.. _program_listing_file_explicitLawsOfTheWall_EquilibriumODEExplicitLawOfTheWall_EquilibriumODEExplicitLawOfTheWall.H:

Program Listing for File EquilibriumODEExplicitLawOfTheWall.H
=============================================================

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

.. |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/>.
   
   Class
       Foam::EquilibriumODEExplicitLawOfTheWall
   
   @brief
       An explicit approximation of the equilibrium ODE wall model.
   
       The equilibrium ODE profile is obtained by integrating
       \f[
           \frac{du^+}{dy^+} =
           \frac{1}{1 + \kappa y^+ \left(1 - \exp(-y^+/A^+)\right)^2}.
       \f]
   
       Evaluating the corresponding wall stress from a sampled velocity requires
       an iterative solve. This class replaces that solve by the explicit
       approximation of Nuca, Mukha, and Parsani. The approximation is constructed
       by adding a Gaussian perturbation to the explicit law of Cai and Sagaut.
   
       The approximation coefficients depend on \f$\kappa\f$ and \f$A^+\f$.
       The \c approximant entry controls which coefficient set is used:
       \verbatim
           auto       Select highRe for kappa=0.387, Aplus=15.2516;
                      select classical for kappa=0.41, Aplus=17;
                      otherwise select global.
           highRe     Fixed three-Gaussian fit for high-Re constants
                      kappa=0.387, Aplus=15.2516. The reported maximum relative
                      error with respect to the original equilibrium ODE model is
                      below 0.04%.
           classical  Fixed three-Gaussian fit for classical constants
                      kappa=0.41, Aplus=17. The reported maximum relative
                      error with respect to the original equilibrium ODE model is
                      below 0.04%.
           global     One-Gaussian regression in kappa and Aplus for other
                      constants. This is the fallback for user-selected constants
                      and is constructed to remain within the 1% relative-error
                      target.
       \endverbatim
   
       Usage:
       \verbatim
       Law
       {
           type        EquilibriumODE;
           kappa      value; (default 0.41)
           Aplus      value; (default 17)
           approximant auto; (default auto; highRe, classical or global)
       }
       \endverbatim
   
       Reference for the explicit approximation:
       \verbatim
           Nuca, R., Mukha, T., and Parsani, M. (2025).
           Explicit formulations of widely used wall models for large-eddy
           simulation.
           Physics of Fluids, 37, 035215.
           https://doi.org/10.1063/5.0253882
       \endverbatim
   
   Contributors/Copyright:
       2024-2026 Timofey Mukha
   
   
   SourceFiles
       EquilibriumODEExplicitLawOfTheWall.C
   
   \*---------------------------------------------------------------------------*/
   
   #ifndef EquilibriumODEExplicitLawOfTheWall_H
   #define EquilibriumODEExplicitLawOfTheWall_H
   
   #include "scalar.H"
   #include "typeInfo.H"
   #include "dictionary.H"
   #include "ExplicitLawOfTheWall.H"
   
   // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
   
   namespace Foam
   {
   
   /*---------------------------------------------------------------------------*\
                       Class EquilibriumODEExplicitLawOfTheWall Declaration
   \*---------------------------------------------------------------------------*/
   
   class EquilibriumODEExplicitLawOfTheWall: public ExplicitLawOfTheWall
   {
   
       // Private data
   
           //- The kappa model constant
           scalar kappa_;
   
           //- The Aplus model constant
           scalar Aplus_;
   
           //- Equivalent log-law B constant for the ODE profile
           scalar B_;
   
           //- Approximation family: auto, highRe, classical or global
           word approximant_;
   
           //- Cai-Sagaut blending parameters
           scalar p_;
           scalar s_;
   
           //- Gaussian perturbation coefficients
           label nGaussians_;
           scalar mu_[3];
           scalar sigma_[3];
           scalar xi_[3];
   
           //- Select and store the approximation coefficients
           void setApproximantCoeffs(const word& approximant);
   
           //- Return whether two constants should be considered matching
           static bool approxEqual(const scalar a, const scalar b);
   
           //- Compute the Cai-Sagaut component of u+
           scalar CaiSagautUPlus(const scalar Re) const;
   
           //- Compute the perturbation component of u+
           scalar deltaUPlus(const scalar log10Re) const;
   
   public:
   
   #if !defined(DOXYGEN_SHOULD_SKIP_THIS)
       TypeName("EquilibriumODE");
   #endif
   
       // Constructors
   
           //- Construct provided dictionary
           EquilibriumODEExplicitLawOfTheWall(const dictionary &);
   
           //- Construct provided TypeName and dictionary
           EquilibriumODEExplicitLawOfTheWall
           (
               const word & lawname,
               const dictionary &
           );
   
           //- Construct from model constants
           EquilibriumODEExplicitLawOfTheWall
           (
               const scalar kappa,
               const scalar Aplus
           );
   
   
           //- Copy constructor
           EquilibriumODEExplicitLawOfTheWall
           (
               const EquilibriumODEExplicitLawOfTheWall &
           ) = default;
   
           //- Assignment
           EquilibriumODEExplicitLawOfTheWall & operator=
           (
               const EquilibriumODEExplicitLawOfTheWall &
           ) = default;
   
           //- Clone
           virtual autoPtr<ExplicitLawOfTheWall> clone() const override
           {
               return autoPtr<ExplicitLawOfTheWall>
               (
                   new EquilibriumODEExplicitLawOfTheWall(*this)
               );
           }
   
       // Destructor
           virtual ~EquilibriumODEExplicitLawOfTheWall() {};
   
       // Member Functions
   
           //- Return the kappa constant
           scalar kappa() const
           {
               return kappa_;
           }
   
           //- Return the Aplus constant
           scalar Aplus() const
           {
               return Aplus_;
           }
   
           //- Return the equivalent log-law B constant
           scalar B() const
           {
               return B_;
           }
   
           //- Return the selected approximant
           word approximant() const
           {
               return approximant_;
           }
   
           //- Return the Cai-Sagaut p coefficient
           scalar p() const
           {
               return p_;
           }
   
           //- Return the Cai-Sagaut s coefficient
           scalar s() const
           {
               return s_;
           }
   
           //- Print info to terminal
           virtual void printCoeffs() const override;
   
           //- Return the value of the friction velocity
           virtual scalar uTau
           (
               const SingleCellSampler & sampler,
               label index,
               scalar nu
           ) const override;
   
   };
   
   
   // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
   
   } // End namespace Foam
   
   // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
   
   #endif