laplacianFoam giving weird results:HELP
 

hi all,

I am using laplacianfoam to simulate the bratu problem laplacian(b)+epsilon*exp(b/(1+mu*b))=0, thou i am getting expected variation on applying BCs: b=100 on both sides of my rectangular domain but on applying b=0 i am getting no changes(why??).
In my new solver i have linearised the exponential term by taylor exp. and have not removed d/dt term of laplacianfoam instead specified steadyState in fvSchemes.

0/b :

FoamFile
{
version 2.0;
format ascii;
class volScalarField;
object b;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
dimensions [0 0 0 0 0 0 0];
internalField uniform 100;
boundaryField
{
patch_1
{
type zeroGradient;
}
patch_2
{
type fixedValue;
value uniform 100;
}
patch_3
{
type zeroGradient;
}
patch_4
{
type fixedValue;
value uniform 100;
}}

and my solver

dimensionedScalar one
(
"one",
dimensionSet(0, 2, -1, 0, 0, 0 ,0),
1.0
);

simpleControl simple(mesh);

// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

Info<< "\nCalculating distribution of b\n" << endl;

while (simple.loop())
{
Info<< "Time = " << runTime.timeName() << nl << endl;

while (simple.correctNonOrthogonal())
{
solve
(
fvm::ddt(b) - fvm::laplacian(one, b) == fvm::Sp(epsilon*((2 + fvc::Sp(1 +2*mu, b)))/(2*(1+fvc::Sp(mu, b))), b)
);
}

#include "write.H"