second order FD upwind scheme
 

Hi,

I was ask by a friend, I had a hard time to answer, so I give the nswer to all of you.

Is there a simple higher order upwind scheme for FD which* also works for non equidistant meshes?

Thank you very much!

Ciao Heinz

Re: second order FD upwind scheme
 

It depends on what do you consider simple. I am using SMART ( a kind of QUICK with limiters) and it works well. The good way to introduce it is using deferred correction (more robust, easy to converge). Here you have an interesting reference:

Darwish M.S. and F. Mokalled (1996), The normalizad weighting factor method: a novel technique for accelerating the convergence od high-resolution convective schemes, Num. Heat Transfer B 30, 217-237

In the paper few high order numerical schemes are explained (also for non uniform grids). You can also find there a deferred correction vs direct introduction of the whole convection term.Even in the paper the authors showed that the direct way is better, I have bad experiences calculating benchmark cases (driven caviity, differentialy heated cavity), so I am using deferred correction. Hope this is enough, if not ask more.

Alex

Re: second order FD upwind scheme
 

It depends on what do you consider simple. I am using SMART (a kind of QUICK with limiters, anyhow it is better to use limiters in second order schemes - no unphysical oscillations) and it works well. The good way to introduce it is using deferred correction (more robust, easy to converge). Here you have an interesting reference:

Darwish M.S. and F. Mokalled (1996), The normalizad weighting factor method: a novel technique for accelerating the convergence od high-resolution convective schemes, Num. Heat Transfer B 30, 217-237

In the paper few high order numerical schemes are explained (also for non uniform grids). You can also find there a deferred correction vs direct introduction of the whole convection term.Even in the paper the authors showed that the direct way is better, I have bad experiences calculating benchmark cases (driven caviity, differentialy heated cavity), so I am using deferred correction. Hope this is enough, if not ask more.

Alex