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Gonski January 25, 2007 00:18

?to implement gamma differencing scheme
Dear all,

I have a structured gas-solid code. its convective item is employed QUICK scheme by deferred mode. Now I have transferred the corresponding solid code to our unstructured code. The current code use CD differencing scheme by deferred correction method. Recently, I found the accuracy of the code was not good enough. Hence want to use high solution Gamma differencing scheme. I only found its success application in openfoam? My questions are, How about it? Can I easily implement it in my existing unstructured code? Need I change the structure of the code? I found Gamma is a little like Partankar's Hybrid scheme in idea, but a little difficult to carry out in the code.

I would appreciate your hint?


zxaar January 25, 2007 01:07

Re: ?to implement gamma differencing scheme
i implemented it in my code (thanks to jasak), i will send you the portion of code to read and implement. At the moment I am very busy, so may be on saturday.

Till then you can read Jasak's thesis for it. send me email on

Gonski January 25, 2007 01:17

Re: ?to implement gamma differencing scheme
Thank you very much. I have sent you a request letter.

rt January 25, 2007 02:52

Re: ?to implement gamma differencing scheme
i don't work with jassake's method but i recommend to implementation of semi-lagrangian method (good accuracy and cfl limitation free).

they need to backtracing streamlines and then interpolate velosity value at deprature point as convective term.

for interpolation u can use finite element bacis function.

recently Xiao published some version of semilag type method on unstructured grid (JCP).

i see several paper related to this subject (semilag) in meteorological literature (they need fast method for weather prediction, large scale), as an excellent resource search in Monthly Weather Review journal that is freely online avalible from:

Hrvoje Jasak January 25, 2007 10:31

Re: ?to implement gamma differencing scheme
"good accuracy and cfl limitation free"

Sounds like science fiction to me...

Hrvoje Jasak

rt January 25, 2007 10:38

Re: ?to implement gamma differencing scheme
Note: "good accuracy" not better accuracy than CFL dominated method,

dealing with large scale real problem having any solution (but not accurate) is more valuable.

(althouth there are some literature that claim better accuracy in the same condition or comparable accuracy with larger CFL, i state good resource in the previous thread)

Mike January 26, 2007 15:27

Re: ?to implement gamma differencing scheme
>"Sounds like science fiction to me... "

what r u? scientist !!!

Hrvoje Jasak January 26, 2007 18:55

Re: ?to implement gamma differencing scheme
Well, let's see: I've got a PhD from 11 years ago, about a dozen journal papers, 3-4 invited lectures on conferences, 20-odd University seminars, a couple of dozen conference papers, three lecture courses, supervising my third PhD student (and the first two are all finished), several ongoing projects with industry and collaborating with 3 or 4 University research groups (depends how you look at it).

Add to that the Second OpenFOAM Workshop (, 4 years at CD-adapco as a Senior Developer, and the 7th year of working in the Ansys-Fluent development team. Oh, forgot a professorship

Yeah, I think I'm a scientist... Want a copy of my CV?


Mike January 27, 2007 02:34

Re: ?to implement gamma differencing scheme
allright u r scientist, but in scienticif comunity acceptance/rejection (anything) fact/fiction need reason, otherwise don't have value (is it?) !

zxaar January 27, 2007 04:12

Re: ?to implement gamma differencing scheme
i think if you read jasak's thesis, you will find the answer to why he said 'sounds like fiction'. He spent lot of effort on this thing only (analyzing the accuracy and stability). It would be interesting read, if you spend time with it.

Mike January 27, 2007 08:13

Re: ?to implement gamma differencing scheme

i search in mentioned resource (really great link, free) with "semi lagrangian" keword (title), more than 100 article were appeared that confirm importance of semi-lag methods in practical application.

how i can called them as "fiction" !!!

Hrvoje Jasak January 27, 2007 10:46

Re: ?to implement gamma differencing scheme
Well, this discussion is getting out of hand, so let's forget the distractions and talk about the actual science.

Indeed, there is a number of combined Eulerian-Lagrangian schemes in literature - the first one I've seen was by B.P. Leonard some years ago - but their Lagrangian nature does not exclude them from normal mathematical rules. The upwind-central balance is the key of this game, rooted in the stability and boundedness analysis and cannot be avoided. Furthermore, using Lagrangian schemes on non-linear convection div(U U) is bound to land you into trouble.

Another issue to consider is the control of matrix coefficients and structure. By nature, first neighbour connectivity will limit you in the Co number and help with controlling matrix properties (e.g. M-matrix) as required by iterative solvers. If you choose not to do this, your matrix structure and addressing will indeed be upwind-biased and more accurate in advenction, but you will end up on direct linear equation solvers. We all know what that implies.

Overall, I would say there is value in Lagrangian schemes but I'm not jumping up and down with excitement. Time will tell: lok at the manuals of commercial CFD in 2-3 years time and if you see the scheme in there it is by all means significant.

My comment on "science fiction" related to a combination of high accuracy and lack of Co number limitation, excluding direct solver use. In any case, I am entitled to my opinion, I have played this game long enough not to be scared to speak my mind and, in any case, this would not be the first time science fiction turned out to be true. Read Jules Verne! :)

Let's reconvene in 2009 and discuss the problem again: the results should be in by then.


rt January 27, 2007 11:33

Re: interesting for disscusion
interesting, here is place for disscussion

note that i am not biased to any method and fairly look for method for solution of practical problem that can be aim of CFD.

at first i cite 3 intersting work among couple of hundreds of articles in the category of semi-lagrangian (not full lag), they remains in my mind as they claime critical applications (spectral element & sharp interface tracking)u can read and then judege, finally i answer to your critical issue related to semi-lag methods:

1. A Semi-Lagrangian High-Order Method for Navierâ€"Stokes Equations, Journal of Computational Physics 172, 658â€"684 (2001):

spectral element method in conjunction with semi-lagrangian scheme is applied, stability is proved, CFL up to 20-30 was used and superior computational efficiency is showed while computational accuracy and stability is preserved, comparison with Eulerian ones is included (note that when u use spectral element u look for high accuracy!!!)

2. A fast and accurate semi-Lagrangian particle level set method, Computers and Structures 83 (2005) 479â€"490:

first order semi-lagrangian method is used for updating level set field for sharp interface tracking, numerical results showed that method has comparable accuracy with CFL=4.9 with Eulerian method (CFL=0.5) with 3rd order TVD RK in time and 5th order HJ-WENO in space.

3. Higher-order schemes with CIP method and adaptive Soroban grid towards mesh-free scheme, Journal of Computational Physics 194 (2004) 57â€"77:

High order CFL free semi-lag method introduced and ...


now answer to your point:

as i understand u concern about sparsity pattern of system of linear equations that arise from momentum eq., but note that in semi-lag methods usually convection is handled explicitly and then diffusion step is done (usually implicitly), mention fractional step method (if u refer to first cited paper, catch hole concept, take few minutes).

With back-tracing characteristics lines and then interpolate vel. your scheme not only has physical meaning but also is always stable and enjoys TVD and boundness properties. Also u release from asymmetric pattern of system of equations and non-linearity of convection terms.

About high order accuracy: recently several methods are presented a famous one is works of Yabe and Xiao (called CIP method) as i cite one of them above (more comprehensive).

Another concern is numerical diffusion and smearing: as interpolation (especially centrally weighted) has smoothing nature, but there are also cure.

Conservation is another issue: some cures were presented.

One of the main limitation: physical time scales.

Consider ease of implementation of semi-lag too.

Finally note that in practical applications (especially large scale problem) having answer (with reasonable accuracy) is better than nothing, we see that in weather prediction that is really large scale, people pressured to found efficient method and we see effective contribution of them in this field (i mention a good link, don't miss it, i see here some interesting original papers that don't find other place).

Excuse me for long letter,

Your opinion?

muhammad javaid January 28, 2007 04:43

Re: ?to implement gamma differencing scheme
Another intersting paper from Monthgly Weather Review is "Eliminating the Interpolation Associated with the Semi-Lagrangian Scheme ", January 1986, pp. 135-146. I am using operator splitting and Semi-langrangian method as well as CPI scheme to rewrite MFIX code in C language for fluidized bed combustion.

Tom January 28, 2007 08:25

Re: ?to implement gamma differencing scheme
If you narrow your search to Meteorology you'll find that most modern Numerical Weather Prediction models are already using semi-Lagrangian schemes as part of there dynamical core (i.e. the bit that solves the fluid equations).

Gonski January 28, 2007 18:00

Re: ?to implement gamma differencing scheme
Thanks everybody here.

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