Timeline for Coupling FEM DG methods to Riemann solvers
Current License: CC BY-SA 3.0
6 events
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| Aug 9, 2012 at 16:08 | comment | added | gnzlbg | @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. | |
| Aug 5, 2012 at 19:20 | comment | added | Jed Brown | @gnzlbg In most cases, use of better Riemann solvers with high order methods is pretty much a wash. For example, this paper compares LxF to HLLC and finds that the latter has at best half the error on the same grid. Being a fifth order method, that is equivalent to refinement by 13%, which has similar incremental cost. Note also that the formally second order type A "WENO5" method is much more accurate than the second order TVD method. | |
| Aug 5, 2012 at 13:56 | comment | added | gnzlbg | @DavidKetcheson if by accuracy he means error yes it does. If he means order of accuracy then it does not. | |
| Aug 5, 2012 at 13:49 | comment | added | gnzlbg | @DavidKetcheson No, a good Riemann solver is not overkill, in particular those very complicated ones that are only a bit mor expensive than Lax-Friedrichs. High order of accuracy and solution error are not the same thing. Although they won't affect the order of accuracy, a good Riemann solver will significantly reduce your error, for a marginal increase in computational cost. | |
| Dec 1, 2011 at 19:58 | comment | added | David Ketcheson | Good point. Complicated Riemann solvers are often overkill, especially if you have a high-order discretization. | |
| Nov 30, 2011 at 19:34 | history | answered | Jed Brown | CC BY-SA 3.0 |