References Discontinuous Galerkin for Navier-Stokes
 

Hello,

I'd like to learn about DG-FEM for incompressible, unsteady Navier-Stokes, in the convection-dominated, possibly turbulent regime.

For some reason I'm having a hard time finding good literature that covers DG for the full incompressible Navier-Stokes case.
There is some information on the Wiki (https://www.cfd-online.com/Wiki/Discontinuous_Galerkin), but apart from Cockburn & Bassi/Rebay, no references are given.


I'd be very grateful if you had any pointers to articles, reviews, books, maybe your own experience, to get started and towards a first own implementation.



Specific things, beyond the general approach, I'd like to learn are: where is the state of the art at? What are the most common schemes? Which are the problems/applications that DG has proven to be efficient for?


Best wishes
David

DG
 

Hello,

Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications is a good start. With that said, it is not an intro book and assumes you have a grasp of Continuous Galerkin Methods and Finite Volume Methods. I would forget about turbulence for the time being and focus on understanding DG. I would start as follows: 2D heat equation, 2D advection equation, 2d advection-diffusion, 2d poisson, 2d navier-stokes. I am not an expert on DG by any means, but DG seems to combine the best of FVM and FEM, albeit at a computational cost. A point of interest is implicit methods for DG as the matter is not as simple as in FEM or FVM.

Have a look to the PhD thesis here, you will find also useful references


https://www.researchgate.net/profile.../contributions

Thanks a lot for the replies! I'll look at the references you mentioned.