[immortality]

in the totalPressure BC at this part:

if (psiName_ == "none" && rhoName_ == "none")
    {
        operator==(p0p - 0.5*(1.0 - pos(phip))*magSqr(Up));
    }
    else if (rhoName_ == "none")
    {
        const fvPatchField<scalar>& psip =
            patch().lookupPatchField<volScalarField, scalar>(psiName_);

        if (gamma_ > 1.0)
        {
            scalar gM1ByG = (gamma_ - 1.0)/gamma_;

            operator==
            (
                p0p
               /pow
                (
                    (1.0 + 0.5*psip*gM1ByG*(1.0 - pos(phip))*magSqr(Up)),
                    1.0/gM1ByG
                )
            );
        }
        else
        {
            operator==(p0p/(1.0 + 0.5*psip*(1.0 - pos(phip))*magSqr(Up)));
        }

there is this well-known formula.but there is some questions
1) why "(1.0 - pos(phip))" term is put in this formula?what it means?
2)does Up and psip stand for internalField(p) and 1/(R*internalField(T))?

p0p
               /pow
                (
                    (1.0 + 0.5*psip*gM1ByG*(1.0 - pos(phip))*magSqr(Up)),
                    1.0/gM1ByG

3)I have written this formula(isentropic relation) in groovyBC in this manner:

p0_2/pow(1+(gamma-1)/2*magSqr(internalField(U))/(gamma*R*internalField(T)),3.5)

is it equivalent correctly to what there is in OF totalPressure code?