[mprinkey]

Most of my experience has been with pressure-based CFD methods. I have recently been investigating density-based...especially explicit methods in earnest, and I bumped into the CE/SE method recently, and it seems impressive--dissipation free even on unstructured meshes, time-accurate local timestepping, no need for directional splitting or Reimannian solvers, etc. It makes me question why it is not more popular.

I've found other short CE/SE discussions on this board in the past, but it seems like it is more of a curiosity to those who have heard of it. Does anyone here have direct experience with the method? Are there any gotchas here that I am missing? Or it is that RK-TVD-Reimann solvers are just too entrenched and this can't gain traction?

Thanks

[praveen]

I have also wondered why there is not much discussion of this. Whenever I read papers on high order methods, people only discuss DG, spectral volume, spectral difference, flux reconstruction, weno, etc. Almost nobody mentions CE/SE method. I did not see any specific advantages of CE/SE method that would make it better than these other methods other than not requiring riemann solvers. When I look at the literature on high order methods in aerospace CFD, it seems to me that DG schemes are the dominant ones (for high Re problems). See e.g., the HIOCFD workshops.

Here is a talk on CE/SE

http://nia-mediasite.nianet.org/NIAM...2-0d8a1a25ea58
http://ossanworld.com/hiroakinishika...Chang_CESE.pdf

[mprinkey]

Originally Posted by praveen

I have also wondered why there is not much discussion of this. Whenever I read papers on high order methods, people only discuss DG, spectral volume, spectral difference, flux reconstruction, weno, etc. Almost nobody mentions CE/SE method. I did not see any specific advantages of CE/SE method that would make it better than these other methods other than not requiring riemann solvers. When I look at the literature on high order methods in aerospace CFD, it seems to me that DG schemes are the dominant ones (for high Re problems). See e.g., the HIOCFD workshops.

Here is a talk on CE/SE

http://nia-mediasite.nianet.org/NIAM...2-0d8a1a25ea58
http://ossanworld.com/hiroakinishika...Chang_CESE.pdf

Thanks for these links. I will give that presentation a careful watch.

I see advantages over DG, mainly in the much less restrictive CFL--for DG, the CFL limit gets increasingly worse as order increases. WENO is an implementation and computational nightmare on unstructured meshes. Even TVD limiting on unstructured meshes...if done in a vector context per Berger's paper ...is a very difficult implementation/computational task (solving a nontrivial linear programming problem per cell per field).

For vector implementations (AVX2/AVX512/OpenCL), avoiding the limiting and Reimannian solvers could be a big performance win just because the code is not loaded with conditionals and iterative stages. I am specifically looking at time-accurate methods and the prospect of local timestepping is very attractive. We likely won't have to deal with boundary layer type cell-size variations, but I would like to avoid having my global timestep limited by the smallest cell.

I honestly wonder if "element" in the name is throwing people off. This is a Finite Volume-type method, even moreso than DG.

[praveen]

There are explicit space-time DG schemes available, where you can do time accurate local time stepping, see papers of Gassner, Munz, Dumbser, etc. You can go to very high orders of accuracy.