[1] * c[1] / Au[1]);
        J.SetValue(4, 5, 0);
 
        J.SetValue(5, 0, 2 * uu[0]);
        J.SetValue(5, 1, 0);
        J.SetValue(5, 2, -2 * uu[2]);
        J.SetValue(5, 3, 2 * c[0] * c[0] / Au[0]);
        J.SetValue(5, 4, 0);
        J.SetValue(5, 5, -2 * c[2] * c[2] / Au[2]);
 
        invJ = J;
        invJ.Invert();
    }
    else if (type == "Merge")
    {
        NekMatrix<NekDouble> J(6, 6);
        Array<OneD, NekDouble> c(3);
 
        for (int i = 0; i < 3; ++i)
        {
            GetC(c[i], beta[i], Au[i], A0[i], alpha[i]);
        }
 
        J.SetValue(0, 0, 1);
        J.SetValue(0, 1, 0);
        J.SetValue(0, 2, 0);
        J.SetValue(0, 3, -c[0] / Au[0]);
        J.SetValue(0, 4, 0);
        J.SetValue(0, 5, 0);
 
        J.SetValue(1, 0, 0);
        J.SetValue(1, 1, 1);
        J.SetValue(1, 2, 0);
        J.SetValue(1, 3, 0);
        J.SetValue(1, 4, c[1] / Au[1]);
        J.SetValue(1, 5, 0);
 
        J.SetValue(2, 0, 0);
        J.SetValue(2, 1, 0);
        J.SetValue(2, 2, 1);
        J.SetValue(2, 3, 0);
        J.SetValue(2, 4, 0);
        J.SetValue(2, 5, c[2] / Au[2]);
 
        J.SetValue(3, 0, Au[0]);
        J.SetValue(3, 1, -Au[1]);
        J.SetValue(3, 2, -Au[2]);
        J.SetValue(3, 3, uu[0]);
        J.SetValue(3, 4, -uu[1]);
        J.SetValue(3, 5, -uu[2]);
 
        J.SetValue(4, 0, 2 * uu[0]);
        J.SetValue(4, 1, -2 * uu[1]);
        J.SetValue(4, 2, 0);
        J.SetValue(4, 3, 2 * c[0] * c[0] / Au[0]);
        J.SetValue(4, 4, -2 * c[1] * c[1] / Au[1]);
        J.SetValue(4, 5, 0);
 
        J.SetValue(5, 0, 2 * uu[0]);
        J.SetValue(5, 1, 0);
        J.SetValue(5, 2, -2 * uu[2]);
        J.SetValue(5, 3, 2 * c[0] * c[0] / Au[0]);
        J.SetValue(5, 4, 0);
        J.SetValue(5, 5, -2 * c[2] * c[2] / Au[2]);
 
        invJ = J;
        invJ.Invert();
    }
    else if (type == "Interface")
    {
        NekMatrix<NekDouble> J(4, 4);
        Array<OneD, NekDouble> c(2);
 
        for (int i = 0; i < 2; ++i)
        {
            GetC(c[i], beta[i], Au[i], A0[i], alpha[i]);
        }
 
        J.SetValue(0, 0, 1);
        J.SetValue(0, 1, 0);
        J.SetValue(0, 2, c[0] / Au[0]);
        J.SetValue(0, 3, 0);
 
        J.SetValue(1, 0, 0);
        J.SetValue(1, 1, 1);
        J.SetValue(1, 2, 0);
        J.SetValue(1, 3, -c[1] / Au[1]);
 
        J.SetValue(2, 0, Au[0]);
        J.SetValue(2, 1, -Au[1]);
        J.SetValue(2, 2, uu[0]);
        J.SetValue(2, 3, -uu[1]);
 
        J.SetValue(3, 0, 2 * uu[0]);
        J.SetValue(3, 1, -2 * uu[1]);
        J.SetValue(3, 2, 2 * c[0] * c[0] / Au[0]);
        J.SetValue(3, 3, -2 * c[1] * c[1] / Au[1]);
 
        invJ = J;
        invJ.Invert();
    }
}
 
} // namespace Nektar