[TehHO]

Hi there. I'm trying to simply solve the steady-state convection-diffusion problem for a global peclet number of 10, and investigate the effects of various finite volume schemes, by doing a convergence analysis of the schemes and compute the rate of convergence for each scheme.

I know that a CDS scheme should have a rate of convergence of 2, in a loglog plot, and a UDS should be of order 1 (because of points in stencil).

I've set up the model in OpenFOAM, but when I investigate my results there seems to be somthing wrong. The error, that is max[abs(t_numerical-T_analytical)], of the two schemes seem to lie (almost right on top of each other, see: http://i.imgur.com/eNyYUDj.jpg).

The scalarTransportFoam tutorial is modified for the exampled of interest.

I've included my two fvSchemes files for the model below, if someone could please tell me why the results are almost identical, that would be very sweet! Thank you!


fvScheme-file for UDS case
/*--------------------------------*- C++ -*----------------------------------*\
| ========= | |
| \\ / F ield | OpenFOAM: The Open Source CFD Toolbox |
| \\ / O peration | Version: 2.1.x |
| \\ / A nd | Web: www.OpenFOAM.org |
| \\/ M anipulation | |
\*---------------------------------------------------------------------------*/
FoamFile
{
version 2.0;
format ascii;
class dictionary;
location "system";
object fvSchemes;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

ddtSchemes
{
default steadyState;
}

gradSchemes
{
default Gauss linear;
grad(phi,T) Gauss upwind;
}

// change : div(phi,T) Gauss upwind ; to
// div (phi,T) Gauss linearUpwind ;
divSchemes
{
default none;
div(phi,T) Gauss upwind;
}

laplacianSchemes
{
default none;
laplacian(DT,T) Gauss linear corrected;
}

interpolationSchemes
{
default linear;
}

snGradSchemes
{
default corrected;
}

fluxRequired
{
default no;
T ;
}


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

fvScheme-file for CDS case
/*--------------------------------*- C++ -*----------------------------------*\
| ========= | |
| \\ / F ield | OpenFOAM: The Open Source CFD Toolbox |
| \\ / O peration | Version: 2.1.x |
| \\ / A nd | Web: www.OpenFOAM.org |
| \\/ M anipulation | |
\*---------------------------------------------------------------------------*/
FoamFile
{
version 2.0;
format ascii;
class dictionary;
location "system";
object fvSchemes;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

ddtSchemes
{
default steadyState;
}

gradSchemes
{
default Gauss linear;
}

// change : div(phi,T) Gauss upwind ; to
// div (phi,T) Gauss linearUpwind ;
divSchemes
{
default none;
div(phi,T) Gauss linear ;
}

laplacianSchemes
{
default none;
laplacian(DT,T) Gauss linear corrected;
}

interpolationSchemes
{
default linear;
}

snGradSchemes
{
default corrected;
}

fluxRequired
{
default no;
T ;
}


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