Program Listing for File SpaldingExplicitLawOfTheWall.H

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

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    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::SpaldingExplicitLawOfTheWall

@brief
    An explicit approximation of Spalding's law.

    \f[
    y^+ = u^+ +  \exp(-\kappa B) \left( \exp (\kappa B) - 1 - \kappa u^+ -
             \frac{1}{2}(\kappa u^+)^2 - \frac{1}{6}(\kappa u^+)^3 \right)
    \f]

    Spalding's law is implicit in the wall stress. In a wall model this means
    that every wall face requires an iterative solve for \f$u_\tau\f$ at every
    update. This class replaces that nonlinear 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,
    which makes the wall-stress evaluation algebraic while retaining the
    accuracy of the original implicit Spalding relation.

    The approximation coefficients depend on the logarithmic-law constants.
    The \c approximant entry controls which coefficient set is used:
    \verbatim
        auto       Select highRe for kappa=0.387, B=4.21;
                   select classical for kappa=0.4, B=5.5;
                   otherwise select global.
        highRe     Fixed three-Gaussian fit for high-Re constants
                   kappa=0.387, B=4.21. The reported maximum relative
                   error with respect to the original Spalding law is
                   below 0.04%.
        classical  Fixed three-Gaussian fit for classical constants
                   kappa=0.4, B=5.5. The reported maximum relative
                   error with respect to the original Spalding law is
                   below 0.04%.
        global     One-Gaussian regression in kappa and B for other constants.
                   This is the fallback for user-selected constants and is
                   constructed to remain within the 1% relative-error target.
    \endverbatim

    The errors above are relative to the wall stress obtained from the original
    implicit Spalding relation solved iteratively.

    Usage:
    \verbatim
    Law
    {
        type        Spalding;
        kappa     value; (default 0.4)
        B         value; (default 5.5)
        approximant auto; (default auto; highRe, classical or global)
    }
    \endverbatim

    Reference for the original law:
    \verbatim
        Spalding, D. B. (1961).
        A single formula for the 'law of the wall'.
        Journal of Applied Mechanics,
        28(3), 455-458.
    \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
    SpaldingExplicitLawOfTheWall.C

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

#ifndef SpaldingExplicitLawOfTheWall_H
#define SpaldingExplicitLawOfTheWall_H

#include "scalar.H"
#include "typeInfo.H"
#include "dictionary.H"
#include "ExplicitLawOfTheWall.H"

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

namespace Foam
{

/*---------------------------------------------------------------------------*\
                    Class SpaldingExplicitLawOfTheWall Declaration
\*---------------------------------------------------------------------------*/

class SpaldingExplicitLawOfTheWall: public ExplicitLawOfTheWall
{

    // Private data

        //- The kappa model constant
        scalar kappa_;

        //- The B model constant
        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("Spalding");
#endif

    // Constructors

        //- Construct provided dictionary
        SpaldingExplicitLawOfTheWall(const dictionary &);

        //- Construct provided TypeName and dictionary
        SpaldingExplicitLawOfTheWall
        (
            const word & lawname,
            const dictionary &
        );

        //- Construct from model constants
        SpaldingExplicitLawOfTheWall
        (
            const scalar kappa,
            const scalar B
        );


        //- Copy constructor
        SpaldingExplicitLawOfTheWall
        (
            const SpaldingExplicitLawOfTheWall &
        ) = default;

        //- Assignment
        SpaldingExplicitLawOfTheWall & operator=
        (
            const SpaldingExplicitLawOfTheWall &
        ) = default;

        //- Clone
        virtual autoPtr<ExplicitLawOfTheWall> clone() const override
        {
            return autoPtr<ExplicitLawOfTheWall>
            (
                new SpaldingExplicitLawOfTheWall(*this)
            );
        }

    // Destructor
        virtual ~SpaldingExplicitLawOfTheWall() {};

    // Member Functions

        //- Return the kappa constant
        scalar kappa() const
        {
            return kappa_;
        }

        //- Return the 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 implicit function defining the law
        virtual scalar uTau
        (
            const SingleCellSampler & sampler,
            label index,
            scalar nu
        ) const override;

};


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

} // End namespace Foam

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

#endif