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DoHander January 14, 2010 14:49

High order finite volume schemes

what are the most used high order finite volume schemes (unstructured grids and order >= 4) for the RANS and NS equations ?

Can you guys recommend me some bibliography ?



shyamdsundar January 14, 2010 22:20

Hi Do,

As far as I know, the ADER FV (By M. Dumbser) schemes can achieve very high order ( > 6 ).

But, a word of caution as an experienced person... If you go for any unstructured scheme > 3rd order, give a serious thought about Discontinuous Galerkin or Spectral Difference kind of schemes. I started off with higher order FV schemes, but, am now currently developing a new scheme similar to SD schemes for NS eqns.


DoHander January 15, 2010 11:49

Thanks - I will check for sure the DG scheme, about spectral methods they are not very appealing to an engineer (too much theory to grasp before you can understand something).


gory January 16, 2010 20:56

Spectral volume
I think spectral volume method (by ZJ Wang) is the simplest high-order method for unstructured grids. To me, DG is too much theoretical and complicated and also very expensive. Spectral volume is just like a finite-volume method on well-systematically subdivided cells. Maybe the spectral volume method of Wang is different from other spectral methods.

DoHander January 16, 2010 21:14

Thanks for your answer Gory, I've seen Wang's articles about SV methods.

shyamdsundar January 19, 2010 01:59

Hi Gory,

You are partly right. By the numerical formulation, Spectral Volume methods do seem to be quite simpler. But, since the focus is on higher order methods, the issue of stability becomes more important. SV schemes of orders more than 4 haven't been developed because of this reason. The partitioning of cells becomes much more tedious to yield a stable scheme.

The DG schemes can obtain arbitrary order of accuracy, provided you can find appropriate quadrature points. All the information are already available in the web, and the method has been widely employed. If one is interested in applications rather than numerics, it is better to stick to DG schemes that have been well tested before.


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