CFD Online Discussion Forums - Vorticity in OpenFOAM; Negative to when I compute from fvc::grad(U)

Hi there,

I output the values of the velocity gradient tensor, as well as, the vorticity for my simulation.

Let's just consider the rotation about the x-axis for simplicity.

The problem that I am having is that when I compute $\omega_x = \frac{\partial w}{\partial y} - \frac{\partial v}{\partial z}$ , this is the definition of curl in the OpenFOAM Programmer's guide 2.1.3. Howeber, I actually get the negative of the vorticity in the standard OpenFOAM output file.

Now, when I again follow the maths in the Progammer's guide, I see that OpenFOAM is actually computing the hodge dual of the rotation rate tensor, so for [math] \omega_x = \omega_{23}[\math]. This should indeed be $\omega_x = \frac{\partial w}{\partial y} - \frac{\partial v}{\partial z}$ .

Now, the only thing I can think of that I may be doing wrong is that I assume that OF is writing the VGT in the following order: $\partial_x{u} ,\partial_y{u},\partial_z{u},\partial_x{v}...$
Any help appreciated.