2nd order upwind and QUICK scheme
Dear all,
How superior is the QUICK scheme to 2nd order upwind scheme in terms of numerical diffusion??? 
Re: 2nd order upwind and QUICK scheme
i often use quick scheme as high order scheme or powerlaw scheme as low scheme i think 2nd order upwind has a strange converge charactericstic

Re: 2nd order upwind and QUICK scheme
QUICK is a second order scheme and it upwinds. It is the obvious way to write a conservative, second order upwind scheme and so I do not recognise "2nd order upwind scheme". What is it?
If you wish to answer to your question, perform a Taylor Series Expansion and examine the coefficients of the error terms. 
Re: 2nd order upwind and QUICK scheme
I think quick scheme is better than 2nd ordr upwind for the most fluid cases!

Re: 2nd order upwind and QUICK scheme
I just finished looking at the dissipation/dispersion characteristics of a variety of algorithms. QUICK is superior to 2nd order upwind  it damps the high frequency components less and has less dispersion as well. QUICK actually is slightly better than MUSCL with regard to damping, although MUSCL has less dispersion. This is true for first or second order time differencing.

Re: 2nd order upwind and QUICK scheme
Where can I find a book that discusses all of these issues from the point of view of various schemes?

Re: 2nd order upwind and QUICK scheme
Most any basic CFD book will have a chapter on Fourier analysis of difference schemes to determine dissipation and damping. You can also find a lot of information on the Internet if you search for damping and dispersion in CFD. Your best bet is to learn how to apply the analysis techniques (it's not that hard) and then use them for the various schemes you are interested in.

Re: 2nd order upwind and QUICK scheme
The Quick scheme is a third order scheme (not a second order), it has stability problems. For full details check the following book Computational Fluid Mechanics, an introduction for engineers by MA Abbott and DR Basco published by Longman Scientific & Technical

Re: 2nd order upwind and QUICK scheme
No. It is a second order scheme. It has no particular stability problems relative to similar schemes so long as you are careful about the implementation next to boundaries. However, it is unbounded which can cause problems for physical quantities which should not become, for example, negative.
When it was originally published Leonard tried to talk up its accuracy with some doubtful hand waving about polynomials (it drops an order of accuracy for the size of the computational molecule inorder to get conservation). This has been a source of confusion. The acid test is to perform a grid refinement study and look at the slope. It will be second order. 
Re: 2nd order upwind and QUICK scheme
As far as I know, the QUICK scheme is third order accurate when the grid is uniform and is second order accurate when the numerical grid is nonuniform. In FVM, even though the grid is uniform, the QUICK scheme is second order accurate since if you want to evaluate the value at west control volume face (w), you need the values at points P. W, WW. and the distances between Pw, wW, WWW are not uniform. However, the QUICK scheme is third order accurate if one uses the FDM with uniform grid.

Re: 2nd order upwind and QUICK scheme
No. It takes about 2 minutes to perform a Taylor Series Expansion and get the leading error term as (dx^2)/24 f''' for df/dx on a uniform grid.

Re: 2nd order upwind and QUICK scheme
Visit the following website
http://widget.ecn.purdue.edu/%7Ejmurthy/me608/main.pdf and read 113 page, 5.6.2 Third Order Upwind Schemes. 
Re: 2nd order upwind and QUICK scheme
The derivation is incomplete because it considers only a single flux. In order to determine the accuracy of a scheme you need to consider a cell. This can be done in a few minutes using a Taylor series expnansion.

Re: 2nd order upwind and QUICK scheme
Andy
I would be a good idea if you check the reference I gave you before, the scheme is well developed there and the stability diagram is published too. Good luck with whatever you are doing 
Re: 2nd order upwind and QUICK scheme
Why? What does it add that is not in Leonard's papers? Or a simple Taylor series expansion or stability analysis?
I did not mind pointing out the "error" in Halim's reference (or more his interpretation of the order of a flux instead of the order of scheme) because it was online and Purdue are a good group. But I am not going to waste my time ordering an introductory CFD book from the library just to point out possible errors in it. 
Quoting Hirsch (Numerical Computation of Internal and External Flow)
Quote:

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