Hi
There is many types of high order methods such as DG, Nodal DG, Spectral element, Spectral difference, Huynh Flux Reconstruction and so on.
Which method do you prefer and why?
Each of them have advantages and disadvantages but which of them do you think is most suitable for industrial applications in future?
Search the Web for articles by Erturk, Corke, and Gökçöl. They discuss higher order methods and also provide some code with which you can experiment. While these derivations are interesting, they may not be particularly useful. Higher order methods do not guarantee greater accuracy in general, even if they do for specific cases.
Personally, I am a great fan of DG methods. I think that they provide the greatest flexibility among all the standard high order alternatives and they make h- and p-refinement very easy (programming issues aside). Parallel open source codes that implement these features efficiently are available, such as for example deal II
https://www.dealii.org/
and I expect these techniques to play an increasing role in industrial applications in the future. I have tried to contributemyself to their application to two areas, numerical weather prediction and LES turbulence modelling, all the related papers are on RG.
Continuous or discontinuous Galerkin formulation with higher-order spatial discretisations, especially triangular/tetrahedral elements because of the ease of mesh generation for complex geometries encountered in industrial problems.
You cannot do much if you stick to quadrilateral/hexahedral elements only.
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