[Aj Nair]

Dear Fomers
Can you guys help me to convert this energy equation to fvscalar matrix equation, i am getting frequent errors in this part of program.


formula.JPG

[mkraposhin]

forAll(A,i)
                {
                    A[i][i] = pEqn.diag()[i];                // inserting diagonal elements in A
                    b[i]    = pEqn.source()[i];                // and in b
                }
                
                const lduAddressing& addr = pEqn.lduAddr();
                const labelList& lowerAddr = addr.lowerAddr();
                const labelList& upperAddr = addr.upperAddr();                
                
                forAll(lowerAddr, i)
                {
                    A[lowerAddr[i]][upperAddr[i]] = pEqn.upper()[i];
                    A[upperAddr[i]][lowerAddr[i]] = pEqn.lower()[i];                                       
                }
                
                forAll(p.boundaryField(),I)
                {
                    const fvPatch &ptch=p.boundaryField()[I].patch();
                    forAll(ptch,J)
                    {
                    int w=ptch.faceCells()[J];
                    A[w][w]+=pEqn.internalCoeffs()[I][J];
                    b[w]   +=pEqn.boundaryCoeffs()[I][J];                    
                    }
                
                }

[Aj Nair]

But Matvej, i have attached an equation below.I had changed that equation as

fvm::ddt(T)+ ((fvc::grad(U))*T)-(lambda\(Cp*rho))*fvm::laplacian(T)

ignoring the epsilon. Is the above equation equivalent to which i attached .Because i get errors when i use this in TEqn

[Bernhard]

Uhm, which errors?

Normally you would discretize the convective term with fvm::div(phi,T).

Have a look in the, for example, buoyantPimpleFoam solver. The h-equation is very similar to your T-equation.

[Aj Nair]

Bernhard, i have uploaded a formula pic in my first post.I got that from a journal.I wanted a fvscalar matrix equation equivalent to that.can u please go through tat equation and give me some suggestions.

[mkraposhin]

Hi, Aj Nair!

My last post was about how to convert from your OF matrix format to 2D array. Now i see, that You are missing some basics of OF.

The problem that you are experiencing, is that OF uses conservative integral solution. Let's think you have equation

fig1.jpg

Then, You must convert this equation to conservative form:

fig2.jpg

But, OF works with integral equations, thus, you have to convert to integral balance:

fig3.jpg

If you will use mean theorem, without second order terms you can write:

fig4.jpg

By splitting terms at the r.h.s You will get:
fig5.jpg

[mkraposhin]

Now, if lambda, rho and Cp are constant, You convert Your equation to:

fig6.jpg

You can find all equations here:
T-equation-from-cfd-online.pdf

Last equation can be discretized with OF:

volScalarField kappa = lambda / rho / Cp;
fvScalarMatrix TEqn
(
    fvm::ddt(T)
    +
    fvm::div(phi,T)
    -
    fvm::Sp(fvc::div(phi), T)
    ==
    fvm::laplacian(kappa, T)
    + (gamma / Cp) * dEpsilonOverDt
);

Please, remember, that we used second order approximations to get this equation, so You don't need schemes with order, higher then 2. You can use my first post in this thread to analyze resuling matrix TEqn (like pEqn)

[Aj Nair]

Thanks a lot Matvej, i will come back to you, if i have any doubt

[Aj Nair]

Sorry for the delay in reply, thanks again Matvej