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how the EulerImplicit chemistry solver solves the concentration?

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Old   October 4, 2019, 03:06
Question how the EulerImplicit chemistry solver solves the concentration?
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Hi, all here!

These days I used the EulerImplicit chemistry solver to solve the reactions in the flow filed.
But I found that the concentration solved by the solver behaved strange in my case,
so I traced into the EulerImplicit chemistry solver source to learn how it solves the concentration.

in the EulerImplicit.C file, there are lines to construct the matrix:
Code:
    for (label i=0; i<nSpecie; i++)
    {
        RR(i, i) += 1/deltaT;                    (1)
        RR.source()[i] = c[i]/deltaT;
    }
the RR is the coefficient matrix contains the reaction rates that constructed in the function updateRRInReactionI:
Code:
const Reaction<typename ChemistryModel::thermoType>& R =
        this->reactions_[index];

    forAll(R.lhs(), s)
    {
        const label si = R.lhs()[s].index;
        const scalar sl = R.lhs()[s].stoichCoeff;
        RR[si][rRef] -= sl*pr*corr;
        RR[si][lRef] += sl*pf*corr;
    }

    forAll(R.rhs(), s)
    {
        const label si = R.rhs()[s].index;
        const scalar sr = R.rhs()[s].stoichCoeff;
        RR[si][lRef] -= sr*pf*corr;
        RR[si][rRef] += sr*pr*corr;
    }
let's consider the concentration of a species, c,
the new concentration after the time step will be c',
then the equation for the code above can be written as:
( RR + 1/dt ) * c'= c/dt

here the ( RR + 1/dt ) comes from the code (1), and RR is the reaction rate which have the unit of kmoles/m^3/s

rearrange the equation, I got
RR * c' = ( c - c' ) / dt = dc/dt

so, here is my question,
why on the left the " RR * c' " appear?
shouldn't it be RR = ( c - c' ) / dt = dc/dt the right equation?
the " RR * c' " has the unit of kmoles/m^3/s * kmoles/m^3, which is different of dc/dt that has the unit of kmoles/m^3/s...

does anyone has the reference of the EulerImplicit chemistry solver that used in the OF?
please help me.
Thank you!
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