primitiveMeshFaceCentresAndAreas.C

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/*---------------------------------------------------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     | Website:  https://openfoam.org
    \\  /    A nd           | Copyright (C) 2011-2020 OpenFOAM Foundation
     \\/     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 3 of the License, or
    (at your option) any later version.

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    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, see <http://www.gnu.org/licenses/>.

Description
    Calculate the face centres and areas.

    Calculate the centre by breaking the face into triangles using the face
    centre and area-weighted averaging their centres.  This method copes with
    small face-concavity.

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

#include "primitiveMesh.H"


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

void Foam::primitiveMesh::calcFaceCentresAndAreas() const
{
    if (debug)
    {
        Pout<< "primitiveMesh::calcFaceCentresAndAreas() : "
            << "Calculating face centres and face areas"
            << endl;
    }

    // It is an error to attempt to recalculate faceCentres
    // if the pointer is already set
    if (faceCentresPtr_ || faceAreasPtr_ || magFaceAreasPtr_)
    {
        FatalErrorInFunction
            << "Face centres or face areas already calculated"
            << abort(FatalError);
    }

    faceCentresPtr_ = new vectorField(nFaces());
    vectorField& fCtrs = *faceCentresPtr_;

    faceAreasPtr_ = new vectorField(nFaces());
    vectorField& fAreas = *faceAreasPtr_;

    magFaceAreasPtr_ = new scalarField(nFaces());
    scalarField& magfAreas = *magFaceAreasPtr_;

    makeFaceCentresAndAreas(points(), fCtrs, fAreas, magfAreas);

    if (debug)
    {
        Pout<< "primitiveMesh::calcFaceCentresAndAreas() : "
            << "Finished calculating face centres and face areas"
            << endl;
    }
}


void Foam::primitiveMesh::makeFaceCentresAndAreas
(
    const pointField& p,
    vectorField& fCtrs,
    vectorField& fAreas,
    scalarField& magfAreas
) const
{
    const faceList& fs = faces();

    forAll(fs, facei)
    {
        const labelList& f = fs[facei];
        label nPoints = f.size();

        // If the face is a triangle, do a direct calculation for efficiency
        // and to avoid round-off error-related problems
        if (nPoints == 3)
        {
            fCtrs[facei] = (1.0/3.0)*(p[f[0]] + p[f[1]] + p[f[2]]);
            fAreas[facei] = 0.5*((p[f[1]] - p[f[0]])^(p[f[2]] - p[f[0]]));
        }

        // For more complex faces, decompose into triangles
        else
        {
            // Compute an estimate of the centre as the average of the points
            point pAvg = p[f[0]];
            for (label pi = 1; pi < nPoints; pi++)
            {
                pAvg += p[f[pi]];
            }
            pAvg /= nPoints;

            // Compute the face area normal and unit normal by summing up the
            // normals of the triangles formed by connecting each edge to the
            // point average.
            vector sumA = Zero;
            forAll(f, i)
            {
                const vector a =
                    (p[f[f.fcIndex(i)]] - p[f[i]])^(pAvg - p[f[i]]);

                sumA += a;
            }
            const vector sumAHat = normalised(sumA);

            // Compute the area-weighted sum of the triangle centres. Note use
            // the triangle area projected in the direction of the face normal
            // as the weight, *not* the triangle area magnitude. Only the
            // former makes the calculation independent of the initial estimate.
            scalar sumAn = 0.0;
            vector sumAnc = Zero;
            forAll(f, i)
            {
                const vector a =
                    (p[f[f.fcIndex(i)]] - p[f[i]])^(pAvg - p[f[i]]);
                const vector c = p[f[i]] + p[f[f.fcIndex(i)]] + pAvg;

                const scalar an = a & sumAHat;

                sumAn += an;
                sumAnc += an*c;
            }

            // Complete calculating centres and areas. If the face is too small
            // for the sums to be reliably divided then just set the centre to
            // the initial estimate.
            if (sumAn > vSmall)
            {
                fCtrs[facei] = (1.0/3.0)*sumAnc/sumAn;
            }
            else
            {
                fCtrs[facei] = pAvg;
            }
            fAreas[facei] = 0.5*sumA;
        }

        magfAreas[facei] = max(mag(fAreas[facei]), vSmall);
    }
}


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

const Foam::vectorField& Foam::primitiveMesh::faceCentres() const
{
    if (!faceCentresPtr_)
    {
        calcFaceCentresAndAreas();
    }

    return *faceCentresPtr_;
}


const Foam::vectorField& Foam::primitiveMesh::faceAreas() const
{
    if (!faceAreasPtr_)
    {
        calcFaceCentresAndAreas();
    }

    return *faceAreasPtr_;
}


const Foam::scalarField& Foam::primitiveMesh::magFaceAreas() const
{
    if (!magFaceAreasPtr_)
    {
        calcFaceCentresAndAreas();
    }

    return *magFaceAreasPtr_;
}


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