Manav Bhatia <[email protected]> writes: > -- How critical is this lack of conservation properties for general > application of CFD for transonic and supersonic aerodynamic analyses?
Ah, a question for the ages. A lot of CFD engineers will say that local conservation is essential and they won't even consider a method that isn't. Most commercial CFD packages use finite volume methods for this reason. At the other end of the spectrum are the FOSLS advocates that say the engineers just don't understand what they want and insist that conservation always sacrifices something else. Other least squares advocates (e.g. Pavel Bochev) insist that conservation is essential, but that you should get it by using compatible spaces in the LS formulation (erasing some notable benefits of LS in the process). In the end, it depends on the problem. > -- Is this apparant non-ideal conservation behavior a primary reason > for interest in DG vs continuous FEM? Yes, conservation and stability. Linear DG satisfies a cell-wise entropy inequality so that it can often be used without limiting. Strict monotonicity is not practically available for continuous FEM. > -- The typical DG methods that I have seen do not add a stabilization > within the domain, but handle the boundary terms to ensure continuity of > flux across the discontinuous elements. However, a straight-forward > application of Galerkin method is known to be unstable. So, I am assuming > that the stabilization and non-oscillatory behavior comes from forgoing the > requirement of continuity and the treatment of boundary terms. However, > would this also not imply that if one continued to increase the element > size while increasing the polynomial order, the solution within the will at > some point become unstable/oscillatory? Yes, DG stability is only cell-wise. Normal flux limiting reduces the method to second order even in smooth regions. So if you go to high-order, you need more exotic limiting to prevent internal oscillations (see Zhang and Shu 2010 and 2011). ------------------------------------------------------------------------------ Precog is a next-generation analytics platform capable of advanced analytics on semi-structured data. The platform includes APIs for building apps and a phenomenal toolset for data science. Developers can use our toolset for easy data analysis & visualization. Get a free account! http://www2.precog.com/precogplatform/slashdotnewsletter _______________________________________________ Libmesh-users mailing list [email protected] https://lists.sourceforge.net/lists/listinfo/libmesh-users
