[babakflame]

Tobi,

I added those under relaxation coefficients to fvSolution as well.

Unfortunately, it still diverges, even for values of less than 9.

[babakflame]

Dear Fellows

The equation

written with the following snippet :

 solve
        (
              fvm::laplacian(phi)  == beta * sinh(phi) 
//          fvm::laplacian(phi) - beta * (phi + (1/6)*pow(phi,3) + (1/120)*pow(phi,5) + (1/362880)*pow(phi,9) + (1/39916800)*pow(phi,11))
        );

crashes for large values of

The following ideas didn't resolve the crashing issue:
1) relaxing the steady equation
2) Solving the transient form (adding time derivative)
3) relaxing the transient form
4) refining the grid
5) replacing with its polynomial counterpart

At the moment, I have found that some people have solved the above equation in a weak variational form in a Galerkin projection:
A Newton iteration strategy is used:



Here shows the iteration number.

I tried to write the above formulation in OpenFoam 2.1.x using the following snippet:

    solve (fvm::laplacian(phi)   == beta * sinh(phi));
    while (runTime.loop())
    {
        Info<< "Iteration = " << runTime.timeName() << nl << endl;


        (fvm::laplacian(phi) - beta * cosh(phi.oldTime()) * phi  == beta * sinh(phi.oldTime())  - beta * cosh(phi.oldTime()) * phi.oldTime();
        runTime.write();

        Info<< "ExecutionTime = " << runTime.elapsedCpuTime() << " s"
            << "  ClockTime = " << runTime.elapsedClockTime() << " s"
            << nl << endl;
    }

As you can see, I used the oldTime() member function to have access to previous iterations and solved the real equation once before the loop to have phi.oldTime() available for the loop. The code compiles correctly, However crashes during simulation with same
error as before.
I have a feeling that I am not implementing correctly the above iterative equation.

Any hint is appreciated

[Zeppo]

Originally Posted by babakflame

    solve (fvm::laplacian(phi)   == beta * sinh(phi));
    while (runTime.loop())
    {
        Info<< "Iteration = " << runTime.timeName() << nl << endl;


        (fvm::laplacian(phi) - beta * cosh(phi.oldTime()) * phi  == beta * sinh(phi.oldTime())  - beta * cosh(phi.oldTime()) * phi.oldTime();
        runTime.write();

        Info<< "ExecutionTime = " << runTime.elapsedCpuTime() << " s"
            << "  ClockTime = " << runTime.elapsedClockTime() << " s"
            << nl << endl;
    }

Just a note to let you know.
Instead of this

(fvm::laplacian(phi) - beta * cosh(phi.oldTime()) * phi  == beta * sinh(phi.oldTime())  - beta * cosh(phi.oldTime()) * phi.oldTime();

you can apply some relaxation to a field phi by this

(fvm::laplacian(phi) == beta * sinh(phi)).solve();
phi.relax();

relax() will read the relaxation coefficient from system/fvSolution dictionary

//- system/fvSolution
relaxationFactors
{
    fields
    {
         phi       0.3;
     }
}

//- src/OpenFOAM/fields/GeometricFields/GeometricField/GeometricField.C
template<class Type, template<class> class PatchField, class GeoMesh>
void Foam::GeometricField<Type, PatchField, GeoMesh>::relax()
{
    word name = this->name();

    if
    (
        this->mesh().data::template lookupOrDefault<bool>
        (
            "finalIteration",
            false
        )
    )
    {
        name += "Final";
    }

    if (this->mesh().relaxField(name))
    {
        relax(this->mesh().fieldRelaxationFactor(name));
    }
}

and another relax(relaxFactor) is then invoked

//- src/OpenFOAM/fields/GeometricFields/GeometricField/GeometricField.C
template<class Type, template<class> class PatchField, class GeoMesh>
void Foam::GeometricField<Type, PatchField, GeoMesh>::relax(const scalar alpha)
{
    if (debug)
    {
        InfoInFunction
           << "Relaxing" << endl << this->info() << " by " << alpha << endl;
    }

    operator==(prevIter() + alpha*(*this - prevIter()));
}

[babakflame]

Dear Sergei

Many thanks for your reply. Actually, I had applied the under-relaxation in a correct way.
http://www.cfd-online.com/Forums/ope...tml#post618146
Either my value was not small enough (0.3) or a specific algorithm for iterating is needed, however, I solved my problem through employing the following solver in fvSolution file:

solver smoothSolver;
    smoother GaussSeidel;
    preconditioner DIC;
    tolerance 1e-11;
    relTol 0.2;

Cuopling the above solver and refinement made me capable of increasing the value of in my non-linear equation.

[Zeppo]

Hi, Bobi
Glad to hear you solved your problem.

[babakflame]

Thanks Bro.