RKDP45.C

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#include "RKDP45.H"
#include "addToRunTimeSelectionTable.H"

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

namespace Foam
{
    defineTypeNameAndDebug(RKDP45, 0);
    addToRunTimeSelectionTable(ODESolver, RKDP45, dictionary);

const scalar
    RKDP45::c2 = 1.0/5.0,
    RKDP45::c3 = 3.0/10.0,
    RKDP45::c4 = 4.0/5.0,
    RKDP45::c5 = 8.0/9.0,

    RKDP45::a21 = 1.0/5.0,

    RKDP45::a31 = 3.0/40.0,
    RKDP45::a32 = 9.0/40.0,

    RKDP45::a41 = 44.0/45.0,
    RKDP45::a42 = -56.0/15.0,
    RKDP45::a43 = 32.0/9.0,

    RKDP45::a51 = 19372.0/6561.0,
    RKDP45::a52 = -25360.0/2187.0,
    RKDP45::a53 = 64448.0/6561.0,
    RKDP45::a54 = -212.0/729.0,

    RKDP45::a61 = 9017.0/3168.0,
    RKDP45::a62 = -355.0/33.0,
    RKDP45::a63 = 46732.0/5247.0,
    RKDP45::a64 = 49.0/176.0,
    RKDP45::a65 = -5103.0/18656.0,

    RKDP45::b1 = 35.0/384.0,
    RKDP45::b3 = 500.0/1113.0,
    RKDP45::b4 = 125.0/192.0,
    RKDP45::b5 = -2187.0/6784.0,
    RKDP45::b6 = 11.0/84.0,

    RKDP45::e1 = 5179.0/57600.0 - RKDP45::b1,
    RKDP45::e3 = 7571.0/16695.0 - RKDP45::b3,
    RKDP45::e4 = 393.0/640.0 - RKDP45::b4,
    RKDP45::e5 = -92097.0/339200.0 - RKDP45::b5,
    RKDP45::e6 = 187.0/2100.0 - RKDP45::b6,
    RKDP45::e7 = 1.0/40.0;
}


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

Foam::RKDP45::RKDP45(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  * * * * * * * * * * * * * //

bool Foam::RKDP45::resize()
{
    if (ODESolver::resize())
    {
        adaptiveSolver::resize(n_);

        resizeField(yTemp_);
        resizeField(k2_);
        resizeField(k3_);
        resizeField(k4_);
        resizeField(k5_);
        resizeField(k6_);
        resizeField(err_);

        return true;
    }
    else
    {
        return false;
    }
}


Foam::scalar Foam::RKDP45::solve
(
    const scalar x0,
    const scalarField& y0,
    const label li,
    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_, li, k2_);

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

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

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

    odes_.derivatives(x0 + c4*dx, yTemp_, li, 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_, li, 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 + dx, yTemp_, li, k6_);

    forAll(y, i)
    {
        y[i] = y0[i]
          + dx*(b1*dydx0[i] + b3*k3_[i] + b4*k4_[i] + b5*k5_[i] + b6*k6_[i]);
    }

    // Reuse k2_ for the derivative of the new state
    odes_.derivatives(x0 + dx, y, li, k2_);

    forAll(err_, i)
    {
        err_[i] =
            dx
           *(e1*dydx0[i] + e3*k3_[i] + e4*k4_[i] + e5*k5_[i] + e6*k6_[i]
             + e7*k2_[i]);
    }

    return normaliseError(y0, y, err_);
}


void Foam::RKDP45::solve
(
    scalar& x,
    scalarField& y,
    const label li,
    scalar& dxTry
) const
{
    adaptiveSolver::solve(odes_, x, y, li, dxTry);
}


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