Implementation of QUICK scheme
Hallo,
I am implementing a QUICK convection scheme into a 2d pressurecorrection (SIMPLElike) RANS code for nonorthogonal grids. The code in formulated in cartesian coordinates. The time discretisation is fullyimplicit. I intend to scaleup the code to 3D later. 1) In the open literature I found the QUICK formulation for nonuniform grids, not for nonorthogonal and bodyfitted grids. So firstly I implemted the scheme proposed for nonuniform but orthogonal grids. Is there an advice or a reference what could be done better with nonorthogonal grids? 2) I neglected the transverse curvature terms. Does someone know some references about the implementation of the QUICK scheme including the transverse curvature contribution and/or its performance for highly convective / turbulent flow? 3) I suppose that the scheme works equally for steadystate and transient solutions, if I use an implicit time discretisation. Am I right? What about an explicit timemarching scheme? I intend to implement an explicit pressurecorrection scheme. Can I expect that I do not have to modify the interpolation scheme? Thanks a lot in advance! Romuald 
Re: Implementation of QUICK scheme
Hi,
You haven't chosen my favourite scheme (you'll have boundedness problems later!), but I think I can help: 1) QUICK for nonuniform grids in fine and you don't need to modify it any further. All 'curvilinear' or 'nonorthogonal' corrections are unnecessary  they will just increase your computational molecule but won't give you any additional accuracy. 2) You did fine  forget about curvature. 3) The scheme is fine. You'll have to underrelax the system for pressure correction (as does everybody else); this kind of stuff is well tested and publicised with both SIMPLE and PISO. The only trouble you can expect (to my knowledge is): a) boundaries need special treatment as there's no "far upwind" node. b) the scheme is unbounded, i.e. for a variable which is laways positive (e.g. T or k) you can get negative face values, which causes trouble. However, there's a bunch of NVDmodifications to QUICK (called SMART of SHARP, I'm not quite sure)  you will need those when you start convecting scalars c) QUICK is a real bitch to implement on unstructured meshes, as you loose the directions. But that's another subject..... Hrv 
Re: Implementation of QUICK scheme
Thank you very much for your quite encouraging advice. Actually, I know about the boundedness problem and intend to implement the SMART scheme, which includes the QUICK scheme. May I ask what is your favourite scheme you mentioned, which does not seem to suffer from boundedness problems, even if no flux limiter is used?
Thanks Romuald 
Re: Implementation of QUICK scheme
Hi,
Unfortunately, there's no linear scheme other than Upwind differencing that does not suffer from unboundedness, so I'm afraid that you'll always need a limiter. I have developed a scheme called Gamma (Int. J. Numer. Meth. Fluids,31:431449, 1999) and it's been extensively tested on a lot of stuff, from combustion to twophase and free surface flows. It is an NVD (limited!) scheme and its main advantages are i) it works on arbitrarily unstructured meshes (no need for "far upwind node") ii) compact support (blends UD and CD) iii) no timestep dependency and iv) (and most important) it's the simplest I could do! However, (I don't know the aim of your project), I think you made a decent choice, unless you ultimately want to make your code arbitrarily unstructured, so I think you can happily just QUICK away! Have fun, Hrv 
Re: Implementation of QUICK scheme
Hi Dr.Hrvoje Jasak
You mentioned that you have tested your Gamma scheme on a lot of practical flow problems. How was accuracy of your Gamma scheme for practical flow calculations when compared with QUICK, SMART, HLPA or SOUCUP schemes ? Seok Ki Choi 
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Could you please send me your paper about your Gamma scheme, i can not find it. Regards 
Your paper
Hi, if it's possible I would also like to get a copy of your paper about the GAMMA scheme. Could you email it to me, if it's not a problem.
Thank you 
Dear Dr HJ
You wrote that QUICK scheme is unbounded, but in OF1.6 UserGuide in: Table 4.10: Behaviour of interpolation schemes used in divSchemes. It is written that QUICK is bounded. could you tell me which statment is correct ? Best, ZM 
There's a link to Prof.(!) Jasak's PhD at
http://openfoamwiki.net/index.php/IcoFoam 
Thank You !
It is really great works ! 
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