CFD Online Discussion Forums - Choice of numerical schemes for high accuracy in vorticity

Hi All,
I am trying to simulate flow over a flat plate in icoFOAM with different BC's to suit my aim.

The Domain :

1) Uniform velocity inlet with Ux = 1, Uy = 0, obviously the flow is in X direction. It is 2D XY domain
2) The lower boundary ( constant y) is zero gradient for pressure and velocity for some initial length after the inlet.
3) After some initial length I introduce a wall(plate) with fixed velocity BC = 0 and zero gradient BC for pressure.
4) The exit boundary is zero gradient for both pressure and velocity.
5) The top (free-stream) boundary is a directionMixed boundary with Uy as fixed value and Ux as fixed gradient.

The top boundary values and gradients are given in such a way that the Z-component of vorticity is 0.

The Numerics :

1) I am running the simulation in default (double precision) mode.
2) My BC field values are specified in double precision accuracy.
3) My fvSchemes are as below

ddtSchemes
{
default Euler;
}

gradSchemes
{
default Gauss linear;
grad(p) Gauss linear;
grad(U) Gauss linear;
}

divSchemes
{
default none;
div(phi,U) Gauss linear;
}

laplacianSchemes
{
default Gauss linear corrected;
}

interpolationSchemes
{
default Gauss linear;
}

snGradSchemes
{
default corrected;
}

fluxRequired
{
default no;
p ;
}

The Problem :

1) I calculate the vorticity using the 'vorticity' tool in OpenFOAM
2) What I am getting is a very large vorticity at the top boundary ( which seems to be due to the way the tool calculates the vorticity
3) In the region between the top boundary and the boundary layer edge the vorticity is reasonable but still not of high accuracy. I expect vorticity to be atleast of order of 10e-6 - 10e-7 with double precision whereas I get at very large mesh count (small cell sizes) to be at best 8e-4

I have tried different things like changing the grad schemes and laplacian schemes before vorticity evaluation but nothing seems to work.

I should also mention that my error scales directly with my velocities, so if I change my velocities to 0.1 times the value, the vorticity goes down by an order of magnitude.

I am not sure what to do, I have tried different things and nothing seems to work towards improving my vorticity accuracy. I am having my doubts on the numerical schemes, although most places it is written that Gauss linear and linear schemes are good enough choices.

Can anyone suggest what schemes should be better for improving accuracy of vorticity.
This is a simple laminar flow which should be pretty easy to get good results with. Any suggestions are appreciated.

Thanks,
D.B