integrationScheme.H

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/*---------------------------------------------------------------------------*\
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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/>.
 
Class
    Foam::integrationScheme
 
Description
    Base for a set of schemes which integrate simple ODEs which arise from
    semi-implicit rate expressions.
 
        \f[
            \frac{d \phi}{d t} = A - B \phi
        \f]
 
    The methods are defined in terms of the effective time-step \f$\Delta
    t_e\f$ by which the explicit rate is multiplied. The effective time-step is
    a function of the actual time step and the implicit coefficient, which must
    be implemented in each derived scheme.
 
        \f[
            \Delta t_e = f(\Delta t, B)
        \f]
        \f[
            \Delta \phi = (A - B \phi^n) \Delta t_e
        \f]
 
    This class also facilitates integration in stages. If the explicit and
    implicit coefficients, \f$A\f$ and \f$B\f$, are a summation of differing
    contributions, \f$\sum \alpha_i\f$ and \f$\sum \beta_i\f$, then the
    integration can be split up to determine the effect of each contribution.
 
        \f[
            \frac{d \phi_i}{d t} = \alpha_i - \beta_i \phi
        \f]
        \f[
            \Delta \phi_i = \alpha_i \Delta t -
            \beta_i \int_0^{\Delta t} \phi d t
        \f]
        \f[
            \Delta \phi_i = (\alpha_i - \beta_i \phi^n) \Delta t -
            \beta_i (A - B \phi^n) \int_0^{\Delta t} t_e dt
        \f]
 
    These partial calculations are defined in terms of the integral of the
    effective time-step, \f$\int_0^{\Delta t} t_e dt\f$, which is also
    implemented in every derivation.
 
SourceFiles
    integrationScheme.C
 
\*---------------------------------------------------------------------------*/
 
#ifndef integrationScheme_H
#define integrationScheme_H
 
#include "autoPtr.H"
#include "runTimeSelectionTables.H"
#include "dictionary.H"
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
namespace Foam
{
 
/*---------------------------------------------------------------------------*\
                      Class integrationScheme Declaration
\*---------------------------------------------------------------------------*/
 
class integrationScheme
{
public:
 
    //- Runtime type information
    TypeName("integrationScheme");
 
 
    //- Declare runtime constructor selection table
 
         declareRunTimeSelectionTable
         (
             autoPtr,
             integrationScheme,
             word,
             (),
             ()
         );
 
 
    // Constructors
 
        //- Construct
        integrationScheme();
 
        //- Construct and return clone
        virtual autoPtr<integrationScheme> clone() const = 0;
 
 
    // Selectors
 
        //- Select an integration scheme
        static autoPtr<integrationScheme> New
        (
            const word& phiName,
            const dictionary& dict
        );
 
 
    //- Destructor
    virtual ~integrationScheme();
 
 
    // Member Functions
 
        //- Perform the integration explicitly
        template<class Type>
        static Type explicitDelta
        (
            const Type& phi,
            const scalar dtEff,
            const Type& Alpha,
            const scalar Beta
        );
 
        //- Perform the integration
        template<class Type>
        Type delta
        (
            const Type& phi,
            const scalar dt,
            const Type& Alpha,
            const scalar Beta
        ) const;
 
        //- Perform a part of the integration
        template<class Type>
        Type partialDelta
        (
            const Type& phi,
            const scalar dt,
            const Type& Alpha,
            const scalar Beta,
            const Type& alphai,
            const scalar betai
        ) const;
 
        //- Return the integration effective time step
        virtual scalar dtEff(const scalar dt, const scalar Beta) const = 0;
 
        //- Return the integral of the effective time step
        virtual scalar sumDtEff(const scalar dt, const scalar Beta) const = 0;
};
 
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
} // End namespace Foam
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
#ifdef NoRepository
    #include "integrationSchemeTemplates.C"
#endif
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
#endif
 
// ************************************************************************* //