openfoam/applications/test/ODETest/ODETest.C

/*---------------------------------------------------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     |
    \\  /    A nd           | Copyright (C) 1991-2009 OpenCFD Ltd.
     \\/     M anipulation  |
-------------------------------------------------------------------------------
License
    This file is part of OpenFOAM.

    OpenFOAM is free software; you can redistribute it and/or modify it
    under the terms of the GNU General Public License as published by the
    Free Software Foundation; either version 2 of the License, or (at your
    option) any later version.

    OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
    FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
    for more details.

    You should have received a copy of the GNU General Public License
    along with OpenFOAM; if not, write to the Free Software Foundation,
    Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA

Description

\*---------------------------------------------------------------------------*/

#include "argList.H"
#include "IOmanip.H"
#include "ODE.H"
#include "ODESolver.H"
#include "RK.H"

using namespace Foam;

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

class testODE
:
    public ODE
{

public:

    testODE()
    {}

    label nEqns() const
    {
        return 4;
    }

    void derivatives
    (
        const scalar x,
        const scalarField& y,
        scalarField& dydx
    ) const
    {
        dydx[0] = -y[1];
        dydx[1] = y[0] - (1.0/x)*y[1];
        dydx[2] = y[1] - (2.0/x)*y[2];
        dydx[3] = y[2] - (3.0/x)*y[3];
    }

    void jacobian
    (
        const scalar x,
        const scalarField& y,
        scalarField& dfdx,
        scalarSquareMatrix& dfdy
    ) const
    {
        dfdx[0] = 0.0;
        dfdx[1] = (1.0/sqr(x))*y[1];
        dfdx[2] = (2.0/sqr(x))*y[2];
        dfdx[3] = (3.0/sqr(x))*y[3];

        dfdy[0][0] = 0.0;
        dfdy[0][1] = -1.0;
        dfdy[0][2] = 0.0;
        dfdy[0][3] = 0.0;

        dfdy[1][0] = 1.0;
        dfdy[1][1] = -1.0/x;
        dfdy[1][2] = 0.0;
        dfdy[1][3] = 0.0;

        dfdy[2][0] = 0.0;
        dfdy[2][1] = 1.0;
        dfdy[2][2] = -2.0/x;
        dfdy[2][3] = 0.0;

        dfdy[3][0] = 0.0;
        dfdy[3][1] = 0.0;
        dfdy[3][2] = 1.0;
        dfdy[3][3] = -3.0/x;
    }
};


// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
// Main program:

int main(int argc, char *argv[])
{
    argList::validArgs.clear();
    argList::validArgs.append("ODESolver");
    argList args(argc, argv);

    word ODESolverName(args.additionalArgs()[0]);

    testODE ode;
    autoPtr<ODESolver> odeSolver = ODESolver::New(ODESolverName, ode);

    scalar xStart = 1.0;
    scalarField yStart(ode.nEqns());
    yStart[0] = ::Foam::j0(xStart);
    yStart[1] = ::Foam::j1(xStart);
    yStart[2] = ::Foam::jn(2, xStart);
    yStart[3] = ::Foam::jn(3, xStart);

    scalarField dyStart(ode.nEqns());
    ode.derivatives(xStart, yStart, dyStart);

    Info<< setw(10) << "eps" << setw(12) << "hEst";
    Info<< setw(13) << "hDid" << setw(14) << "hNext" << endl;
    Info<< setprecision(6);

    for (label i=0; i<15; i++)
    {
        scalar eps = ::Foam::exp(-scalar(i + 1));

        scalar x = xStart;
        scalarField y = yStart;
        scalarField dydx = dyStart;

        scalarField yScale(ode.nEqns(), 1.0);
        scalar hEst = 0.6;
        scalar hDid, hNext;

        odeSolver->solve(ode, x, y, dydx, eps, yScale, hEst, hDid, hNext);

        Info<< scientific << setw(13) << eps;
        Info<< fixed << setw(11) << hEst;
        Info<< setw(13) << hDid << setw(13) << hNext
            << setw(13) << y[0] << setw(13) << y[1]
            << setw(13) << y[2] << setw(13) << y[3]
            << endl;
    }

    scalar x = xStart;
    scalar xEnd = x + 1.0;
    scalarField y = yStart;

    scalarField yEnd(ode.nEqns());
    yEnd[0] = ::Foam::j0(xEnd);
    yEnd[1] = ::Foam::j1(xEnd);
    yEnd[2] = ::Foam::jn(2, xEnd);
    yEnd[3] = ::Foam::jn(3, xEnd);

    scalar hEst = 0.5;

    odeSolver->solve(ode, x, xEnd, y, 1e-4, hEst);

    Info<< nl << "Analytical: y(2.0) = " << yEnd << endl;
    Info      << "Numerical:  y(2.0) = " << y << ", hEst = " << hEst << endl;

    Info<< "\nEnd\n" << endl;

    return 0;
}


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