i would like to know the following: *** if central differencing schemes are 2nd order then they are not dissipative but are dispersive. ***

however the quick scheme is 2nd order, but it is upwind biased. this would therefore suggest that it is also non-disspervive, however the upwind part would make it dissipative!?! ***

what is of most importance here, is it the order of the scheme or is it the 'biased' of the scheme (upwind or central)??? ***

is the quick or central scheme the most dissipative?

Paul, I'll throw my hat into the ring on this one...

Central discretisation adds no intentional additional dissipation to the flow regime, whereas Quick is a form of fancy upwinding. Upwinding takes its information from the upstream node, thus damping out certain fluctuations inbetween nodes.

I would say that CD allows both dispersive & dissipative phenomena a more free reign to express themselves. Upwinding & its relatives basically attempt to impose unphysical limitations on the true physics of the flow problem.

The end result is that CD can lead to instability, with Quick etc tending to provide more stable 'bulk flow' solutions.

In my research I understand where the upwinding approach has got it wrong & use absolutely no convection-stabilisation tricks whatsoever. Yes, I use CD. I am happy to accept that the instability is telling me something about the flow regime, instead of trying to strap it into an (often) erroneous 'stable solution'.

In my opinion, you cannot dictate to the flow physics what it can, or can't do... it is, after all, physics.

diaw...

thankyou diaw for your comments you clearly know the subject well.

the question still remains however, if quick scheme is second order, then the leading error term (taylor series) suggests the error is disspersive.

so ... is the quick scheme dissipative due to an unpwind contribution, or is is dispersive due to a second order accuracy???

i appologies if your first comments already covered this point.

QUICK is more dissipative but less dispersive than CD. Central difference has very little dissipation. In order to do a proper analysis you need to look at the equivalent PDE that arises from the differencing scheme, and see what terms enter in through the truncation. Dispersion is not directly tied to second-order accuracy.

Nice, compact answer 'ag'.

I tend to take a larger view of the physics & governing equations in my research work. The N-S equations show the presence of a number of dispersive-dissipative phenomena which I am investigating. I choose to work with schemes that are as simple & uncluttered as possible.

I do not spend too much time worrying about the particular details of first versus second order accuracy & what scheme is 'champ' etc, but go directly for CD (FVM) & get simulating. In parallel, I also run various FEM schemes. Again, these are also as 'uncluttered' as possible - most of them transient.

For commercial work & projects with 'must have' answers & extremely complex geometries, I use a blend of around 95% CD, with 5% UD in 'steady'-flows. Basically, I break most of the 'rules' laid down in the text-books. Some folks think I am crazy, but then, the end results & solution clarity are great.

I am also able to send information back upstream via CD - this is useful to me. Fully biased UD schemes make this difficult.

diaw...

thanks ag and diaw,

"The N-S equations show the presence of a number of dispersive-dissipative phenomena which I am investigating".

what do you mean by this? what sort of phenomena are these, how do they show themselves and how do you detect them?

just intersted really on the details of the physics contained in the NS.

Dear Colleagues

- please move Your discussion into the CFD-Wiki

It would be better for all

http://www.cfd-online.com/Wiki/Appro...ructured_grids

and

http://www.cfd-online.com/Wiki/Appro...s_and_examples

Michail

"The N-S equations show the presence of a number of dispersive-dissipative phenomena which I am investigating".

--------

Hi Paul,

The global physics of the N-S equations (N2x/x-momentum, N2y/y-momentum) is reasonably straightforward, when understood in an equilibrium, or otherwise, context. In other words, at 'force-balance' level.

The mechanisms of some individual terms, & the mechanisms of some groups of terms is what underpins what effects the N-S solutions can show us - shocks, bumps, waves... From detailed research at such fundamental level, without even initially resorting to simulation, certain 'critical points' can be understood.

Moving onto the simulation evaluation of the predicted phenomena is simply fascinating. The N-S are indeed, amazing deterministic 'chaos' generators. Even simple CD-based simulations can showcase physics in an amazing way.

For example, I have been able to simulate & understand the classic Reynolds experiment. The mechanisms are very straightforward when viewed from the correct perspective.

I encourage you, if you are interested, to get more deeply into the Physics of the N-S. Unfortunately, all books I have read approach the N-S & their derivation from a Mathematical viewpoint, rather than from a Physics viewpoint. IMHO, this is why the N-S have been shrouded in mystery for so long. When the terms are all put in their correct places, the understanding becomes reasonably straightforward. (I plan to author a book soon, which should hopefully put some of this research in interested hands).

diaw...

Hi Michail,

A good thought, but the dynamics of a forum (thought-exchange) is a little different to a Wiki (?one-way input?). Would it be possible for one of the Wiki editors to extract the 'meat' of many of the forum discussions & place them in the Wiki (acknowledgements & all)?

This is what has kept me from working on the Wiki. I personally find it much more intimidating than open forums...

diaw...

Dear Diaw, thankyou very much for your help.

i have posted a new question on this forum again based on dissipation and upwinding. i thought it was best to start a new string as the subject is a little different to this string.

it may interest you and i wondered what your thoughs on this new question is. Dissipation (upwind) posted by Paul on the 18th Dec.

quick is third order scheme, it is not a second order scheme, i disspite less than the CD scheme , but both of them are dispertive , you can compare the leading error of the two schemem

ztdep: Could you please post a reference showing where QUICK is less dissipative than Central Difference?

Although diaw thinks that CD (central difference) is much better than Upwind in terms of revealing "true" physics, I still have the impression that upwind is a must-do for certain flows such as supercritical flows, and the true physics about these kind of flows will generate shocks which can't be resolved by any model based on discretized grids and CD, while can be solved to some degree by discretized grids+Upwind. It really depends on what you are looking at and what you are looking for.

A less accurate solution is better than no solution in engineering.