| /*---------------------------------------------------------------------------*\ | |
| ========= | | |
| \\ / 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/>. | |
| \*---------------------------------------------------------------------------*/ | |
| // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * // | |
| 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); | |
| } | |
| // ************************************************************************* // | |