Talk:Flux limiter

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I have added additional flux limiter definitions along with references for each type, which I hope will make the article clearer. Griffgruff 15:25, 11 October 2006 (UTC)[reply]

The conditions for a scheme to be second order accurate TVD are less tringent than mentioned in this article:"This means that they are designed such that they pass through a certain region of the solution, known as the TVD region, in order to guarantee stability of the scheme." Most authors limit their attention to this region, as does LeVeque. However, the condition for second order accuracy (away from local maxima) is that the limiter goes smoothly through (1,1). The condition for being TVD is that 0<phi<2 for r>0 (and phi=0 for r<0). Any flux limiter that satisfies these conditions gives a second order accurate TVD scheme. The TVD region is chosen for additional reasons, such as the amount of compression. This may be a concern in a specific application, or it may be irrelevant. --Roger Jeurissen (talk) 22:19, 28 January 2010 (UTC)[reply]

Are flux limiter only usefull for incompressible flow ? It is possible to use the same method for both compressible and incompressible flow ? Thanks to add more precisions on this. 199.212.17.130 (talk) 12:25, 16 March 2010 (UTC)[reply]

Is there a typo in the Koren limiter? I get the Koren limiter as -> max[0,min(2r,(2+r)/3,2)] (209.89.17.156 (talk) 16:04, 1 April 2010 (UTC))[reply]

The Koren limiter is specified correctly. Griffgruff (talk) 23:22, 24 April 2010 (UTC)[reply]

I may be wrong, but I believe the CHARM, HCUS, HQUICK and smart limiters do not constitute TVD schemes (unless the scheme is somehow constructed in a different manner to the classic method as given on this page). As is clearly stated by the limit of each scheme, phi will exceed 2 for certain values of r, and unless these methods are meant for some specific use (i.e predesignated value of the courant number), this means they cannot be guaranteed to have the total variation non-increasing property, even if they still work as advection approximations (this should also be stated on the page). However, I may be wrong in my assumptions here, and I have also been unable to access the references for these schemes, so please correct me if I am wrong! Also, the phi(r) graph for the Koren limiter does not match the definition given on the page, which again I cannot find the original reference for, but is different to that given by H. Hassanzadeh et al, Computers and Chemical Engineering, (2008). 82.32.185.59 (talk) 14:42, 10 April 2011 (UTC)[reply]

The CHARM, HCUS, HQUICK and smart limiters are clearly marked as being "not 2nd order TVD" and have been since I created the page in 2006. The Koren Limiter graph does match the definition, which is correct - try plotting it in Matlab or Maple! Also, the Koren limiter definition given here is sometimes referred to in the literature as the "original" Koren limiter. Graham W. Griffiths (talk) 22:49, 13 April 2011 (UTC)[reply]
- The graph for the Koren limiter is actually plotting phi(r) = max(0,min(2r,(2r+1)/3,2)), and does not match the definition currently given on this page - whether or not this has been changed from your original definition I do not know. As for the previously mentioned limiters, they do not fall within the admitted TVD region as referenced to Sweby, 1984. They are indeed flux limiters, but not TVD flux limiters - they satisfy other boundary conditions given by positivity and CBC criterions, and are hence "local-extremum diminishing" flux-limiters (Waterson & Deconinck, 2007). All the flux-limiters labelled as "not 2nd order TVD" on the page (other than van Albada 2, which is TVD, but not 2nd order), should in fact be marked "not TVD," or simply removed as they are somewhat misleading. Also, this page could be expanded significantly be discussing non-TVD flux-limiter schemes. 144.173.5.197 (talk) 11:36, 18 April 2011 (UTC)[reply]
  - Thank you for your perseverance. The Koren limiter definition was correct until it appears to have been changed on 10th July, 2010 by the user Olegrog to ϕ_kn(r) = max(0,min(2r,(2+r)/3,2)). At the same time, Olegrog appears to have also reverted the definition of r back to the correct form, which he had incorrectly changed on 7th July. I will revert back to the correct form for the Koren limiter. I apologize for missing the point you were making. As Wikipedia is a collection of collaborative articles, please feel free to expand/improve this page as you feel appropriate. Graham W. Griffiths (talk) 00:56, 19 April 2011 (UTC)[reply]

The expression for the limiter, given by Koren (1993), is max(0,min(2*r, 2, (1+2r)/3)), where r=(c_{i+1} - c_i)/(c_i - c_{i-1}). In the wiki article the ratio of gradients is defined as r=(c_{i} - c_{i-1})/(c_{i+1} - c_{i}). Hence, the formula from the original paper of Koren should be adapted for the wiki article. The Koren limiter expression in the context of the current article will be max(0,min(2*r, 2, (2+r)/3)) — Preceding unsigned comment added by Pprokharau (talk • contribs) 12:53, 20 October 2011 (UTC)[reply]

I corrected the Koren limiter. In the process, I added that this is a special case of the Koren Kappa limiter with kappa = 1/3. Later one this note was removed and and replaced by "third-order accurate for sufficiently smooth data". This is true for this specific value of kappa, in which case the scheme becomes a third-order biased upwind scheme. — Preceding unsigned comment added by 99.236.200.42 (talk) 22:01, 11 November 2011 (UTC)[reply]

I think it is unclear what the article means with "high precision, low resolution" and vice versa. To me this appears contradicting. I would expect one to be a low resolution/precision scheme and one to be a high resolution/precision scheme. Right now I cannot tell which is which by reading the article. — Preceding unsigned comment added by 134.169.221.217 (talk) 15:22, 22 March 2017 (UTC)[reply]