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    interFoam family: Add support for MULES-bounded Crank-Nicolson 2nd-order ddt(alpha) · f78d33b6
    Henry authored
    This is an experimental feature demonstrating the potential of MULES to
    create bounded solution which are 2nd-order in time AND space.
    
    Crank-Nicolson may be selected on U and/or alpha but will only be fully
    2nd-order if used on both within the PIMPLE-loop to converge the
    interaction between the flux and phase-fraction.  Note also that
    Crank-Nicolson may not be used with sub-cycling but all the features of
    semi-implicit MULES are available in particular MULESCorr and
    alphaApplyPrevCorr.
    
    Examples of ddt specification:
    
    ddtSchemes
    {
        default         Euler;
    }
    
    ddtSchemes
    {
        default         CrankNicolson 0.9;
    }
    
    ddtSchemes
    {
        default         none;
        ddt(alpha)      CrankNicolson 0.9;
        ddt(rho,U)      CrankNicolson 0.9;
    }
    
    ddtSchemes
    {
        default         none;
        ddt(alpha)      Euler;
        ddt(rho,U)      CrankNicolson 0.9;
    }
    
    ddtSchemes
    {
        default         none;
        ddt(alpha)      CrankNicolson 0.9;
        ddt(rho,U)      Euler;
    }
    
    In these examples a small amount of off-centering in used to stabilize
    the Crank-Nicolson scheme.  Also the specification for alpha1 is via the
    generic phase-fraction name to ensure in multiphase solvers (when
    Crank-Nicolson support is added) the scheme is identical for all phase
    fractions.
    f78d33b6