"Kirk, Benjamin (JSC-EG311)" <[email protected]> writes:
> No tunable parameters? What approximate Riemann solver are you > referring to? The plethora of choices seems like a "tunable > parameter" to me, let alone eigenvalue limiting, entropy fixes, etc.. > Granted, as the difference between left and right states decreases (as > is the case for high order DG with smooth solutions) the importance of > these choices is lessened, but still… The Godunov flux may be impractical, but it's useful for testing (on sufficiently simple problems that you have it available). Beyond that, there is a well-developed theory of what constitutes a stable flux. With high order methods (mostly WENO and DG), it's common to use a Rusanov flux because it's cheap an simple to implement. Here, you need an estimate of the fastest wave speed present in the Riemann problem. For a convex flux, this speed is not hard to compute exactly. I've liked methods based on Riemann solvers because they decouple discretization components, allowing us to analyze components in isolation and to write more loosely coupled software. If you want monotonicity/positivity, there is a well-defined way to get it. We can have non-oscillatory/positivity properties without reducing the order of accuracy in smooth regions. The straightforward conservation statements are satisfied exactly, independent of variable material properties. DG and FV also have easily-accessible nonlinear multigrid smoothers. I'll concede that stabilized continuous FEM appears to be the way to go any time (a) it works reliably in validation experiments and (b) assembled matrices are used for solving the resulting PDEs. I think you guys are doing impressive work with stabilized FEM and there's real value in the implementation consistency of using continuous spaces everywhere. ------------------------------------------------------------------------------ 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
