[Phil_]

Hello Foamers,

I'm running a simple steady-state incompressible 2D laminar test-case of a divergent-convergent channel on OF 2.3.0. In order to estimate the discretization error I performed a mesh study with the "Richardson-Extrapolation" (See e.g. "Computational Methods for Fluid Dynamics" by Ferziger and Peric).

The three hex-meshes were refined in x- and y-direction by a factor of r=2.

The numerical schemes are of second order

ddtSchemes
{
    default         steadyState;
}

gradSchemes
{
    default         leastSquares;
}

divSchemes
{
    default         none;
    div(phi,U)      Gauss linear;
    div((nuEff*dev(T(grad(U))))) Gauss linear;
}

laplacianSchemes
{
    default         Gauss linear corrected;
}

interpolationSchemes
{
    default         linear;
}

snGradSchemes
{
    default         corrected;
}

fluxRequired
{
    default         no;
    p               ;
}

The order of accuracy can also be estimated by:

p = log[(Phi_2h - Phi_4h)/(Phi_h - Phi_2h)] / log r

with index h for the finest mesh, index 4h for the coarsest mesh, and the refinement factor r (here r=2).

For several sample-points along the flow-direction, when using the x-velocity-component, I get orders varying from 1.2 to 3.3. Where do these differences originate from? Are these indicators of local mesh quality and fineness? So if the estimated order is low, the mesh should be refined in this area?

Also for some sample points, the pressure does not increase monotonically, but decreases from the middle to the fine mesh. I'll check the values and samples again, but does anyone have an explanation for that?

In order to estimate the discretization error afterwards, the following equation is used:

epsilon = (Phi_h - Phi_2h)/(r^p - 1)

Best regards

Philip