RKCK45.C

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/*---------------------------------------------------------------------------*\
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  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
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    \\  /    A nd           | Copyright (C) 2013 OpenFOAM Foundation
     \\/     M anipulation  |
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#include "RKCK45.H"
#include "addToRunTimeSelectionTable.H"

// * * * * * * * * * * * * * * Static Data Members * * * * * * * * * * * * * //

namespace Foam
{
    defineTypeNameAndDebug(RKCK45, 0);
    addToRunTimeSelectionTable(ODESolver, RKCK45, dictionary);

const scalar
    RKCK45::c2 = 1.0/5.0,
    RKCK45::c3 = 3.0/10.0,
    RKCK45::c4 = 3.0/5.0,
    RKCK45::c5 = 1.0,
    RKCK45::c6 = 7.0/8.0,

    RKCK45::a21 = 1.0/5.0,
    RKCK45::a31 = 3.0/40.0,
    RKCK45::a32 = 9.0/40.0,
    RKCK45::a41 = 3.0/10.0,
    RKCK45::a42 = -9.0/10.0,
    RKCK45::a43 = 6.0/5.0,
    RKCK45::a51 = -11.0/54.0,
    RKCK45::a52 = 5.0/2.0,
    RKCK45::a53 = -70.0/27.0,
    RKCK45::a54 = 35.0/27.0,
    RKCK45::a61 = 1631.0/55296.0,
    RKCK45::a62 = 175.0/512.0,
    RKCK45::a63 = 575.0/13824.0,
    RKCK45::a64 = 44275.0/110592.0,
    RKCK45::a65 = 253.0/4096.0,

    RKCK45::b1 = 37.0/378.0,
    RKCK45::b3 = 250.0/621.0,
    RKCK45::b4 = 125.0/594.0,
    RKCK45::b6 = 512.0/1771.0,

    RKCK45::e1 = RKCK45::b1 - 2825.0/27648.0,
    RKCK45::e3 = RKCK45::b3 - 18575.0/48384.0,
    RKCK45::e4 = RKCK45::b4 - 13525.0/55296.0,
    RKCK45::e5 = -277.00/14336.0,
    RKCK45::e6 = RKCK45::b6 - 0.25;
}


// * * * * * * * * * * * * * * * * Constructors  * * * * * * * * * * * * * * //

Foam::RKCK45::RKCK45(const ODESystem& ode, const dictionary& dict)
:
    ODESolver(ode, dict),
    adaptiveSolver(ode, dict),
    yTemp_(n_),
    k2_(n_),
    k3_(n_),
    k4_(n_),
    k5_(n_),
    k6_(n_),
    err_(n_)
{}


// * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //

Foam::scalar Foam::RKCK45::solve
(
    const scalar x0,
    const scalarField& y0,
    const scalarField& dydx0,
    const scalar dx,
    scalarField& y
) const
{
    forAll(yTemp_, i)
    {
        yTemp_[i] = y0[i] + a21*dx*dydx0[i];
    }

    odes_.derivatives(x0 + c2*dx, yTemp_, k2_);

    forAll(yTemp_, i)
    {
        yTemp_[i] = y0[i] + dx*(a31*dydx0[i] + a32*k2_[i]);
    }

    odes_.derivatives(x0 + c3*dx, yTemp_, k3_);

    forAll(yTemp_, i)
    {
        yTemp_[i] = y0[i] + dx*(a41*dydx0[i] + a42*k2_[i] + a43*k3_[i]);
    }

    odes_.derivatives(x0 + c4*dx, yTemp_, k4_);

    forAll(yTemp_, i)
    {
        yTemp_[i] = y0[i]
          + dx*(a51*dydx0[i] + a52*k2_[i] + a53*k3_[i] + a54*k4_[i]);
    }

    odes_.derivatives(x0 + c5*dx, yTemp_, k5_);

    forAll(yTemp_, i)
    {
        yTemp_[i] = y0[i]
          + dx
           *(a61*dydx0[i] + a62*k2_[i] + a63*k3_[i] + a64*k4_[i] + a65*k5_[i]);
    }

    odes_.derivatives(x0 + c6*dx, yTemp_, k6_);

    forAll(y, i)
    {
        y[i] = y0[i]
          + dx*(b1*dydx0[i] + b3*k3_[i] + b4*k4_[i] + b6*k6_[i]);
    }

    forAll(err_, i)
    {
        err_[i] =
            dx
           *(e1*dydx0[i] + e3*k3_[i] + e4*k4_[i] + e5*k5_[i] + e6*k6_[i]);
    }

    return normalizeError(y0, y, err_);
}


void Foam::RKCK45::solve
(
    scalar& x,
    scalarField& y,
    scalar& dxTry
) const
{
    adaptiveSolver::solve(odes_, x, y, dxTry);
}


// ************************************************************************* //