# Coupling FEM DG methods to Riemann solvers

Are there any good papers and or codes that couple discontinuous galerkin finite element solvers with Riemann solvers?

I need to explore coupling elliptic and hyperbolic problems but most splitting methods are ad hoc at best. Since I have a large amount of FEniCS code, I would like to just couple the Riemann solver with it. While a simple Roe solver would be a beginning, I'm looking for guidance on using more complicated methods.

• All DG solvers for hyperbolic problems use Riemann solvers. Maybe you really want to ask about solving mixed hyperbolic-elliptic methods with DG methods? – David Ketcheson Nov 30 '11 at 17:47
• @DavidKetcheson I see in your first comment to the question : >*All DG solvers for hyperbolic problems use Riemann solvers* I'm working on the code form Warburton for 1D euler. They do have slope limiters as is expected from most DG codes, but i am not sure of having seen a function that solves the discontinuous fluxes on the interfaces based on the flow direction. I am just a beginner in CFD, and have not come across a Riemann Solver code untill yet. I do have a code by Dr. Katate Masatsuka using Roe's approximate Riemann solver but is a FV code. I am not sure if there is a Riemann Solver imp – Suyash Sharma Jul 6 '16 at 2:14
• If you have a new question, please ask it by clicking the Ask Question button. Include a link to this question if it helps provide context. - From Review – Christian Clason Jul 6 '16 at 6:19

• @JedBrown Indeed, I completely agree with you for HLL, HLLC, Roe... those are quite general fluxes, accurate, and also pretty heavy on computational cost. I meant, however, specialized fluxes like AUSM (Euler eqts. and NS for compressible flow), which are very cheap (almost same cost as LxF) and very accurate. Furthermore, one also has to considere how the time step scales with refinement ($\Delta t \approx O(h^2/p)$ I guess). Also, if you have discontinuities, h-refinement and low p won't cut it, you'll need a good flux. I can't however comment on ENO/WENO schemes, only DG. – gnzlbg Aug 9 '12 at 16:08