.. _program_listing_file_explicitLawsOfTheWall_EquilibriumODEExplicitLawOfTheWall_EquilibriumODEExplicitLawOfTheWall.C:

Program Listing for File EquilibriumODEExplicitLawOfTheWall.C
=============================================================

|exhale_lsh| :ref:`Return to documentation for file <file_explicitLawsOfTheWall_EquilibriumODEExplicitLawOfTheWall_EquilibriumODEExplicitLawOfTheWall.C>` (``explicitLawsOfTheWall/EquilibriumODEExplicitLawOfTheWall/EquilibriumODEExplicitLawOfTheWall.C``)

.. |exhale_lsh| unicode:: U+021B0 .. UPWARDS ARROW WITH TIP LEFTWARDS

.. code-block:: cpp

   /*---------------------------------------------------------------------------* \
   License
       This file is part of libWallModelledLES.
   
       libWallModelledLES 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.
   
       libWallModelledLES 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 libWallModelledLES.
       If not, see <http://www.gnu.org/licenses/>.
   
   \*---------------------------------------------------------------------------*/
   
   #include "EquilibriumODEExplicitLawOfTheWall.H"
   #include "dictionary.H"
   #include "error.H"
   #include "addToRunTimeSelectionTable.H"
   #include "scalarListIOList.H"
   #include "SingleCellSampler.H"
   #include <boost/math/special_functions/lambert_w.hpp>
   #include "helpers.H"
   #include "AdaptiveIntegrator.hpp"
   #include <functional>
   
   typedef std::function<Foam::scalar(const Foam::scalar)> IntegrandFunc;
   
   Foam::scalar get_B(const Foam::scalar kappa, const Foam::scalar Aplus);
   
   #if !defined(DOXYGEN_SHOULD_SKIP_THIS)
   namespace Foam
   {
       defineTypeNameAndDebug(EquilibriumODEExplicitLawOfTheWall, 0);
       addToRunTimeSelectionTable(ExplicitLawOfTheWall, EquilibriumODEExplicitLawOfTheWall, Dictionary);
       addToRunTimeSelectionTable(ExplicitLawOfTheWall, EquilibriumODEExplicitLawOfTheWall, TypeAndDictionary);
   }
   #endif
   
   // * * * * * * * * * * * * * * * * Constructors  * * * * * * * * * * * * * * //
   
   Foam::EquilibriumODEExplicitLawOfTheWall::EquilibriumODEExplicitLawOfTheWall
   (
       const scalar kappa,
       const scalar Aplus
   )
   :
       ExplicitLawOfTheWall(),
       kappa_(kappa),
       Aplus_(Aplus),
       B_(get_B(kappa_, Aplus_)),
       approximant_("auto"),
       p_(0),
       s_(0),
       nGaussians_(0),
       mu_{0, 0, 0},
       sigma_{0, 0, 0},
       xi_{0, 0, 0}
   {
       constDict_.add("kappa", kappa);
       constDict_.add("Aplus", Aplus);
       setApproximantCoeffs(approximant_);
       constDict_.add("approximant", approximant_);
   
       if (debug)
       {
           printCoeffs();
       }
   
   }
   
   Foam::EquilibriumODEExplicitLawOfTheWall::EquilibriumODEExplicitLawOfTheWall
   (
       const dictionary & dict
   )
   :
       ExplicitLawOfTheWall(dict),
       kappa_(constDict_.lookupOrAddDefault<scalar>("kappa", 0.41)),
       Aplus_(constDict_.lookupOrAddDefault<scalar>("Aplus", 17)),
       B_(get_B(kappa_, Aplus_)),
       approximant_(constDict_.lookupOrAddDefault<word>("approximant", "auto")),
       p_(0),
       s_(0),
       nGaussians_(0),
       mu_{0, 0, 0},
       sigma_{0, 0, 0},
       xi_{0, 0, 0}
   
   {
       setApproximantCoeffs(approximant_);
       constDict_.set("approximant", approximant_);
   
       if (debug)
       {
           printCoeffs();
       }
   }
   
   Foam::EquilibriumODEExplicitLawOfTheWall::EquilibriumODEExplicitLawOfTheWall
   (
       const word & lawName,
       const dictionary & dict
   )
   :
       EquilibriumODEExplicitLawOfTheWall(dict)
   {
   }
   
   
   // * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
   
   bool Foam::EquilibriumODEExplicitLawOfTheWall::approxEqual
   (
       const scalar a,
       const scalar b
   )
   {
       return mag(a - b) < 1e-6;
   }
   
   
   void Foam::EquilibriumODEExplicitLawOfTheWall::setApproximantCoeffs
   (
       const word& approximant
   )
   {
       word selected(approximant);
   
       if (selected == "auto")
       {
           if (approxEqual(kappa_, 0.387) && approxEqual(Aplus_, 15.2516))
           {
               selected = "highRe";
           }
           else if (approxEqual(kappa_, 0.41) && approxEqual(Aplus_, 17))
           {
               selected = "classical";
           }
           else
           {
               selected = "global";
           }
       }
   
       if (selected == "highRe")
       {
           nGaussians_ = 3;
           mu_[0] = 2.747578886341323; sigma_[0] = 2.986331718406963; xi_[0] = 0.14158434859130883;
           mu_[1] = 3.217234942007338; sigma_[1] = 0.5812144329347989; xi_[1] = 0.053147124312226554;
           mu_[2] = 4.155551202580644; sigma_[2] = 0.945720164071122; xi_[2] = -0.03125681152478188;
           p_ = 1.1907235645597454;
           s_ = 218.72498935725267;
       }
       else if (selected == "classical")
       {
           nGaussians_ = 3;
           mu_[0] = 2.712195304468856; sigma_[0] = 1.153331759918931; xi_[0] = 0.04253708716912398;
           mu_[1] = 2.785538268044812; sigma_[1] = 3.1614868745529012; xi_[1] = 0.13731053348456193;
           mu_[2] = 2.547620704489551; sigma_[2] = 0.6124242434703746; xi_[2] = 0.012277142724028153;
           p_ = 1.2029211749614945;
           s_ = 247.0697345675632;
       }
       else if (selected == "global")
       {
           nGaussians_ = 1;
           mu_[0] = 3.498902867914008*kappa_ + 0.13030217331542102*Aplus_ - 0.9085784915858164;
           sigma_[0] = -1.2191000776979632*kappa_ - 0.02844761945101745*Aplus_ + 1.5494923375953826;
           xi_[0] = -0.39993239380818907*kappa_ - 0.0072855142653190505*Aplus_ + 0.3209799815846869;
           mu_[1] = 0; sigma_[1] = 0; xi_[1] = 0;
           mu_[2] = 0; sigma_[2] = 0; xi_[2] = 0;
           p_ = 0.22127889108172996*kappa_ + 0.0052185898765612845*Aplus_ + 1.0616974939891426;
           s_ = -130.48555166521916*kappa_ + 7.964453719974989*Aplus_ + 10.6631049793274;
       }
       else
       {
           FatalErrorInFunction
               << "Unknown EquilibriumODE explicit approximant " << selected << nl
               << "Valid options are auto, highRe, classical and global."
               << abort(FatalError);
       }
   
       approximant_ = selected;
   }
   
   
   Foam::scalar Foam::EquilibriumODEExplicitLawOfTheWall::CaiSagautUPlus
   (
       const scalar Re
   ) const
   {
       const scalar f = exp(-Re / s_);
       const scalar E = exp(kappa_ * B_);
   
       scalar uPlus = Foam::pow(f, p_) * Foam::sqrt(Re);
       uPlus += Foam::pow(1 - f, p_) / kappa_
           * boost::math::lambert_w0(kappa_*E*Re);
   
       return uPlus;
   }
   
   
   Foam::scalar Foam::EquilibriumODEExplicitLawOfTheWall::deltaUPlus
   (
       const scalar log10Re
   ) const
   {
       scalar delta = 0;
   
       for (label i = 0; i < nGaussians_; i++)
       {
           delta += Helpers::gaussian(mu_[i], sigma_[i], xi_[i], log10Re);
       }
   
       return delta;
   }
   
   
   void Foam::EquilibriumODEExplicitLawOfTheWall::printCoeffs() const
   {
       Info<< nl << "EquilibriumODEExplicit law of the wall" << nl;
       Info<< token::BEGIN_BLOCK << incrIndent << nl;
       Info<< indent << "kappa" << indent << kappa_ << nl;
       Info<< indent << "Aplus" << indent <<  Aplus_ << nl;
       Info<< indent << "approximant" << indent <<  approximant_ << nl;
       Info<< token::END_BLOCK << nl << nl;
   }
   
   
   Foam::scalar Foam::EquilibriumODEExplicitLawOfTheWall::uTau
   (
       const SingleCellSampler & sampler,
       label index,
       scalar nu
   ) const
   {
       const scalarListIOList & U = sampler.db().lookupObject<scalarListIOList>("U");
       const scalar u = mag(vector(U[index][0], U[index][1], U[index][2]));
       const scalar y = sampler.h()[index];
       const scalar re = u * y / nu;
   
       const scalar uPlus = CaiSagautUPlus(re) + deltaUPlus(Foam::log10(re));
   
       return u / uPlus;
   
   }
   
   Foam::scalar get_B(const Foam::scalar kappa, const Foam::scalar Aplus)
   {
       IntegrandFunc nut_func = [kappa, Aplus](const Foam::scalar yPlus)
       {
           return kappa * yPlus * Foam::sqr(1 - Foam::exp(-yPlus / Aplus));
       };
   
       IntegrandFunc integrand = [nut_func](const Foam::scalar yPlus)
       {
           return 1.0 / (1.0 + nut_func(yPlus));
       };
   
       Foam::scalar yPlus = 100000;
   
       AdaptiveIntegrator<Foam::scalar (Foam::scalar)> quad;
       Foam::scalar up = quad.integrate(integrand, 0.0, yPlus, 1e-3);
   
       return up - 1/kappa * Foam::log(yPlus);
   }
   
   
   // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //