[aerosonali]

Can anyone comment on the efficacy of LDG viscous flux schemes for high order methods like DG, spectral volume or the spectral difference methods. I have read about it and it looks very simple and elegant in contrast to other formulations like the penalty formulation etc. However, has anyone experienced any undesirable features (due to its lack of symmetry) , while using LDG?

Sonali

[sunyughi]

Hi Sonali,
well, LDG is great with respect to its simplicity, easy to use approach and lack of a length scale (which is really something worth mentioning for heavily skewed and non-uniform grids). Thus it has been used in several areas of engineering (not just confined to aerodynamics) [2].

However it has been shown by Kannan and Wang [1] to be very dissipative, when compared to the penalty and the BR2 formulations. This paper, describes the process using a very clean eigen value analysis.

Very recently Kannan and Wang[3] came up with a variant of LDG : called LDG2. This is more symmetrical than LDG, but still has the advantages of LDG( like simplicity, lack of a length scale etc). This was shown to have more accuracy than the LDG.

1. R. Kannan and Z.J. Wang, “A study of viscous flux formulations for a p-multigrid spectral volume Navier stokes solver”, Journal of Scientific Computing, Volume 41, Number 2, November, 2009.
2. R. Kannan, “An Implicit LU-SGS Spectral Volume Method for the Moment Models in Device Simulations: Formulation in 1D and application to a p-multigrid algorithm”, International Journal for Numerical Methods in Biomedical Engineering (formerly Communications in numerical methods in engineering), accepted on October 11, 2009, Published Online: 1 Feb 2010.
3. Kannan R. and Wang., "LDG2: A Variant of the LDG Flux Formulation for the Spectral Volume Method", Journal of Scientific Computing, Received: 28 April 2009 Revised: 27 May 2010 Accepted: 31 May 2010 Published online: 20 June 2010

Hope this helps
Yughi

[aerosonali]

That was am informative post Yughi.
Thanks
Sonali