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========= |
\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
\\ / O peration | Website: https://openfoam.org
\\ / A nd | Copyright (C) 2011-2023 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.
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, see <http://www.gnu.org/licenses/>.
\*---------------------------------------------------------------------------*/
#include "kShellIntegration.H"
#include "mathematicalConstants.H"
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
Foam::Pair<Foam::scalarField> Foam::kShellIntegration
(
const complexVectorField& Ek,
const Kmesh& K
)
{
// evaluate the radial component of the spectra as an average
// over the shells of thickness dk
Pair<scalarField> kShellMeanEk(kShellMean(Ek, K));
const scalarField& x = kShellMeanEk.first();
scalarField& y = kShellMeanEk.second();
// now multiply by 4pi k^2 (the volume of each shell) to get the
// spectra E(k). int E(k) dk is now the total energy in a box
// of side 2pi
y *= sqr(x)*4.0*constant::mathematical::pi;
// now scale this to get the energy in a box of side l0
scalar l0(K.sizeOfBox()[0]*(scalar(K.nn()[0])/(scalar(K.nn()[0])-1.0)));
scalar factor = pow((l0/(2.0*constant::mathematical::pi)),3.0);
y *= factor;
// and divide by the number of points in the box, to give the
// energy density.
y /= scalar(K.size());
return kShellMeanEk;
}
// kShellMean : average over the points in a k-shell to evaluate the
// radial part of the energy spectrum.
Foam::Pair<Foam::scalarField> Foam::kShellMean
(
const complexVectorField& Ek,
const Kmesh& K
)
{
const label tnp = Ek.size();
const label NoSubintervals = label
(
pow(scalar(tnp), 1.0/vector::dim)*pow(1.0/vector::dim, 0.5) - 0.5
);
scalarField k1D(NoSubintervals);
scalarField Ek1D(NoSubintervals);
scalarField EWeight(NoSubintervals);
scalar kmax = K.max()*pow(1.0/vector::dim,0.5);
scalar delta_k = kmax/(NoSubintervals);
forAll(Ek1D, a)
{
k1D[a] = (a + 1)*delta_k;
Ek1D[a] = 0.0;
EWeight[a] = 0;
}
forAll(K, l)
{
scalar kmag = mag(K[l]);
for (label a=0; a<NoSubintervals; a++)
{
if
(
kmag <= ((a + 1)*delta_k + delta_k/2.0)
&& kmag > ((a + 1)*delta_k - delta_k/2.0)
)
{
scalar dist = delta_k/2.0 - mag((a + 1)*delta_k - kmag);
Ek1D[a] += dist*
magSqr
(
vector
(
mag(Ek[l].x()),
mag(Ek[l].y()),
mag(Ek[l].z())
)
);
EWeight[a] += dist;
}
}
}
for (label a=0; a<NoSubintervals; a++)
{
if (EWeight[a] > 0)
{
Ek1D[a] /= EWeight[a];
}
}
return Pair<scalarField>(k1D, Ek1D);
}
// ************************************************************************* //
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